ci: install torch separately to avoid --index-url replacing PyPI

Strip ipa.kindred.internal CA trust steps. Replace Node-dependent
actions with raw git commands for act runner compatibility.

.gitea/workflows/ci.yaml

@@ -0,0 +1,180 @@
+name: CI
+
+on:
+  push:
+    branches: [main, public]
+  pull_request:
+    branches: [main, public]
+  workflow_dispatch:
+    inputs:
+      run_datagen:
+        description: "Run dataset generation"
+        required: false
+        type: boolean
+        default: false
+      num_assemblies:
+        description: "Number of assemblies to generate"
+        required: false
+        type: string
+        default: "100000"
+      num_workers:
+        description: "Parallel workers for datagen"
+        required: false
+        type: string
+        default: "4"
+
+env:
+  PIP_CACHE_DIR: /tmp/pip-cache-solver
+  TORCH_INDEX: https://download.pytorch.org/whl/cpu
+  VIRTUAL_ENV: /tmp/solver-venv
+
+jobs:
+  # ---------------------------------------------------------------------------
+  # Lint — fast, no torch required
+  # ---------------------------------------------------------------------------
+  lint:
+    runs-on: ubuntu-latest
+    env:
+      PATH: /tmp/solver-venv/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+    steps:
+      - name: Checkout
+        run: |
+          git config --global --add safe.directory "$GITHUB_WORKSPACE"
+          git clone --depth 1 --branch "${GITHUB_REF_NAME}" \
+            "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE" \
+            || git clone --depth 1 "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE"
+          cd "$GITHUB_WORKSPACE"
+          git checkout "$GITHUB_SHA" 2>/dev/null || true
+
+      - name: Set up venv
+        run: python3 -m venv $VIRTUAL_ENV
+
+      - name: Install lint tools
+        run: pip install --cache-dir $PIP_CACHE_DIR ruff
+
+      - name: Ruff check
+        run: ruff check solver/ freecad/ tests/ scripts/
+
+      - name: Ruff format check
+        run: ruff format --check solver/ freecad/ tests/ scripts/
+
+  # ---------------------------------------------------------------------------
+  # Type check
+  # ---------------------------------------------------------------------------
+  type-check:
+    runs-on: ubuntu-latest
+    env:
+      PATH: /tmp/solver-venv/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+    steps:
+      - name: Checkout
+        run: |
+          git config --global --add safe.directory "$GITHUB_WORKSPACE"
+          git clone --depth 1 --branch "${GITHUB_REF_NAME}" \
+            "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE" \
+            || git clone --depth 1 "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE"
+          cd "$GITHUB_WORKSPACE"
+          git checkout "$GITHUB_SHA" 2>/dev/null || true
+
+      - name: Set up venv
+        run: python3 -m venv $VIRTUAL_ENV
+
+      - name: Install dependencies
+        run: |
+          pip install --cache-dir $PIP_CACHE_DIR torch --index-url $TORCH_INDEX
+          pip install --cache-dir $PIP_CACHE_DIR torch-geometric
+          pip install --cache-dir $PIP_CACHE_DIR mypy numpy scipy
+          pip install --cache-dir $PIP_CACHE_DIR -e ".[dev]"
+
+      - name: Mypy
+        run: mypy solver/ freecad/
+
+  # ---------------------------------------------------------------------------
+  # Tests
+  # ---------------------------------------------------------------------------
+  test:
+    runs-on: ubuntu-latest
+    env:
+      PATH: /tmp/solver-venv/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+    steps:
+      - name: Checkout
+        run: |
+          git config --global --add safe.directory "$GITHUB_WORKSPACE"
+          git clone --depth 1 --branch "${GITHUB_REF_NAME}" \
+            "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE" \
+            || git clone --depth 1 "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE"
+          cd "$GITHUB_WORKSPACE"
+          git checkout "$GITHUB_SHA" 2>/dev/null || true
+
+      - name: Set up venv
+        run: python3 -m venv $VIRTUAL_ENV
+
+      - name: Install dependencies
+        run: |
+          pip install --cache-dir $PIP_CACHE_DIR torch --index-url $TORCH_INDEX
+          pip install --cache-dir $PIP_CACHE_DIR torch-geometric
+          pip install --cache-dir $PIP_CACHE_DIR -e ".[train,dev]"
+
+      - name: Run tests
+        run: pytest tests/ freecad/tests/ -v --tb=short
+
+  # ---------------------------------------------------------------------------
+  # Dataset generation — manual trigger or on main/public push
+  # ---------------------------------------------------------------------------
+  datagen:
+    runs-on: ubuntu-latest
+    if: >-
+      (github.event_name == 'workflow_dispatch' && inputs.run_datagen == true) ||
+      (github.event_name == 'push' && (github.ref == 'refs/heads/main' || github.ref == 'refs/heads/public'))
+    needs: [test]
+    env:
+      PATH: /tmp/solver-venv/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin
+    steps:
+      - name: Checkout
+        run: |
+          git config --global --add safe.directory "$GITHUB_WORKSPACE"
+          git clone --depth 1 --branch "${GITHUB_REF_NAME}" \
+            "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE" \
+            || git clone --depth 1 "${GITHUB_SERVER_URL}/${GITHUB_REPOSITORY}.git" "$GITHUB_WORKSPACE"
+          cd "$GITHUB_WORKSPACE"
+          git checkout "$GITHUB_SHA" 2>/dev/null || true
+
+      - name: Set up venv
+        run: python3 -m venv $VIRTUAL_ENV
+
+      - name: Install dependencies
+        run: |
+          pip install --cache-dir $PIP_CACHE_DIR torch --index-url $TORCH_INDEX
+          pip install --cache-dir $PIP_CACHE_DIR torch-geometric
+          pip install --cache-dir $PIP_CACHE_DIR -e ".[train]"
+
+      - name: Generate dataset
+        run: |
+          NUM=${INPUTS_NUM_ASSEMBLIES:-100000}
+          WORKERS=${INPUTS_NUM_WORKERS:-4}
+          echo "Generating ${NUM} assemblies with ${WORKERS} workers"
+          python3 scripts/generate_synthetic.py \
+            --num-assemblies "${NUM}" \
+            --num-workers "${WORKERS}" \
+            --output-dir data/synthetic
+        env:
+          INPUTS_NUM_ASSEMBLIES: ${{ inputs.num_assemblies }}
+          INPUTS_NUM_WORKERS: ${{ inputs.num_workers }}
+
+      - name: Print summary
+        if: always()
+        run: |
+          echo "=== Dataset Generation Results ==="
+          if [ -f data/synthetic/stats.json ]; then
+            python3 -c "
+          import json
+          with open('data/synthetic/stats.json') as f:
+              s = json.load(f)
+          print(f'Total examples: {s[\"total_examples\"]}')
+          print(f'Classification: {json.dumps(s[\"classification_distribution\"], indent=2)}')
+          print(f'Rigid: {s[\"rigidity\"][\"rigid_fraction\"]*100:.1f}%')
+          print(f'Degeneracy: {s[\"geometric_degeneracy\"][\"fraction_with_degeneracy\"]*100:.1f}%')
+          "
+          else
+            echo "stats.json not found — generation may have failed"
+            ls -la data/synthetic/ 2>/dev/null || echo "output dir missing"
+          fi

.gitignore

@@ -1,44 +1,83 @@
-# Prerequisites
+# C++ compiled objects
 *.d
-
-# Compiled Object files
 *.slo
 *.lo
 *.o
 *.obj
-
-# Precompiled Headers
 *.gch
 *.pch
 
-# Compiled Dynamic libraries
+# C++ libraries
 *.so
 *.dylib
 *.dll
-
-# Fortran module files
-*.mod
-*.smod
-
-# Compiled Static libraries
 *.lai
 *.la
 *.a
 *.lib
 
-# Executables
+# C++ executables
 *.exe
 *.out
 *.app
 
-.vs
+# C++ build
+build/
+cmake-build-debug/
+.vs/
 x64/
+temp/
+
+# OndselSolver test artifacts
 *.bak
 assembly.asmt
-
-build
-cmake-build-debug
-.idea
-temp/
 /testapp/draggingBackhoe.log
 /testapp/runPreDragBackhoe.asmt
+
+# Python
+__pycache__/
+*.py[cod]
+*$py.class
+*.egg-info/
+dist/
+*.egg
+
+# Virtual environments
+.venv/
+venv/
+
+# IDE
+.vscode/
+.idea/
+*.swp
+*.swo
+*~
+
+# mypy / ruff / pytest
+.mypy_cache/
+.ruff_cache/
+.pytest_cache/
+
+# Data (large files tracked separately)
+data/synthetic/*.pt
+data/fusion360/*.json
+data/fusion360/*.step
+data/processed/*.pt
+!data/**/.gitkeep
+
+# Model checkpoints
+*.ckpt
+*.pth
+*.onnx
+*.torchscript
+
+# Experiment tracking
+wandb/
+runs/
+
+# OS
+.DS_Store
+Thumbs.db
+
+# Environment
+.env

.pre-commit-config.yaml

@@ -0,0 +1,23 @@
+repos:
+  - repo: https://github.com/astral-sh/ruff-pre-commit
+    rev: v0.3.4
+    hooks:
+      - id: ruff
+        args: [--fix]
+      - id: ruff-format
+
+  - repo: https://github.com/pre-commit/mirrors-mypy
+    rev: v1.8.0
+    hooks:
+      - id: mypy
+        additional_dependencies:
+          - torch>=2.2
+          - numpy>=1.26
+        args: [--ignore-missing-imports]
+
+  - repo: https://github.com/compilerla/conventional-pre-commit
+    rev: v3.1.0
+    hooks:
+      - id: conventional-pre-commit
+        stages: [commit-msg]
+        args: [feat, fix, docs, style, refactor, perf, test, build, ci, chore, revert]

Dockerfile

@@ -0,0 +1,61 @@
+FROM nvidia/cuda:12.4.1-devel-ubuntu22.04 AS base
+
+ENV DEBIAN_FRONTEND=noninteractive
+ENV PYTHONUNBUFFERED=1
+
+# System deps
+RUN apt-get update && apt-get install -y --no-install-recommends \
+    python3.11 python3.11-venv python3.11-dev python3-pip \
+    git wget curl \
+    # FreeCAD headless deps
+    freecad \
+    libgl1-mesa-glx libglib2.0-0 \
+    && rm -rf /var/lib/apt/lists/*
+
+RUN update-alternatives --install /usr/bin/python python /usr/bin/python3.11 1
+
+# Create venv
+RUN python -m venv /opt/venv
+ENV PATH="/opt/venv/bin:$PATH"
+
+# Install PyTorch with CUDA
+RUN pip install --no-cache-dir \
+    torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu124
+
+# Install PyG
+RUN pip install --no-cache-dir \
+    torch-geometric \
+    pyg_lib torch_scatter torch_sparse torch_cluster torch_spline_conv \
+    -f https://data.pyg.org/whl/torch-2.4.0+cu124.html
+
+WORKDIR /workspace
+
+# Install project
+COPY pyproject.toml .
+RUN pip install --no-cache-dir -e ".[train,dev]" || true
+
+COPY . .
+RUN pip install --no-cache-dir -e ".[train,dev]"
+
+# -------------------------------------------------------------------
+FROM base AS cpu
+
+# CPU-only variant (for CI and non-GPU environments)
+FROM python:3.11-slim AS cpu-only
+
+ENV PYTHONUNBUFFERED=1
+
+RUN apt-get update && apt-get install -y --no-install-recommends \
+    git freecad libgl1-mesa-glx libglib2.0-0 \
+    && rm -rf /var/lib/apt/lists/*
+
+WORKDIR /workspace
+
+COPY pyproject.toml .
+RUN pip install --no-cache-dir torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu
+RUN pip install --no-cache-dir torch-geometric
+
+COPY . .
+RUN pip install --no-cache-dir -e ".[train,dev]"
+
+CMD ["pytest", "tests/", "-v"]

Makefile

@@ -0,0 +1,48 @@
+.PHONY: train test lint data-gen export format type-check install dev clean help
+
+PYTHON ?= python
+PYTEST ?= pytest
+RUFF ?= ruff
+MYPY ?= mypy
+
+help: ## Show this help
+	@grep -E '^[a-zA-Z_-]+:.*?## .*$$' $(MAKEFILE_LIST) | sort | \
+		awk 'BEGIN {FS = ":.*?## "}; {printf "\033[36m%-20s\033[0m %s\n", $$1, $$2}'
+
+install: ## Install core dependencies
+	pip install -e .
+
+dev: ## Install all dependencies including dev tools
+	pip install -e ".[train,dev]"
+	pre-commit install
+	pre-commit install --hook-type commit-msg
+
+train: ## Run training (pass CONFIG=path/to/config.yaml)
+	$(PYTHON) -m solver.training.train $(if $(CONFIG),--config-path $(CONFIG))
+
+test: ## Run test suite
+	$(PYTEST) tests/ freecad/tests/ -v --tb=short
+
+lint: ## Run ruff linter
+	$(RUFF) check solver/ freecad/ tests/ scripts/
+
+format: ## Format code with ruff
+	$(RUFF) format solver/ freecad/ tests/ scripts/
+	$(RUFF) check --fix solver/ freecad/ tests/ scripts/
+
+type-check: ## Run mypy type checker
+	$(MYPY) solver/ freecad/
+
+data-gen: ## Generate synthetic dataset (pass CONFIG=path/to/config.yaml)
+	$(PYTHON) scripts/generate_synthetic.py $(if $(CONFIG),--config-path $(CONFIG))
+
+export: ## Export trained model for deployment
+	$(PYTHON) export/package_model.py $(if $(MODEL),--model $(MODEL))
+
+clean: ## Remove build artifacts and caches
+	rm -rf build/ dist/ *.egg-info/
+	rm -rf .mypy_cache/ .pytest_cache/ .ruff_cache/
+	find . -type d -name __pycache__ -exec rm -rf {} + 2>/dev/null || true
+	find . -type f -name "*.pyc" -delete 2>/dev/null || true
+
+check: lint type-check test ## Run all checks (lint, type-check, test)

README.md

@@ -1,7 +1,91 @@
-# MbDCode
-Assembly Constraints and Multibody Dynamics code
+# Kindred Solver
 
-Install freecad9a.exe from ar-cad.com. Run program and read Explain menu items for documentations. (edited) 
+Assembly constraint solver for [Kindred Create](https://git.kindred-systems.com/kindred/create). Combines a numerical multibody dynamics engine (OndselSolver) with a GNN-based constraint prediction layer.
 
-The MbD theory is at
-https://github.com/Ondsel-Development/MbDTheory
+## Components
+
+### OndselSolver (C++)
+
+Numerical assembly constraint solver using multibody dynamics. Solves joint constraints between rigid bodies using a Newton-Raphson iterative approach. Used by FreeCAD's Assembly workbench as the backend solver.
+
+- Source: `OndselSolver/`
+- Entry point: `OndselSolverMain/`
+- Tests: `tests/`, `testapp/`
+- Build: CMake
+
+**Theory:** [MbDTheory](https://github.com/Ondsel-Development/MbDTheory)
+
+#### Building
+
+```bash
+cmake -B build -DCMAKE_BUILD_TYPE=Release
+cmake --build build
+```
+
+### ML Solver Layer (Python)
+
+Graph neural network that predicts constraint independence and per-body degrees of freedom. Trained on synthetic assembly data generated via the pebble game algorithm, with the goal of augmenting or replacing the numerical solver for common assembly patterns.
+
+- Core library: `solver/`
+- Data generation: `solver/datagen/` (pebble game, synthetic assemblies, labeling)
+- Model architectures: `solver/models/` (GIN, GAT, NNConv)
+- Training: `solver/training/`
+- Inference: `solver/inference/`
+- FreeCAD integration: `freecad/`
+- Configuration: `configs/` (Hydra)
+
+#### Setup
+
+```bash
+pip install -e ".[train,dev]"
+pre-commit install
+```
+
+#### Usage
+
+```bash
+make help          # show all targets
+make dev           # install all deps + pre-commit hooks
+make test          # run tests
+make lint          # run ruff linter
+make check         # lint + type-check + test
+make data-gen      # generate synthetic data
+make train         # run training
+make export        # export model
+```
+
+Docker is also supported:
+
+```bash
+docker compose up train       # GPU training
+docker compose up test        # run tests
+docker compose up data-gen    # generate synthetic data
+```
+
+## Repository structure
+
+```
+kindred-solver/
+├── OndselSolver/       # C++ numerical solver library
+├── OndselSolverMain/   # C++ solver CLI entry point
+├── tests/              # C++ unit tests + Python tests
+├── testapp/            # C++ test application
+├── solver/             # Python ML solver library
+│   ├── datagen/        # Synthetic data generation (pebble game)
+│   ├── datasets/       # PyG dataset adapters
+│   ├── models/         # GNN architectures
+│   ├── training/       # Training loops
+│   ├── evaluation/     # Metrics and visualization
+│   └── inference/      # Runtime prediction API
+├── freecad/            # FreeCAD workbench integration
+├── configs/            # Hydra configs (dataset, model, training, export)
+├── scripts/            # CLI utilities
+├── data/               # Datasets (not committed)
+├── export/             # Model packaging
+└── docs/               # Documentation
+```
+
+## License
+
+OndselSolver: LGPL-2.1-or-later (see [LICENSE](LICENSE))
+ML Solver Layer: Apache-2.0

configs/dataset/fusion360.yaml

@@ -0,0 +1,12 @@
+# Fusion 360 Gallery dataset config
+name: fusion360
+data_dir: data/fusion360
+output_dir: data/processed
+
+splits:
+  train: 0.8
+  val: 0.1
+  test: 0.1
+
+stratify_by: complexity
+seed: 42

configs/dataset/synthetic.yaml

@@ -0,0 +1,26 @@
+# Synthetic dataset generation config
+name: synthetic
+num_assemblies: 100000
+output_dir: data/synthetic
+shard_size: 1000
+
+complexity_distribution:
+  simple: 0.4    # 2-5 bodies
+  medium: 0.4    # 6-15 bodies
+  complex: 0.2   # 16-50 bodies
+
+body_count:
+  min: 2
+  max: 50
+
+templates:
+  - chain
+  - tree
+  - loop
+  - star
+  - mixed
+
+grounded_ratio: 0.5
+seed: 42
+num_workers: 4
+checkpoint_every: 5

configs/export/production.yaml

@@ -0,0 +1,25 @@
+# Production model export config
+model_checkpoint: checkpoints/finetune/best_val_loss.ckpt
+output_dir: export/
+
+formats:
+  onnx:
+    enabled: true
+    opset_version: 17
+    dynamic_axes: true
+  torchscript:
+    enabled: true
+
+model_card:
+  version: "0.1.0"
+  architecture: baseline
+  training_data:
+    - synthetic_100k
+    - fusion360_gallery
+
+size_budget_mb: 50
+
+inference:
+  device: cpu
+  batch_size: 1
+  confidence_threshold: 0.8

configs/model/baseline.yaml

@@ -0,0 +1,24 @@
+# Baseline GIN model config
+name: baseline
+architecture: gin
+
+encoder:
+  num_layers: 3
+  hidden_dim: 128
+  dropout: 0.1
+
+node_features_dim: 22
+edge_features_dim: 22
+
+heads:
+  edge_classification:
+    enabled: true
+    hidden_dim: 64
+  graph_classification:
+    enabled: true
+    num_classes: 4  # rigid, under, over, mixed
+  joint_type:
+    enabled: true
+    num_classes: 12
+  dof_regression:
+    enabled: true

configs/model/gat.yaml

@@ -0,0 +1,28 @@
+# Advanced GAT model config
+name: gat_solver
+architecture: gat
+
+encoder:
+  num_layers: 4
+  hidden_dim: 256
+  num_heads: 8
+  dropout: 0.1
+  residual: true
+
+node_features_dim: 22
+edge_features_dim: 22
+
+heads:
+  edge_classification:
+    enabled: true
+    hidden_dim: 128
+  graph_classification:
+    enabled: true
+    num_classes: 4
+  joint_type:
+    enabled: true
+    num_classes: 12
+  dof_regression:
+    enabled: true
+  dof_tracking:
+    enabled: true

configs/training/finetune.yaml

@@ -0,0 +1,45 @@
+# Fine-tuning on real data config
+phase: finetune
+
+dataset: fusion360
+model: baseline
+
+pretrained_checkpoint: checkpoints/pretrain/best_val_loss.ckpt
+
+optimizer:
+  name: adamw
+  lr: 1e-5
+  weight_decay: 1e-4
+
+scheduler:
+  name: cosine_annealing
+  T_max: 50
+  eta_min: 1e-7
+
+training:
+  epochs: 50
+  batch_size: 32
+  gradient_clip: 1.0
+  early_stopping_patience: 10
+  amp: true
+  freeze_encoder: false  # set true for frozen encoder experiment
+
+loss:
+  edge_weight: 1.0
+  graph_weight: 0.5
+  joint_type_weight: 0.3
+  dof_weight: 0.2
+  redundant_penalty: 2.0
+
+checkpointing:
+  save_best_val_loss: true
+  save_best_val_accuracy: true
+  save_every_n_epochs: 5
+  checkpoint_dir: checkpoints/finetune
+
+logging:
+  backend: wandb
+  project: kindred-solver
+  log_every_n_steps: 20
+
+seed: 42

configs/training/pretrain.yaml

@@ -0,0 +1,42 @@
+# Synthetic pre-training config
+phase: pretrain
+
+dataset: synthetic
+model: baseline
+
+optimizer:
+  name: adamw
+  lr: 1e-3
+  weight_decay: 1e-4
+
+scheduler:
+  name: cosine_annealing
+  T_max: 100
+  eta_min: 1e-6
+
+training:
+  epochs: 100
+  batch_size: 64
+  gradient_clip: 1.0
+  early_stopping_patience: 10
+  amp: true
+
+loss:
+  edge_weight: 1.0
+  graph_weight: 0.5
+  joint_type_weight: 0.3
+  dof_weight: 0.2
+  redundant_penalty: 2.0  # safety loss multiplier
+
+checkpointing:
+  save_best_val_loss: true
+  save_best_val_accuracy: true
+  save_every_n_epochs: 10
+  checkpoint_dir: checkpoints/pretrain
+
+logging:
+  backend: wandb  # or tensorboard
+  project: kindred-solver
+  log_every_n_steps: 50
+
+seed: 42

docker-compose.yml

@@ -0,0 +1,39 @@
+services:
+  train:
+    build:
+      context: .
+      dockerfile: Dockerfile
+      target: base
+    volumes:
+      - .:/workspace
+      - ./data:/workspace/data
+    deploy:
+      resources:
+        reservations:
+          devices:
+            - driver: nvidia
+              count: all
+              capabilities: [gpu]
+    command: make train
+    environment:
+      - CUDA_VISIBLE_DEVICES=${CUDA_VISIBLE_DEVICES:-0}
+      - WANDB_API_KEY=${WANDB_API_KEY:-}
+
+  test:
+    build:
+      context: .
+      dockerfile: Dockerfile
+      target: cpu-only
+    volumes:
+      - .:/workspace
+    command: make check
+
+  data-gen:
+    build:
+      context: .
+      dockerfile: Dockerfile
+      target: base
+    volumes:
+      - .:/workspace
+      - ./data:/workspace/data
+    command: make data-gen

pyproject.toml

@@ -0,0 +1,97 @@
+[build-system]
+requires = ["hatchling"]
+build-backend = "hatchling.build"
+
+[project]
+name = "kindred-solver"
+version = "0.1.0"
+description = "Assembly constraint prediction via GNN for Kindred Create"
+readme = "README.md"
+license = "Apache-2.0"
+requires-python = ">=3.11"
+authors = [
+    { name = "Kindred Systems" },
+]
+classifiers = [
+    "Development Status :: 3 - Alpha",
+    "License :: OSI Approved :: Apache Software License",
+    "Programming Language :: Python :: 3",
+    "Programming Language :: Python :: 3.11",
+    "Programming Language :: Python :: 3.12",
+    "Topic :: Scientific/Engineering",
+]
+dependencies = [
+    "torch>=2.2",
+    "torch-geometric>=2.5",
+    "numpy>=1.26",
+    "scipy>=1.12",
+]
+
+[project.optional-dependencies]
+train = [
+    "wandb>=0.16",
+    "tensorboard>=2.16",
+    "hydra-core>=1.3",
+    "omegaconf>=2.3",
+    "matplotlib>=3.8",
+    "networkx>=3.2",
+]
+freecad = [
+    "pyside6>=6.6",
+]
+dev = [
+    "pytest>=8.0",
+    "pytest-cov>=4.1",
+    "ruff>=0.3",
+    "mypy>=1.8",
+    "pre-commit>=3.6",
+]
+
+[project.urls]
+Repository = "https://git.kindred-systems.com/kindred/solver"
+
+[tool.hatch.build.targets.wheel]
+packages = ["solver", "freecad"]
+
+[tool.ruff]
+target-version = "py311"
+line-length = 100
+
+[tool.ruff.lint]
+select = [
+    "E",    # pycodestyle errors
+    "W",    # pycodestyle warnings
+    "F",    # pyflakes
+    "I",    # isort
+    "N",    # pep8-naming
+    "UP",   # pyupgrade
+    "B",    # flake8-bugbear
+    "SIM",  # flake8-simplify
+    "TCH",  # flake8-type-checking
+    "RUF",  # ruff-specific
+]
+
+[tool.ruff.lint.isort]
+known-first-party = ["solver", "freecad"]
+
+[tool.mypy]
+python_version = "3.11"
+warn_return_any = true
+warn_unused_configs = true
+disallow_untyped_defs = true
+check_untyped_defs = true
+
+[[tool.mypy.overrides]]
+module = [
+    "torch.*",
+    "torch_geometric.*",
+    "scipy.*",
+    "wandb.*",
+    "hydra.*",
+    "omegaconf.*",
+]
+ignore_missing_imports = true
+
+[tool.pytest.ini_options]
+testpaths = ["tests", "freecad/tests"]
+addopts = "-v --tb=short"

scripts/generate_synthetic.py

@@ -0,0 +1,115 @@
+#!/usr/bin/env python3
+"""Generate synthetic assembly dataset for kindred-solver training.
+
+Usage (argparse fallback — always available)::
+
+    python scripts/generate_synthetic.py --num-assemblies 1000 --num-workers 4
+
+Usage (Hydra — when hydra-core is installed)::
+
+    python scripts/generate_synthetic.py num_assemblies=1000 num_workers=4
+"""
+
+from __future__ import annotations
+
+
+def _try_hydra_main() -> bool:
+    """Attempt to run via Hydra.  Returns *True* if Hydra handled it."""
+    try:
+        import hydra  # type: ignore[import-untyped]
+        from omegaconf import DictConfig, OmegaConf  # type: ignore[import-untyped]
+    except ImportError:
+        return False
+
+    @hydra.main(
+        config_path="../configs/dataset",
+        config_name="synthetic",
+        version_base=None,
+    )
+    def _run(cfg: DictConfig) -> None:  # type: ignore[type-arg]
+        from solver.datagen.dataset import DatasetConfig, DatasetGenerator
+
+        config_dict = OmegaConf.to_container(cfg, resolve=True)
+        config = DatasetConfig.from_dict(config_dict)  # type: ignore[arg-type]
+        DatasetGenerator(config).run()
+
+    _run()  # type: ignore[no-untyped-call]
+    return True
+
+
+def _argparse_main() -> None:
+    """Fallback CLI using argparse."""
+    import argparse
+
+    parser = argparse.ArgumentParser(
+        description="Generate synthetic assembly dataset",
+    )
+    parser.add_argument(
+        "--config",
+        type=str,
+        default=None,
+        help="Path to YAML config file (optional)",
+    )
+    parser.add_argument("--num-assemblies", type=int, default=None, help="Number of assemblies")
+    parser.add_argument("--output-dir", type=str, default=None, help="Output directory")
+    parser.add_argument("--shard-size", type=int, default=None, help="Assemblies per shard")
+    parser.add_argument("--body-count-min", type=int, default=None, help="Min body count")
+    parser.add_argument("--body-count-max", type=int, default=None, help="Max body count")
+    parser.add_argument("--grounded-ratio", type=float, default=None, help="Grounded ratio")
+    parser.add_argument("--seed", type=int, default=None, help="Random seed")
+    parser.add_argument("--num-workers", type=int, default=None, help="Parallel workers")
+    parser.add_argument(
+        "--checkpoint-every",
+        type=int,
+        default=None,
+        help="Checkpoint interval (shards)",
+    )
+    parser.add_argument(
+        "--no-resume",
+        action="store_true",
+        help="Do not resume from existing checkpoints",
+    )
+
+    args = parser.parse_args()
+
+    from solver.datagen.dataset import (
+        DatasetConfig,
+        DatasetGenerator,
+        parse_simple_yaml,
+    )
+
+    config_dict: dict[str, object] = {}
+    if args.config:
+        config_dict = parse_simple_yaml(args.config)  # type: ignore[assignment]
+
+    # CLI args override config file (only when explicitly provided)
+    _override_map = {
+        "num_assemblies": args.num_assemblies,
+        "output_dir": args.output_dir,
+        "shard_size": args.shard_size,
+        "body_count_min": args.body_count_min,
+        "body_count_max": args.body_count_max,
+        "grounded_ratio": args.grounded_ratio,
+        "seed": args.seed,
+        "num_workers": args.num_workers,
+        "checkpoint_every": args.checkpoint_every,
+    }
+    for key, val in _override_map.items():
+        if val is not None:
+            config_dict[key] = val
+
+    if args.no_resume:
+        config_dict["resume"] = False
+
+    config = DatasetConfig.from_dict(config_dict)  # type: ignore[arg-type]
+    DatasetGenerator(config).run()
+
+
+def main() -> None:
+    """Entry point: try Hydra first, fall back to argparse."""
+    if not _try_hydra_main():
+        _argparse_main()
+
+
+if __name__ == "__main__":
+    main()

solver/datagen/__init__.py

@@ -0,0 +1,37 @@
+"""Data generation utilities for assembly constraint training data."""
+
+from solver.datagen.analysis import analyze_assembly
+from solver.datagen.dataset import DatasetConfig, DatasetGenerator
+from solver.datagen.generator import (
+    COMPLEXITY_RANGES,
+    AxisStrategy,
+    SyntheticAssemblyGenerator,
+)
+from solver.datagen.jacobian import JacobianVerifier
+from solver.datagen.labeling import AssemblyLabels, label_assembly
+from solver.datagen.pebble_game import PebbleGame3D
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    PebbleState,
+    RigidBody,
+)
+
+__all__ = [
+    "COMPLEXITY_RANGES",
+    "AssemblyLabels",
+    "AxisStrategy",
+    "ConstraintAnalysis",
+    "DatasetConfig",
+    "DatasetGenerator",
+    "JacobianVerifier",
+    "Joint",
+    "JointType",
+    "PebbleGame3D",
+    "PebbleState",
+    "RigidBody",
+    "SyntheticAssemblyGenerator",
+    "analyze_assembly",
+    "label_assembly",
+]

solver/datagen/analysis.py

@@ -0,0 +1,140 @@
+"""Combined pebble game + Jacobian verification analysis.
+
+Provides :func:`analyze_assembly`, the main entry point for full rigidity
+analysis of an assembly using both combinatorial and numerical methods.
+"""
+
+from __future__ import annotations
+
+import numpy as np
+
+from solver.datagen.jacobian import JacobianVerifier
+from solver.datagen.pebble_game import PebbleGame3D
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    RigidBody,
+)
+
+__all__ = ["analyze_assembly"]
+
+_GROUND_ID = -1
+
+
+def analyze_assembly(
+    bodies: list[RigidBody],
+    joints: list[Joint],
+    ground_body: int | None = None,
+) -> ConstraintAnalysis:
+    """Full rigidity analysis of an assembly using both methods.
+
+    Args:
+        bodies: List of rigid bodies in the assembly.
+        joints: List of joints connecting bodies.
+        ground_body: If set, this body is fixed (adds 6 implicit constraints).
+
+    Returns:
+        ConstraintAnalysis with combinatorial and numerical results.
+    """
+    # --- Pebble Game ---
+    pg = PebbleGame3D()
+    all_edge_results = []
+
+    # Add a virtual ground body (id=-1) if grounding is requested.
+    # Grounding body X means adding a fixed joint between X and
+    # the virtual ground. This properly lets the pebble game account
+    # for the 6 removed DOF without breaking invariants.
+    if ground_body is not None:
+        pg.add_body(_GROUND_ID)
+
+    for body in bodies:
+        pg.add_body(body.body_id)
+
+    if ground_body is not None:
+        ground_joint = Joint(
+            joint_id=-1,
+            body_a=ground_body,
+            body_b=_GROUND_ID,
+            joint_type=JointType.FIXED,
+            anchor_a=bodies[0].position if bodies else np.zeros(3),
+            anchor_b=bodies[0].position if bodies else np.zeros(3),
+        )
+        pg.add_joint(ground_joint)
+        # Don't include ground joint edges in the output labels
+        # (they're infrastructure, not user constraints)
+
+    for joint in joints:
+        results = pg.add_joint(joint)
+        all_edge_results.extend(results)
+
+    combinatorial_independent = len(pg.state.independent_edges)
+    grounded = ground_body is not None
+
+    # The virtual ground body contributes 6 pebbles to the total.
+    # Subtract those from the reported DOF for user-facing numbers.
+    raw_dof = pg.get_dof()
+    ground_offset = 6 if grounded else 0
+    effective_dof = raw_dof - ground_offset
+    effective_internal_dof = max(0, effective_dof - (0 if grounded else 6))
+
+    # Classify based on effective (adjusted) DOF, not raw pebble game output,
+    # because the virtual ground body skews the raw numbers.
+    redundant = pg.get_redundant_count()
+    if redundant > 0 and effective_internal_dof > 0:
+        combinatorial_classification = "mixed"
+    elif redundant > 0:
+        combinatorial_classification = "overconstrained"
+    elif effective_internal_dof > 0:
+        combinatorial_classification = "underconstrained"
+    else:
+        combinatorial_classification = "well-constrained"
+
+    # --- Jacobian Verification ---
+    verifier = JacobianVerifier(bodies)
+
+    for joint in joints:
+        verifier.add_joint_constraints(joint)
+
+    # If grounded, remove the ground body's columns (fix its DOF)
+    j = verifier.get_jacobian()
+    if ground_body is not None and j.size > 0:
+        idx = verifier.body_index[ground_body]
+        cols_to_remove = list(range(idx * 6, (idx + 1) * 6))
+        j = np.delete(j, cols_to_remove, axis=1)
+
+    if j.size > 0:
+        sv = np.linalg.svd(j, compute_uv=False)
+        jacobian_rank = int(np.sum(sv > 1e-8))
+    else:
+        jacobian_rank = 0
+
+    n_cols = j.shape[1] if j.size > 0 else 6 * len(bodies)
+    jacobian_nullity = n_cols - jacobian_rank
+
+    dependent = verifier.find_dependencies()
+
+    # Adjust for ground
+    trivial_dof = 0 if ground_body is not None else 6
+    jacobian_internal_dof = jacobian_nullity - trivial_dof
+
+    geometric_degeneracies = max(0, combinatorial_independent - jacobian_rank)
+
+    # Rigidity: numerically rigid if nullity == trivial DOF
+    is_rigid = jacobian_nullity <= trivial_dof
+    is_minimally_rigid = is_rigid and len(dependent) == 0
+
+    return ConstraintAnalysis(
+        combinatorial_dof=effective_dof,
+        combinatorial_internal_dof=effective_internal_dof,
+        combinatorial_redundant=pg.get_redundant_count(),
+        combinatorial_classification=combinatorial_classification,
+        per_edge_results=all_edge_results,
+        jacobian_rank=jacobian_rank,
+        jacobian_nullity=jacobian_nullity,
+        jacobian_internal_dof=max(0, jacobian_internal_dof),
+        numerically_dependent=dependent,
+        geometric_degeneracies=geometric_degeneracies,
+        is_rigid=is_rigid,
+        is_minimally_rigid=is_minimally_rigid,
+    )

solver/datagen/dataset.py

@@ -0,0 +1,624 @@
+"""Dataset generation orchestrator with sharding, checkpointing, and statistics.
+
+Provides :class:`DatasetConfig` for configuration and :class:`DatasetGenerator`
+for parallel generation of synthetic assembly training data.
+"""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import logging
+import math
+import sys
+import time
+from concurrent.futures import ProcessPoolExecutor, as_completed
+from dataclasses import dataclass, field
+from pathlib import Path
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "DatasetConfig",
+    "DatasetGenerator",
+    "parse_simple_yaml",
+]
+
+logger = logging.getLogger(__name__)
+
+# ---------------------------------------------------------------------------
+# Configuration
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class DatasetConfig:
+    """Configuration for synthetic dataset generation."""
+
+    name: str = "synthetic"
+    num_assemblies: int = 100_000
+    output_dir: str = "data/synthetic"
+    shard_size: int = 1000
+    complexity_distribution: dict[str, float] = field(
+        default_factory=lambda: {"simple": 0.4, "medium": 0.4, "complex": 0.2}
+    )
+    body_count_min: int = 2
+    body_count_max: int = 50
+    templates: list[str] = field(default_factory=lambda: ["chain", "tree", "loop", "star", "mixed"])
+    grounded_ratio: float = 0.5
+    seed: int = 42
+    num_workers: int = 4
+    checkpoint_every: int = 5
+    resume: bool = True
+
+    @classmethod
+    def from_dict(cls, d: dict[str, Any]) -> DatasetConfig:
+        """Construct from a parsed config dict (e.g. YAML or OmegaConf).
+
+        Handles both flat keys (``body_count_min``) and nested forms
+        (``body_count: {min: 2, max: 50}``).
+        """
+        kw: dict[str, Any] = {}
+        for key in (
+            "name",
+            "num_assemblies",
+            "output_dir",
+            "shard_size",
+            "grounded_ratio",
+            "seed",
+            "num_workers",
+            "checkpoint_every",
+            "resume",
+        ):
+            if key in d:
+                kw[key] = d[key]
+
+        # Handle nested body_count dict
+        if "body_count" in d and isinstance(d["body_count"], dict):
+            bc = d["body_count"]
+            if "min" in bc:
+                kw["body_count_min"] = int(bc["min"])
+            if "max" in bc:
+                kw["body_count_max"] = int(bc["max"])
+        else:
+            if "body_count_min" in d:
+                kw["body_count_min"] = int(d["body_count_min"])
+            if "body_count_max" in d:
+                kw["body_count_max"] = int(d["body_count_max"])
+
+        if "complexity_distribution" in d:
+            cd = d["complexity_distribution"]
+            if isinstance(cd, dict):
+                kw["complexity_distribution"] = {str(k): float(v) for k, v in cd.items()}
+        if "templates" in d and isinstance(d["templates"], list):
+            kw["templates"] = [str(t) for t in d["templates"]]
+
+        return cls(**kw)
+
+
+# ---------------------------------------------------------------------------
+# Shard specification / result
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class ShardSpec:
+    """Specification for generating a single shard."""
+
+    shard_id: int
+    start_example_id: int
+    count: int
+    seed: int
+    complexity_distribution: dict[str, float]
+    body_count_min: int
+    body_count_max: int
+    grounded_ratio: float
+
+
+@dataclass
+class ShardResult:
+    """Result returned from a shard worker."""
+
+    shard_id: int
+    num_examples: int
+    file_path: str
+    generation_time_s: float
+
+
+# ---------------------------------------------------------------------------
+# Seed derivation
+# ---------------------------------------------------------------------------
+
+
+def _derive_shard_seed(global_seed: int, shard_id: int) -> int:
+    """Derive a deterministic per-shard seed from the global seed."""
+    h = hashlib.sha256(f"{global_seed}:{shard_id}".encode()).hexdigest()
+    return int(h[:8], 16)
+
+
+# ---------------------------------------------------------------------------
+# Progress display
+# ---------------------------------------------------------------------------
+
+
+class _PrintProgress:
+    """Fallback progress display when tqdm is unavailable."""
+
+    def __init__(self, total: int) -> None:
+        self.total = total
+        self.current = 0
+        self.start_time = time.monotonic()
+
+    def update(self, n: int = 1) -> None:
+        self.current += n
+        elapsed = time.monotonic() - self.start_time
+        rate = self.current / elapsed if elapsed > 0 else 0.0
+        eta = (self.total - self.current) / rate if rate > 0 else 0.0
+        pct = 100.0 * self.current / self.total
+        sys.stdout.write(
+            f"\r[{pct:5.1f}%] {self.current}/{self.total} shards"
+            f" | {rate:.1f} shards/s | ETA: {eta:.0f}s"
+        )
+        sys.stdout.flush()
+
+    def close(self) -> None:
+        sys.stdout.write("\n")
+        sys.stdout.flush()
+
+
+def _make_progress(total: int) -> _PrintProgress:
+    """Create a progress tracker (tqdm if available, else print-based)."""
+    try:
+        from tqdm import tqdm  # type: ignore[import-untyped]
+
+        return tqdm(total=total, desc="Generating shards", unit="shard")  # type: ignore[no-any-return,return-value]
+    except ImportError:
+        return _PrintProgress(total)
+
+
+# ---------------------------------------------------------------------------
+# Shard I/O
+# ---------------------------------------------------------------------------
+
+
+def _save_shard(
+    shard_id: int,
+    examples: list[dict[str, Any]],
+    shards_dir: Path,
+) -> Path:
+    """Save a shard to disk (.pt if torch available, else .json)."""
+    shards_dir.mkdir(parents=True, exist_ok=True)
+    try:
+        import torch  # type: ignore[import-untyped]
+
+        path = shards_dir / f"shard_{shard_id:05d}.pt"
+        torch.save(examples, path)
+    except ImportError:
+        path = shards_dir / f"shard_{shard_id:05d}.json"
+        with open(path, "w") as f:
+            json.dump(examples, f)
+    return path
+
+
+def _load_shard(path: Path) -> list[dict[str, Any]]:
+    """Load a shard from disk (.pt or .json)."""
+    if path.suffix == ".pt":
+        import torch  # type: ignore[import-untyped]
+
+        result: list[dict[str, Any]] = torch.load(path, weights_only=False)
+        return result
+    with open(path) as f:
+        result = json.load(f)
+    return result
+
+
+def _shard_format() -> str:
+    """Return the shard file extension based on available libraries."""
+    try:
+        import torch  # type: ignore[import-untyped]  # noqa: F401
+
+        return ".pt"
+    except ImportError:
+        return ".json"
+
+
+# ---------------------------------------------------------------------------
+# Shard worker (module-level for pickling)
+# ---------------------------------------------------------------------------
+
+
+def _generate_shard_worker(spec: ShardSpec, output_dir: str) -> ShardResult:
+    """Generate a single shard — top-level function for ProcessPoolExecutor."""
+    from solver.datagen.generator import SyntheticAssemblyGenerator
+
+    t0 = time.monotonic()
+    gen = SyntheticAssemblyGenerator(seed=spec.seed)
+    rng = np.random.default_rng(spec.seed + 1)
+
+    tiers = list(spec.complexity_distribution.keys())
+    probs_list = [spec.complexity_distribution[t] for t in tiers]
+    total = sum(probs_list)
+    probs = [p / total for p in probs_list]
+
+    examples: list[dict[str, Any]] = []
+    for i in range(spec.count):
+        tier_idx = int(rng.choice(len(tiers), p=probs))
+        tier = tiers[tier_idx]
+        try:
+            batch = gen.generate_training_batch(
+                batch_size=1,
+                complexity_tier=tier,  # type: ignore[arg-type]
+                grounded_ratio=spec.grounded_ratio,
+            )
+            ex = batch[0]
+            ex["example_id"] = spec.start_example_id + i
+            ex["complexity_tier"] = tier
+            examples.append(ex)
+        except Exception:
+            logger.warning(
+                "Shard %d, example %d failed — skipping",
+                spec.shard_id,
+                i,
+                exc_info=True,
+            )
+
+    shards_dir = Path(output_dir) / "shards"
+    path = _save_shard(spec.shard_id, examples, shards_dir)
+
+    elapsed = time.monotonic() - t0
+    return ShardResult(
+        shard_id=spec.shard_id,
+        num_examples=len(examples),
+        file_path=str(path),
+        generation_time_s=elapsed,
+    )
+
+
+# ---------------------------------------------------------------------------
+# Minimal YAML parser
+# ---------------------------------------------------------------------------
+
+
+def _parse_scalar(value: str) -> int | float | bool | str:
+    """Parse a YAML scalar value."""
+    # Strip inline comments (space + #)
+    if "  #" in value:
+        value = value[: value.index("  #")].strip()
+    elif "	#" in value:
+        value = value[: value.index("	#")].strip()
+    v = value.strip()
+    if v.lower() in ("true", "yes"):
+        return True
+    if v.lower() in ("false", "no"):
+        return False
+    try:
+        return int(v)
+    except ValueError:
+        pass
+    try:
+        return float(v)
+    except ValueError:
+        pass
+    return v.strip("'\"")
+
+
+def parse_simple_yaml(path: str) -> dict[str, Any]:
+    """Parse a simple YAML file (flat scalars, one-level dicts, lists).
+
+    This is **not** a full YAML parser.  It handles the structure of
+    ``configs/dataset/synthetic.yaml``.
+    """
+    result: dict[str, Any] = {}
+    current_key: str | None = None
+
+    with open(path) as f:
+        for raw_line in f:
+            line = raw_line.rstrip()
+
+            # Skip blank lines and full-line comments
+            if not line or line.lstrip().startswith("#"):
+                continue
+
+            indent = len(line) - len(line.lstrip())
+
+            if indent == 0 and ":" in line:
+                key, _, value = line.partition(":")
+                key = key.strip()
+                value = value.strip()
+                if value:
+                    result[key] = _parse_scalar(value)
+                    current_key = None
+                else:
+                    current_key = key
+                    result[key] = {}
+                continue
+
+            if indent > 0 and line.lstrip().startswith("- "):
+                item = line.lstrip()[2:].strip()
+                if current_key is not None:
+                    if isinstance(result.get(current_key), dict) and not result[current_key]:
+                        result[current_key] = []
+                    if isinstance(result.get(current_key), list):
+                        result[current_key].append(_parse_scalar(item))
+                continue
+
+            if indent > 0 and ":" in line and current_key is not None:
+                k, _, v = line.partition(":")
+                k = k.strip()
+                v = v.strip()
+                if v:
+                    # Strip inline comments
+                    if "  #" in v:
+                        v = v[: v.index("  #")].strip()
+                    if not isinstance(result.get(current_key), dict):
+                        result[current_key] = {}
+                    result[current_key][k] = _parse_scalar(v)
+                continue
+
+    return result
+
+
+# ---------------------------------------------------------------------------
+# Dataset generator orchestrator
+# ---------------------------------------------------------------------------
+
+
+class DatasetGenerator:
+    """Orchestrates parallel dataset generation with sharding and checkpointing."""
+
+    def __init__(self, config: DatasetConfig) -> None:
+        self.config = config
+        self.output_path = Path(config.output_dir)
+        self.shards_dir = self.output_path / "shards"
+        self.checkpoint_file = self.output_path / ".checkpoint.json"
+        self.index_file = self.output_path / "index.json"
+        self.stats_file = self.output_path / "stats.json"
+
+    # -- public API --
+
+    def run(self) -> None:
+        """Generate the full dataset."""
+        self.output_path.mkdir(parents=True, exist_ok=True)
+        self.shards_dir.mkdir(parents=True, exist_ok=True)
+
+        shards = self._plan_shards()
+        total_shards = len(shards)
+
+        # Resume: find already-completed shards
+        completed: set[int] = set()
+        if self.config.resume:
+            completed = self._find_completed_shards()
+
+        pending = [s for s in shards if s.shard_id not in completed]
+
+        if not pending:
+            logger.info("All %d shards already complete.", total_shards)
+        else:
+            logger.info(
+                "Generating %d shards (%d already complete).",
+                len(pending),
+                len(completed),
+            )
+            progress = _make_progress(len(pending))
+            workers = max(1, self.config.num_workers)
+            checkpoint_counter = 0
+
+            with ProcessPoolExecutor(max_workers=workers) as pool:
+                futures = {
+                    pool.submit(
+                        _generate_shard_worker,
+                        spec,
+                        str(self.output_path),
+                    ): spec.shard_id
+                    for spec in pending
+                }
+                for future in as_completed(futures):
+                    shard_id = futures[future]
+                    try:
+                        result = future.result()
+                        completed.add(result.shard_id)
+                        logger.debug(
+                            "Shard %d: %d examples in %.1fs",
+                            result.shard_id,
+                            result.num_examples,
+                            result.generation_time_s,
+                        )
+                    except Exception:
+                        logger.error("Shard %d failed", shard_id, exc_info=True)
+                    progress.update(1)
+                    checkpoint_counter += 1
+                    if checkpoint_counter >= self.config.checkpoint_every:
+                        self._update_checkpoint(completed, total_shards)
+                        checkpoint_counter = 0
+
+            progress.close()
+
+        # Finalize
+        self._build_index()
+        stats = self._compute_statistics()
+        self._write_statistics(stats)
+        self._print_summary(stats)
+
+        # Remove checkpoint (generation complete)
+        if self.checkpoint_file.exists():
+            self.checkpoint_file.unlink()
+
+    # -- internal helpers --
+
+    def _plan_shards(self) -> list[ShardSpec]:
+        """Divide num_assemblies into shards."""
+        n = self.config.num_assemblies
+        size = self.config.shard_size
+        num_shards = math.ceil(n / size)
+        shards: list[ShardSpec] = []
+        for i in range(num_shards):
+            start = i * size
+            count = min(size, n - start)
+            shards.append(
+                ShardSpec(
+                    shard_id=i,
+                    start_example_id=start,
+                    count=count,
+                    seed=_derive_shard_seed(self.config.seed, i),
+                    complexity_distribution=dict(self.config.complexity_distribution),
+                    body_count_min=self.config.body_count_min,
+                    body_count_max=self.config.body_count_max,
+                    grounded_ratio=self.config.grounded_ratio,
+                )
+            )
+        return shards
+
+    def _find_completed_shards(self) -> set[int]:
+        """Scan shards directory for existing shard files."""
+        completed: set[int] = set()
+        if not self.shards_dir.exists():
+            return completed
+
+        for p in self.shards_dir.iterdir():
+            if p.stem.startswith("shard_"):
+                try:
+                    shard_id = int(p.stem.split("_")[1])
+                    # Verify file is non-empty
+                    if p.stat().st_size > 0:
+                        completed.add(shard_id)
+                except (ValueError, IndexError):
+                    pass
+        return completed
+
+    def _update_checkpoint(self, completed: set[int], total_shards: int) -> None:
+        """Write checkpoint file."""
+        data = {
+            "completed_shards": sorted(completed),
+            "total_shards": total_shards,
+            "timestamp": time.strftime("%Y-%m-%dT%H:%M:%SZ", time.gmtime()),
+        }
+        with open(self.checkpoint_file, "w") as f:
+            json.dump(data, f)
+
+    def _build_index(self) -> None:
+        """Build index.json mapping shard files to assembly ID ranges."""
+        shards_info: dict[str, dict[str, int]] = {}
+        total_assemblies = 0
+
+        for p in sorted(self.shards_dir.iterdir()):
+            if not p.stem.startswith("shard_"):
+                continue
+            try:
+                shard_id = int(p.stem.split("_")[1])
+            except (ValueError, IndexError):
+                continue
+            examples = _load_shard(p)
+            count = len(examples)
+            start_id = shard_id * self.config.shard_size
+            shards_info[p.name] = {"start_id": start_id, "count": count}
+            total_assemblies += count
+
+        fmt = _shard_format().lstrip(".")
+        index = {
+            "format_version": 1,
+            "total_assemblies": total_assemblies,
+            "total_shards": len(shards_info),
+            "shard_format": fmt,
+            "shards": shards_info,
+        }
+        with open(self.index_file, "w") as f:
+            json.dump(index, f, indent=2)
+
+    def _compute_statistics(self) -> dict[str, Any]:
+        """Aggregate statistics across all shards."""
+        classification_counts: dict[str, int] = {}
+        body_count_hist: dict[int, int] = {}
+        joint_type_counts: dict[str, int] = {}
+        dof_values: list[int] = []
+        degeneracy_values: list[int] = []
+        rigid_count = 0
+        minimally_rigid_count = 0
+        total = 0
+
+        for p in sorted(self.shards_dir.iterdir()):
+            if not p.stem.startswith("shard_"):
+                continue
+            examples = _load_shard(p)
+            for ex in examples:
+                total += 1
+                cls = str(ex.get("assembly_classification", "unknown"))
+                classification_counts[cls] = classification_counts.get(cls, 0) + 1
+                nb = int(ex.get("n_bodies", 0))
+                body_count_hist[nb] = body_count_hist.get(nb, 0) + 1
+                for j in ex.get("joints", []):
+                    jt = str(j.get("type", "unknown"))
+                    joint_type_counts[jt] = joint_type_counts.get(jt, 0) + 1
+                dof_values.append(int(ex.get("internal_dof", 0)))
+                degeneracy_values.append(int(ex.get("geometric_degeneracies", 0)))
+                if ex.get("is_rigid"):
+                    rigid_count += 1
+                if ex.get("is_minimally_rigid"):
+                    minimally_rigid_count += 1
+
+        dof_arr = np.array(dof_values) if dof_values else np.zeros(1)
+        deg_arr = np.array(degeneracy_values) if degeneracy_values else np.zeros(1)
+
+        return {
+            "total_examples": total,
+            "classification_distribution": dict(sorted(classification_counts.items())),
+            "body_count_histogram": dict(sorted(body_count_hist.items())),
+            "joint_type_distribution": dict(sorted(joint_type_counts.items())),
+            "dof_statistics": {
+                "mean": float(dof_arr.mean()),
+                "std": float(dof_arr.std()),
+                "min": int(dof_arr.min()),
+                "max": int(dof_arr.max()),
+                "median": float(np.median(dof_arr)),
+            },
+            "geometric_degeneracy": {
+                "assemblies_with_degeneracy": int(np.sum(deg_arr > 0)),
+                "fraction_with_degeneracy": float(np.mean(deg_arr > 0)),
+                "mean_degeneracies": float(deg_arr.mean()),
+            },
+            "rigidity": {
+                "rigid_count": rigid_count,
+                "rigid_fraction": (rigid_count / total if total > 0 else 0.0),
+                "minimally_rigid_count": minimally_rigid_count,
+                "minimally_rigid_fraction": (minimally_rigid_count / total if total > 0 else 0.0),
+            },
+        }
+
+    def _write_statistics(self, stats: dict[str, Any]) -> None:
+        """Write stats.json."""
+        with open(self.stats_file, "w") as f:
+            json.dump(stats, f, indent=2)
+
+    def _print_summary(self, stats: dict[str, Any]) -> None:
+        """Print a human-readable summary to stdout."""
+        print("\n=== Dataset Generation Summary ===")
+        print(f"Total examples: {stats['total_examples']}")
+        print(f"Output directory: {self.output_path}")
+        print()
+        print("Classification distribution:")
+        for cls, count in stats["classification_distribution"].items():
+            frac = count / max(stats["total_examples"], 1) * 100
+            print(f"  {cls}: {count} ({frac:.1f}%)")
+        print()
+        print("Joint type distribution:")
+        for jt, count in stats["joint_type_distribution"].items():
+            print(f"  {jt}: {count}")
+        print()
+        dof = stats["dof_statistics"]
+        print(
+            f"DOF: mean={dof['mean']:.1f}, std={dof['std']:.1f}, range=[{dof['min']}, {dof['max']}]"
+        )
+        rig = stats["rigidity"]
+        print(
+            f"Rigidity: {rig['rigid_count']}/{stats['total_examples']} "
+            f"({rig['rigid_fraction'] * 100:.1f}%) rigid, "
+            f"{rig['minimally_rigid_count']} minimally rigid"
+        )
+        deg = stats["geometric_degeneracy"]
+        print(
+            f"Degeneracy: {deg['assemblies_with_degeneracy']} assemblies "
+            f"({deg['fraction_with_degeneracy'] * 100:.1f}%)"
+        )

solver/datagen/generator.py

@@ -0,0 +1,893 @@
+"""Synthetic assembly graph generator for training data production.
+
+Generates assembly graphs with known constraint classifications using
+the pebble game and Jacobian verification. Each assembly is fully labeled
+with per-constraint independence flags and assembly-level classification.
+"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Literal
+
+import numpy as np
+from scipy.spatial.transform import Rotation
+
+from solver.datagen.analysis import analyze_assembly
+from solver.datagen.labeling import label_assembly
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    RigidBody,
+)
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "COMPLEXITY_RANGES",
+    "AxisStrategy",
+    "ComplexityTier",
+    "SyntheticAssemblyGenerator",
+]
+
+# ---------------------------------------------------------------------------
+# Complexity tiers — ranges use exclusive upper bound for rng.integers()
+# ---------------------------------------------------------------------------
+
+ComplexityTier = Literal["simple", "medium", "complex"]
+
+COMPLEXITY_RANGES: dict[str, tuple[int, int]] = {
+    "simple": (2, 6),
+    "medium": (6, 16),
+    "complex": (16, 51),
+}
+
+# ---------------------------------------------------------------------------
+# Axis sampling strategies
+# ---------------------------------------------------------------------------
+
+AxisStrategy = Literal["cardinal", "random", "near_parallel"]
+
+
+class SyntheticAssemblyGenerator:
+    """Generates assembly graphs with known minimal constraint sets.
+
+    Uses the pebble game to incrementally build assemblies, tracking
+    exactly which constraints are independent at each step. This produces
+    labeled training data: (assembly_graph, constraint_set, labels).
+
+    Labels per constraint:
+        - independent: bool (does this constraint remove a DOF?)
+        - redundant: bool (is this constraint overconstrained?)
+        - minimal_set: bool (part of a minimal rigidity basis?)
+    """
+
+    def __init__(self, seed: int = 42) -> None:
+        self.rng = np.random.default_rng(seed)
+
+    # ------------------------------------------------------------------
+    # Private helpers
+    # ------------------------------------------------------------------
+
+    def _random_position(self, scale: float = 5.0) -> np.ndarray:
+        """Generate random 3D position within [-scale, scale] cube."""
+        return self.rng.uniform(-scale, scale, size=3)
+
+    def _random_axis(self) -> np.ndarray:
+        """Generate random normalized 3D axis."""
+        axis = self.rng.standard_normal(3)
+        axis /= np.linalg.norm(axis)
+        return axis
+
+    def _random_orientation(self) -> np.ndarray:
+        """Generate a random 3x3 rotation matrix."""
+        mat: np.ndarray = Rotation.random(random_state=self.rng).as_matrix()
+        return mat
+
+    def _cardinal_axis(self) -> np.ndarray:
+        """Pick uniformly from the six signed cardinal directions."""
+        axes = np.array(
+            [
+                [1, 0, 0],
+                [-1, 0, 0],
+                [0, 1, 0],
+                [0, -1, 0],
+                [0, 0, 1],
+                [0, 0, -1],
+            ],
+            dtype=float,
+        )
+        result: np.ndarray = axes[int(self.rng.integers(6))]
+        return result
+
+    def _near_parallel_axis(
+        self,
+        base_axis: np.ndarray,
+        perturbation_scale: float = 0.05,
+    ) -> np.ndarray:
+        """Return *base_axis* with a small random perturbation, re-normalized."""
+        perturbed = base_axis + self.rng.standard_normal(3) * perturbation_scale
+        return perturbed / np.linalg.norm(perturbed)
+
+    def _sample_axis(self, strategy: AxisStrategy = "random") -> np.ndarray:
+        """Sample a joint axis using the specified strategy."""
+        if strategy == "cardinal":
+            return self._cardinal_axis()
+        if strategy == "near_parallel":
+            return self._near_parallel_axis(np.array([0.0, 0.0, 1.0]))
+        return self._random_axis()
+
+    def _resolve_axis(
+        self,
+        strategy: AxisStrategy,
+        parallel_axis_prob: float,
+        shared_axis: np.ndarray | None,
+    ) -> tuple[np.ndarray, np.ndarray | None]:
+        """Return (axis_for_this_joint, shared_axis_to_propagate).
+
+        On the first call where *shared_axis* is ``None`` and parallel
+        injection triggers, a base axis is chosen and returned as
+        *shared_axis* for subsequent calls.
+        """
+        if shared_axis is not None:
+            return self._near_parallel_axis(shared_axis), shared_axis
+        if parallel_axis_prob > 0 and self.rng.random() < parallel_axis_prob:
+            base = self._sample_axis(strategy)
+            return base.copy(), base
+        return self._sample_axis(strategy), None
+
+    def _select_joint_type(
+        self,
+        joint_types: JointType | list[JointType],
+    ) -> JointType:
+        """Select a joint type from a single type or list."""
+        if isinstance(joint_types, list):
+            idx = int(self.rng.integers(0, len(joint_types)))
+            return joint_types[idx]
+        return joint_types
+
+    def _create_joint(
+        self,
+        joint_id: int,
+        body_a_id: int,
+        body_b_id: int,
+        pos_a: np.ndarray,
+        pos_b: np.ndarray,
+        joint_type: JointType,
+        *,
+        axis: np.ndarray | None = None,
+        orient_a: np.ndarray | None = None,
+        orient_b: np.ndarray | None = None,
+    ) -> Joint:
+        """Create a joint between two bodies.
+
+        When orientations are provided, anchor points are offset from
+        each body's center along a random local direction rotated into
+        world frame, rather than placed at the midpoint.
+        """
+        if orient_a is not None and orient_b is not None:
+            dist = max(float(np.linalg.norm(pos_b - pos_a)), 0.1)
+            offset_scale = dist * 0.2
+            local_a = self.rng.standard_normal(3) * offset_scale
+            local_b = self.rng.standard_normal(3) * offset_scale
+            anchor_a = pos_a + orient_a @ local_a
+            anchor_b = pos_b + orient_b @ local_b
+        else:
+            anchor = (pos_a + pos_b) / 2.0
+            anchor_a = anchor
+            anchor_b = anchor
+
+        return Joint(
+            joint_id=joint_id,
+            body_a=body_a_id,
+            body_b=body_b_id,
+            joint_type=joint_type,
+            anchor_a=anchor_a,
+            anchor_b=anchor_b,
+            axis=axis if axis is not None else self._random_axis(),
+        )
+
+    # ------------------------------------------------------------------
+    # Original generators (chain / rigid / overconstrained)
+    # ------------------------------------------------------------------
+
+    def generate_chain_assembly(
+        self,
+        n_bodies: int,
+        joint_type: JointType = JointType.REVOLUTE,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate a serial kinematic chain.
+
+        Simple but useful: each body connects to the next with the
+        specified joint type. Results in an underconstrained assembly
+        (serial chain is never rigid without closing loops).
+        """
+        bodies = []
+        joints = []
+
+        for i in range(n_bodies):
+            pos = np.array([i * 2.0, 0.0, 0.0])
+            bodies.append(
+                RigidBody(
+                    body_id=i,
+                    position=pos,
+                    orientation=self._random_orientation(),
+                )
+            )
+
+        shared_axis: np.ndarray | None = None
+        for i in range(n_bodies - 1):
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    i,
+                    i,
+                    i + 1,
+                    bodies[i].position,
+                    bodies[i + 1].position,
+                    joint_type,
+                    axis=axis,
+                    orient_a=bodies[i].orientation,
+                    orient_b=bodies[i + 1].orientation,
+                )
+            )
+
+        analysis = analyze_assembly(
+            bodies,
+            joints,
+            ground_body=0 if grounded else None,
+        )
+        return bodies, joints, analysis
+
+    def generate_rigid_assembly(
+        self,
+        n_bodies: int,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate a minimally rigid assembly by adding joints until rigid.
+
+        Strategy: start with fixed joints on a spanning tree (guarantees
+        rigidity), then randomly relax some to weaker joint types while
+        maintaining rigidity via the pebble game check.
+        """
+        bodies = []
+        for i in range(n_bodies):
+            bodies.append(
+                RigidBody(
+                    body_id=i,
+                    position=self._random_position(),
+                    orientation=self._random_orientation(),
+                )
+            )
+
+        # Build spanning tree with fixed joints (overconstrained)
+        joints: list[Joint] = []
+        shared_axis: np.ndarray | None = None
+        for i in range(1, n_bodies):
+            parent = int(self.rng.integers(0, i))
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    i - 1,
+                    parent,
+                    i,
+                    bodies[parent].position,
+                    bodies[i].position,
+                    JointType.FIXED,
+                    axis=axis,
+                    orient_a=bodies[parent].orientation,
+                    orient_b=bodies[i].orientation,
+                )
+            )
+
+        # Try relaxing joints to weaker types while maintaining rigidity
+        weaker_types = [
+            JointType.REVOLUTE,
+            JointType.CYLINDRICAL,
+            JointType.BALL,
+        ]
+
+        ground = 0 if grounded else None
+        for idx in self.rng.permutation(len(joints)):
+            original_type = joints[idx].joint_type
+            for candidate in weaker_types:
+                joints[idx].joint_type = candidate
+                analysis = analyze_assembly(bodies, joints, ground_body=ground)
+                if analysis.is_rigid:
+                    break  # Keep the weaker type
+            else:
+                joints[idx].joint_type = original_type
+
+        analysis = analyze_assembly(bodies, joints, ground_body=ground)
+        return bodies, joints, analysis
+
+    def generate_overconstrained_assembly(
+        self,
+        n_bodies: int,
+        extra_joints: int = 2,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate an assembly with known redundant constraints.
+
+        Starts with a rigid assembly, then adds extra joints that
+        the pebble game will flag as redundant.
+        """
+        bodies, joints, _ = self.generate_rigid_assembly(
+            n_bodies,
+            grounded=grounded,
+            axis_strategy=axis_strategy,
+            parallel_axis_prob=parallel_axis_prob,
+        )
+
+        joint_id = len(joints)
+        shared_axis: np.ndarray | None = None
+        for _ in range(extra_joints):
+            a, b = self.rng.choice(n_bodies, size=2, replace=False)
+            _overcon_types = [
+                JointType.REVOLUTE,
+                JointType.FIXED,
+                JointType.BALL,
+            ]
+            jtype = _overcon_types[int(self.rng.integers(len(_overcon_types)))]
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    joint_id,
+                    int(a),
+                    int(b),
+                    bodies[int(a)].position,
+                    bodies[int(b)].position,
+                    jtype,
+                    axis=axis,
+                    orient_a=bodies[int(a)].orientation,
+                    orient_b=bodies[int(b)].orientation,
+                )
+            )
+            joint_id += 1
+
+        ground = 0 if grounded else None
+        analysis = analyze_assembly(bodies, joints, ground_body=ground)
+        return bodies, joints, analysis
+
+    # ------------------------------------------------------------------
+    # New topology generators
+    # ------------------------------------------------------------------
+
+    def generate_tree_assembly(
+        self,
+        n_bodies: int,
+        joint_types: JointType | list[JointType] = JointType.REVOLUTE,
+        branching_factor: int = 3,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate a random tree topology with configurable branching.
+
+        Creates a tree where each body can have up to *branching_factor*
+        children. Different branches can use different joint types if a
+        list is provided. Always underconstrained (no closed loops).
+
+        Args:
+            n_bodies: Total bodies (root + children).
+            joint_types: Single type or list to sample from per joint.
+            branching_factor: Max children per parent (1-5 recommended).
+        """
+        bodies: list[RigidBody] = [
+            RigidBody(
+                body_id=0,
+                position=np.zeros(3),
+                orientation=self._random_orientation(),
+            )
+        ]
+        joints: list[Joint] = []
+
+        available_parents = [0]
+        next_id = 1
+        joint_id = 0
+        shared_axis: np.ndarray | None = None
+
+        while next_id < n_bodies and available_parents:
+            pidx = int(self.rng.integers(0, len(available_parents)))
+            parent_id = available_parents[pidx]
+            parent_pos = bodies[parent_id].position
+
+            max_children = min(branching_factor, n_bodies - next_id)
+            n_children = int(self.rng.integers(1, max_children + 1))
+
+            for _ in range(n_children):
+                direction = self._random_axis()
+                distance = self.rng.uniform(1.5, 3.0)
+                child_pos = parent_pos + direction * distance
+                child_orient = self._random_orientation()
+
+                bodies.append(
+                    RigidBody(
+                        body_id=next_id,
+                        position=child_pos,
+                        orientation=child_orient,
+                    )
+                )
+                jtype = self._select_joint_type(joint_types)
+                axis, shared_axis = self._resolve_axis(
+                    axis_strategy,
+                    parallel_axis_prob,
+                    shared_axis,
+                )
+                joints.append(
+                    self._create_joint(
+                        joint_id,
+                        parent_id,
+                        next_id,
+                        parent_pos,
+                        child_pos,
+                        jtype,
+                        axis=axis,
+                        orient_a=bodies[parent_id].orientation,
+                        orient_b=child_orient,
+                    )
+                )
+
+                available_parents.append(next_id)
+                next_id += 1
+                joint_id += 1
+                if next_id >= n_bodies:
+                    break
+
+            # Retire parent if it reached branching limit or randomly
+            if n_children >= branching_factor or self.rng.random() < 0.3:
+                available_parents.pop(pidx)
+
+        analysis = analyze_assembly(
+            bodies,
+            joints,
+            ground_body=0 if grounded else None,
+        )
+        return bodies, joints, analysis
+
+    def generate_loop_assembly(
+        self,
+        n_bodies: int,
+        joint_types: JointType | list[JointType] = JointType.REVOLUTE,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate a single closed loop (ring) of bodies.
+
+        The closing constraint introduces redundancy, making this
+        useful for generating overconstrained training data.
+
+        Args:
+            n_bodies: Bodies in the ring (>= 3).
+            joint_types: Single type or list to sample from per joint.
+
+        Raises:
+            ValueError: If *n_bodies* < 3.
+        """
+        if n_bodies < 3:
+            msg = "Loop assembly requires at least 3 bodies"
+            raise ValueError(msg)
+
+        bodies: list[RigidBody] = []
+        joints: list[Joint] = []
+
+        base_radius = max(2.0, n_bodies * 0.4)
+        for i in range(n_bodies):
+            angle = 2 * np.pi * i / n_bodies
+            radius = base_radius + self.rng.uniform(-0.5, 0.5)
+            x = radius * np.cos(angle)
+            y = radius * np.sin(angle)
+            z = float(self.rng.uniform(-0.2, 0.2))
+            bodies.append(
+                RigidBody(
+                    body_id=i,
+                    position=np.array([x, y, z]),
+                    orientation=self._random_orientation(),
+                )
+            )
+
+        shared_axis: np.ndarray | None = None
+        for i in range(n_bodies):
+            next_i = (i + 1) % n_bodies
+            jtype = self._select_joint_type(joint_types)
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    i,
+                    i,
+                    next_i,
+                    bodies[i].position,
+                    bodies[next_i].position,
+                    jtype,
+                    axis=axis,
+                    orient_a=bodies[i].orientation,
+                    orient_b=bodies[next_i].orientation,
+                )
+            )
+
+        analysis = analyze_assembly(
+            bodies,
+            joints,
+            ground_body=0 if grounded else None,
+        )
+        return bodies, joints, analysis
+
+    def generate_star_assembly(
+        self,
+        n_bodies: int,
+        joint_types: JointType | list[JointType] = JointType.REVOLUTE,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate a star topology with central hub and satellites.
+
+        Body 0 is the hub; all other bodies connect directly to it.
+        Underconstrained because there are no inter-satellite connections.
+
+        Args:
+            n_bodies: Total bodies including hub (>= 2).
+            joint_types: Single type or list to sample from per joint.
+
+        Raises:
+            ValueError: If *n_bodies* < 2.
+        """
+        if n_bodies < 2:
+            msg = "Star assembly requires at least 2 bodies"
+            raise ValueError(msg)
+
+        hub_orient = self._random_orientation()
+        bodies: list[RigidBody] = [
+            RigidBody(
+                body_id=0,
+                position=np.zeros(3),
+                orientation=hub_orient,
+            )
+        ]
+        joints: list[Joint] = []
+
+        shared_axis: np.ndarray | None = None
+        for i in range(1, n_bodies):
+            direction = self._random_axis()
+            distance = self.rng.uniform(2.0, 5.0)
+            pos = direction * distance
+            sat_orient = self._random_orientation()
+            bodies.append(RigidBody(body_id=i, position=pos, orientation=sat_orient))
+
+            jtype = self._select_joint_type(joint_types)
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    i - 1,
+                    0,
+                    i,
+                    np.zeros(3),
+                    pos,
+                    jtype,
+                    axis=axis,
+                    orient_a=hub_orient,
+                    orient_b=sat_orient,
+                )
+            )
+
+        analysis = analyze_assembly(
+            bodies,
+            joints,
+            ground_body=0 if grounded else None,
+        )
+        return bodies, joints, analysis
+
+    def generate_mixed_assembly(
+        self,
+        n_bodies: int,
+        joint_types: JointType | list[JointType] = JointType.REVOLUTE,
+        edge_density: float = 0.3,
+        *,
+        grounded: bool = True,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+    ) -> tuple[list[RigidBody], list[Joint], ConstraintAnalysis]:
+        """Generate a mixed topology combining tree and loop elements.
+
+        Builds a spanning tree for connectivity, then adds extra edges
+        based on *edge_density* to create loops and redundancy.
+
+        Args:
+            n_bodies: Number of bodies.
+            joint_types: Single type or list to sample from per joint.
+            edge_density: Fraction of non-tree edges to add (0.0-1.0).
+
+        Raises:
+            ValueError: If *edge_density* not in [0.0, 1.0].
+        """
+        if not 0.0 <= edge_density <= 1.0:
+            msg = "edge_density must be in [0.0, 1.0]"
+            raise ValueError(msg)
+
+        bodies: list[RigidBody] = []
+        joints: list[Joint] = []
+
+        for i in range(n_bodies):
+            bodies.append(
+                RigidBody(
+                    body_id=i,
+                    position=self._random_position(),
+                    orientation=self._random_orientation(),
+                )
+            )
+
+        # Phase 1: spanning tree
+        joint_id = 0
+        existing_edges: set[frozenset[int]] = set()
+        shared_axis: np.ndarray | None = None
+        for i in range(1, n_bodies):
+            parent = int(self.rng.integers(0, i))
+            jtype = self._select_joint_type(joint_types)
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    joint_id,
+                    parent,
+                    i,
+                    bodies[parent].position,
+                    bodies[i].position,
+                    jtype,
+                    axis=axis,
+                    orient_a=bodies[parent].orientation,
+                    orient_b=bodies[i].orientation,
+                )
+            )
+            existing_edges.add(frozenset([parent, i]))
+            joint_id += 1
+
+        # Phase 2: extra edges based on density
+        candidates: list[tuple[int, int]] = []
+        for i in range(n_bodies):
+            for j in range(i + 1, n_bodies):
+                if frozenset([i, j]) not in existing_edges:
+                    candidates.append((i, j))
+
+        n_extra = int(edge_density * len(candidates))
+        self.rng.shuffle(candidates)
+
+        for a, b in candidates[:n_extra]:
+            jtype = self._select_joint_type(joint_types)
+            axis, shared_axis = self._resolve_axis(
+                axis_strategy,
+                parallel_axis_prob,
+                shared_axis,
+            )
+            joints.append(
+                self._create_joint(
+                    joint_id,
+                    a,
+                    b,
+                    bodies[a].position,
+                    bodies[b].position,
+                    jtype,
+                    axis=axis,
+                    orient_a=bodies[a].orientation,
+                    orient_b=bodies[b].orientation,
+                )
+            )
+            joint_id += 1
+
+        analysis = analyze_assembly(
+            bodies,
+            joints,
+            ground_body=0 if grounded else None,
+        )
+        return bodies, joints, analysis
+
+    # ------------------------------------------------------------------
+    # Batch generation
+    # ------------------------------------------------------------------
+
+    def generate_training_batch(
+        self,
+        batch_size: int = 100,
+        n_bodies_range: tuple[int, int] | None = None,
+        complexity_tier: ComplexityTier | None = None,
+        *,
+        axis_strategy: AxisStrategy = "random",
+        parallel_axis_prob: float = 0.0,
+        grounded_ratio: float = 1.0,
+    ) -> list[dict[str, Any]]:
+        """Generate a batch of labeled training examples.
+
+        Each example contains body positions, joint descriptions,
+        per-joint independence labels, and assembly-level classification.
+
+        Args:
+            batch_size: Number of assemblies to generate.
+            n_bodies_range: ``(min, max_exclusive)`` body count.
+                Overridden by *complexity_tier* when both are given.
+            complexity_tier: Predefined range (``"simple"`` / ``"medium"``
+                / ``"complex"``).  Overrides *n_bodies_range*.
+            axis_strategy: Axis sampling strategy for joint axes.
+            parallel_axis_prob: Probability of parallel axis injection.
+            grounded_ratio: Fraction of examples that are grounded.
+        """
+        if complexity_tier is not None:
+            n_bodies_range = COMPLEXITY_RANGES[complexity_tier]
+        elif n_bodies_range is None:
+            n_bodies_range = (3, 8)
+
+        _joint_pool = [
+            JointType.REVOLUTE,
+            JointType.BALL,
+            JointType.CYLINDRICAL,
+            JointType.FIXED,
+        ]
+
+        geo_kw: dict[str, Any] = {
+            "axis_strategy": axis_strategy,
+            "parallel_axis_prob": parallel_axis_prob,
+        }
+
+        examples: list[dict[str, Any]] = []
+
+        for i in range(batch_size):
+            n = int(self.rng.integers(*n_bodies_range))
+            gen_idx = int(self.rng.integers(7))
+            grounded = bool(self.rng.random() < grounded_ratio)
+
+            if gen_idx == 0:
+                _chain_types = [
+                    JointType.REVOLUTE,
+                    JointType.BALL,
+                    JointType.CYLINDRICAL,
+                ]
+                jtype = _chain_types[int(self.rng.integers(len(_chain_types)))]
+                bodies, joints, analysis = self.generate_chain_assembly(
+                    n,
+                    jtype,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "chain"
+            elif gen_idx == 1:
+                bodies, joints, analysis = self.generate_rigid_assembly(
+                    n,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "rigid"
+            elif gen_idx == 2:
+                extra = int(self.rng.integers(1, 4))
+                bodies, joints, analysis = self.generate_overconstrained_assembly(
+                    n,
+                    extra,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "overconstrained"
+            elif gen_idx == 3:
+                branching = int(self.rng.integers(2, 5))
+                bodies, joints, analysis = self.generate_tree_assembly(
+                    n,
+                    _joint_pool,
+                    branching,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "tree"
+            elif gen_idx == 4:
+                n = max(n, 3)
+                bodies, joints, analysis = self.generate_loop_assembly(
+                    n,
+                    _joint_pool,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "loop"
+            elif gen_idx == 5:
+                n = max(n, 2)
+                bodies, joints, analysis = self.generate_star_assembly(
+                    n,
+                    _joint_pool,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "star"
+            else:
+                density = float(self.rng.uniform(0.2, 0.5))
+                bodies, joints, analysis = self.generate_mixed_assembly(
+                    n,
+                    _joint_pool,
+                    density,
+                    grounded=grounded,
+                    **geo_kw,
+                )
+                gen_name = "mixed"
+
+            # Produce ground truth labels (includes ConstraintAnalysis)
+            ground = 0 if grounded else None
+            labels = label_assembly(bodies, joints, ground_body=ground)
+            analysis = labels.analysis
+
+            # Build per-joint labels from edge results
+            joint_labels: dict[int, dict[str, int]] = {}
+            for result in analysis.per_edge_results:
+                jid = result["joint_id"]
+                if jid not in joint_labels:
+                    joint_labels[jid] = {
+                        "independent_constraints": 0,
+                        "redundant_constraints": 0,
+                        "total_constraints": 0,
+                    }
+                joint_labels[jid]["total_constraints"] += 1
+                if result["independent"]:
+                    joint_labels[jid]["independent_constraints"] += 1
+                else:
+                    joint_labels[jid]["redundant_constraints"] += 1
+
+            examples.append(
+                {
+                    "example_id": i,
+                    "generator_type": gen_name,
+                    "grounded": grounded,
+                    "n_bodies": len(bodies),
+                    "n_joints": len(joints),
+                    "body_positions": [b.position.tolist() for b in bodies],
+                    "body_orientations": [b.orientation.tolist() for b in bodies],
+                    "joints": [
+                        {
+                            "joint_id": j.joint_id,
+                            "body_a": j.body_a,
+                            "body_b": j.body_b,
+                            "type": j.joint_type.name,
+                            "axis": j.axis.tolist(),
+                        }
+                        for j in joints
+                    ],
+                    "joint_labels": joint_labels,
+                    "labels": labels.to_dict(),
+                    "assembly_classification": (analysis.combinatorial_classification),
+                    "is_rigid": analysis.is_rigid,
+                    "is_minimally_rigid": analysis.is_minimally_rigid,
+                    "internal_dof": analysis.jacobian_internal_dof,
+                    "geometric_degeneracies": (analysis.geometric_degeneracies),
+                }
+            )
+
+        return examples

solver/datagen/jacobian.py

@@ -0,0 +1,517 @@
+"""Numerical Jacobian rank verification for assembly constraint analysis.
+
+Builds the constraint Jacobian matrix and analyzes its numerical rank
+to detect geometric degeneracies that the combinatorial pebble game
+cannot identify (e.g., parallel revolute axes creating hidden dependencies).
+
+References:
+    - Chappuis, "Constraints Derivation for Rigid Body Simulation in 3D"
+"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+from solver.datagen.types import Joint, JointType, RigidBody
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = ["JacobianVerifier"]
+
+
+class JacobianVerifier:
+    """Builds and analyzes the constraint Jacobian for numerical rank check.
+
+    The pebble game gives a combinatorial *necessary* condition for
+    rigidity. However, geometric special cases (e.g., all revolute axes
+    parallel, creating a hidden dependency) require numerical verification.
+
+    For each joint, we construct the constraint Jacobian rows that map
+    the 6n-dimensional generalized velocity vector to the constraint
+    violation rates. The rank of this Jacobian equals the number of
+    truly independent constraints.
+
+    The generalized velocity vector for n bodies is::
+
+        v = [v1_x, v1_y, v1_z, w1_x, w1_y, w1_z, ..., vn_x, ..., wn_z]
+
+    Each scalar constraint C_i contributes one row to J such that::
+
+        dC_i/dt = J_i @ v = 0
+    """
+
+    def __init__(self, bodies: list[RigidBody]) -> None:
+        self.bodies = {b.body_id: b for b in bodies}
+        self.body_index = {b.body_id: i for i, b in enumerate(bodies)}
+        self.n_bodies = len(bodies)
+        self.jacobian_rows: list[np.ndarray] = []
+        self.row_labels: list[dict[str, Any]] = []
+
+    def _body_cols(self, body_id: int) -> tuple[int, int]:
+        """Return the column range [start, end) for a body in J."""
+        idx = self.body_index[body_id]
+        return idx * 6, (idx + 1) * 6
+
+    def add_joint_constraints(self, joint: Joint) -> int:
+        """Add Jacobian rows for all scalar constraints of a joint.
+
+        Returns the number of rows added.
+        """
+        builder = {
+            JointType.FIXED: self._build_fixed,
+            JointType.REVOLUTE: self._build_revolute,
+            JointType.CYLINDRICAL: self._build_cylindrical,
+            JointType.SLIDER: self._build_slider,
+            JointType.BALL: self._build_ball,
+            JointType.PLANAR: self._build_planar,
+            JointType.DISTANCE: self._build_distance,
+            JointType.PARALLEL: self._build_parallel,
+            JointType.PERPENDICULAR: self._build_perpendicular,
+            JointType.UNIVERSAL: self._build_universal,
+            JointType.SCREW: self._build_screw,
+        }
+
+        rows_before = len(self.jacobian_rows)
+        builder[joint.joint_type](joint)
+        return len(self.jacobian_rows) - rows_before
+
+    def _make_row(self) -> np.ndarray:
+        """Create a zero row of width 6*n_bodies."""
+        return np.zeros(6 * self.n_bodies)
+
+    def _skew(self, v: np.ndarray) -> np.ndarray:
+        """Skew-symmetric matrix for cross product: ``skew(v) @ w = v x w``."""
+        return np.array(
+            [
+                [0, -v[2], v[1]],
+                [v[2], 0, -v[0]],
+                [-v[1], v[0], 0],
+            ]
+        )
+
+    # --- Ball-and-socket (spherical) joint: 3 translation constraints ---
+
+    def _build_ball(self, joint: Joint) -> None:
+        """Ball joint: coincident point constraint.
+
+        ``C_trans = (x_b + R_b @ r_b) - (x_a + R_a @ r_a) = 0``
+        (3 equations)
+
+        Jacobian rows (for each of x, y, z):
+            body_a linear:  -I
+            body_a angular: +skew(R_a @ r_a)
+            body_b linear:  +I
+            body_b angular: -skew(R_b @ r_b)
+        """
+        # Use anchor positions directly as world-frame offsets
+        r_a = joint.anchor_a - self.bodies[joint.body_a].position
+        r_b = joint.anchor_b - self.bodies[joint.body_b].position
+
+        col_a_start, col_a_end = self._body_cols(joint.body_a)
+        col_b_start, col_b_end = self._body_cols(joint.body_b)
+
+        for axis_idx in range(3):
+            row = self._make_row()
+            e = np.zeros(3)
+            e[axis_idx] = 1.0
+
+            row[col_a_start : col_a_start + 3] = -e
+            row[col_a_start + 3 : col_a_end] = np.cross(r_a, e)
+
+            row[col_b_start : col_b_start + 3] = e
+            row[col_b_start + 3 : col_b_end] = -np.cross(r_b, e)
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "ball_translation",
+                    "axis": axis_idx,
+                }
+            )
+
+    # --- Fixed joint: 3 translation + 3 rotation constraints ---
+
+    def _build_fixed(self, joint: Joint) -> None:
+        """Fixed joint = ball joint + locked rotation.
+
+        Translation part: same as ball joint (3 rows).
+        Rotation part: relative angular velocity must be zero (3 rows).
+        """
+        self._build_ball(joint)
+
+        col_a_start, _ = self._body_cols(joint.body_a)
+        col_b_start, _ = self._body_cols(joint.body_b)
+
+        for axis_idx in range(3):
+            row = self._make_row()
+            row[col_a_start + 3 + axis_idx] = -1.0
+            row[col_b_start + 3 + axis_idx] = 1.0
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "fixed_rotation",
+                    "axis": axis_idx,
+                }
+            )
+
+    # --- Revolute (hinge) joint: 3 translation + 2 rotation constraints ---
+
+    def _build_revolute(self, joint: Joint) -> None:
+        """Revolute joint: rotation only about one axis.
+
+        Translation: same as ball (3 rows).
+        Rotation: relative angular velocity must be parallel to hinge axis.
+        """
+        self._build_ball(joint)
+
+        axis = joint.axis / np.linalg.norm(joint.axis)
+        t1, t2 = self._perpendicular_pair(axis)
+
+        col_a_start, _ = self._body_cols(joint.body_a)
+        col_b_start, _ = self._body_cols(joint.body_b)
+
+        for i, t in enumerate((t1, t2)):
+            row = self._make_row()
+            row[col_a_start + 3 : col_a_start + 6] = -t
+            row[col_b_start + 3 : col_b_start + 6] = t
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "revolute_rotation",
+                    "perp_axis": i,
+                }
+            )
+
+    # --- Cylindrical joint: 2 translation + 2 rotation constraints ---
+
+    def _build_cylindrical(self, joint: Joint) -> None:
+        """Cylindrical joint: allows rotation + translation along one axis.
+
+        Translation: constrain motion perpendicular to axis (2 rows).
+        Rotation: constrain rotation perpendicular to axis (2 rows).
+        """
+        axis = joint.axis / np.linalg.norm(joint.axis)
+        t1, t2 = self._perpendicular_pair(axis)
+
+        r_a = joint.anchor_a - self.bodies[joint.body_a].position
+        r_b = joint.anchor_b - self.bodies[joint.body_b].position
+
+        col_a_start, col_a_end = self._body_cols(joint.body_a)
+        col_b_start, col_b_end = self._body_cols(joint.body_b)
+
+        for i, t in enumerate((t1, t2)):
+            row = self._make_row()
+            row[col_a_start : col_a_start + 3] = -t
+            row[col_a_start + 3 : col_a_end] = np.cross(r_a, t)
+            row[col_b_start : col_b_start + 3] = t
+            row[col_b_start + 3 : col_b_end] = -np.cross(r_b, t)
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "cylindrical_translation",
+                    "perp_axis": i,
+                }
+            )
+
+        for i, t in enumerate((t1, t2)):
+            row = self._make_row()
+            row[col_a_start + 3 : col_a_start + 6] = -t
+            row[col_b_start + 3 : col_b_start + 6] = t
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "cylindrical_rotation",
+                    "perp_axis": i,
+                }
+            )
+
+    # --- Slider (prismatic) joint: 2 translation + 3 rotation constraints ---
+
+    def _build_slider(self, joint: Joint) -> None:
+        """Slider/prismatic joint: translation along one axis only.
+
+        Translation: perpendicular translation constrained (2 rows).
+        Rotation: all relative rotation constrained (3 rows).
+        """
+        axis = joint.axis / np.linalg.norm(joint.axis)
+        t1, t2 = self._perpendicular_pair(axis)
+
+        r_a = joint.anchor_a - self.bodies[joint.body_a].position
+        r_b = joint.anchor_b - self.bodies[joint.body_b].position
+
+        col_a_start, col_a_end = self._body_cols(joint.body_a)
+        col_b_start, col_b_end = self._body_cols(joint.body_b)
+
+        for i, t in enumerate((t1, t2)):
+            row = self._make_row()
+            row[col_a_start : col_a_start + 3] = -t
+            row[col_a_start + 3 : col_a_end] = np.cross(r_a, t)
+            row[col_b_start : col_b_start + 3] = t
+            row[col_b_start + 3 : col_b_end] = -np.cross(r_b, t)
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "slider_translation",
+                    "perp_axis": i,
+                }
+            )
+
+        for axis_idx in range(3):
+            row = self._make_row()
+            row[col_a_start + 3 + axis_idx] = -1.0
+            row[col_b_start + 3 + axis_idx] = 1.0
+
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "slider_rotation",
+                    "axis": axis_idx,
+                }
+            )
+
+    # --- Planar joint: 1 translation + 2 rotation constraints ---
+
+    def _build_planar(self, joint: Joint) -> None:
+        """Planar joint: constrains to a plane.
+
+        Translation: motion along plane normal constrained (1 row).
+        Rotation: rotation about axes in the plane constrained (2 rows).
+        """
+        normal = joint.axis / np.linalg.norm(joint.axis)
+        t1, t2 = self._perpendicular_pair(normal)
+
+        r_a = joint.anchor_a - self.bodies[joint.body_a].position
+        r_b = joint.anchor_b - self.bodies[joint.body_b].position
+
+        col_a_start, col_a_end = self._body_cols(joint.body_a)
+        col_b_start, col_b_end = self._body_cols(joint.body_b)
+
+        row = self._make_row()
+        row[col_a_start : col_a_start + 3] = -normal
+        row[col_a_start + 3 : col_a_end] = np.cross(r_a, normal)
+        row[col_b_start : col_b_start + 3] = normal
+        row[col_b_start + 3 : col_b_end] = -np.cross(r_b, normal)
+        self.jacobian_rows.append(row)
+        self.row_labels.append(
+            {
+                "joint_id": joint.joint_id,
+                "type": "planar_translation",
+            }
+        )
+
+        for i, t in enumerate((t1, t2)):
+            row = self._make_row()
+            row[col_a_start + 3 : col_a_start + 6] = -t
+            row[col_b_start + 3 : col_b_start + 6] = t
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "planar_rotation",
+                    "perp_axis": i,
+                }
+            )
+
+    # --- Distance constraint: 1 scalar ---
+
+    def _build_distance(self, joint: Joint) -> None:
+        """Distance constraint: ``||p_b - p_a|| = d``.
+
+        Single row: ``direction . (v_b + w_b x r_b - v_a - w_a x r_a) = 0``
+        where ``direction = normalized(p_b - p_a)``.
+        """
+        p_a = joint.anchor_a
+        p_b = joint.anchor_b
+        diff = p_b - p_a
+        dist = np.linalg.norm(diff)
+        direction = np.array([1.0, 0.0, 0.0]) if dist < 1e-12 else diff / dist
+
+        r_a = joint.anchor_a - self.bodies[joint.body_a].position
+        r_b = joint.anchor_b - self.bodies[joint.body_b].position
+
+        col_a_start, col_a_end = self._body_cols(joint.body_a)
+        col_b_start, col_b_end = self._body_cols(joint.body_b)
+
+        row = self._make_row()
+        row[col_a_start : col_a_start + 3] = -direction
+        row[col_a_start + 3 : col_a_end] = np.cross(r_a, direction)
+        row[col_b_start : col_b_start + 3] = direction
+        row[col_b_start + 3 : col_b_end] = -np.cross(r_b, direction)
+
+        self.jacobian_rows.append(row)
+        self.row_labels.append(
+            {
+                "joint_id": joint.joint_id,
+                "type": "distance",
+            }
+        )
+
+    # --- Parallel constraint: 3 rotation constraints ---
+
+    def _build_parallel(self, joint: Joint) -> None:
+        """Parallel: all relative rotation constrained (same as fixed rotation).
+
+        In practice only 2 of 3 are independent for a single axis, but
+        we emit 3 and let the rank check sort it out.
+        """
+        col_a_start, _ = self._body_cols(joint.body_a)
+        col_b_start, _ = self._body_cols(joint.body_b)
+
+        for axis_idx in range(3):
+            row = self._make_row()
+            row[col_a_start + 3 + axis_idx] = -1.0
+            row[col_b_start + 3 + axis_idx] = 1.0
+            self.jacobian_rows.append(row)
+            self.row_labels.append(
+                {
+                    "joint_id": joint.joint_id,
+                    "type": "parallel_rotation",
+                    "axis": axis_idx,
+                }
+            )
+
+    # --- Perpendicular constraint: 1 angular ---
+
+    def _build_perpendicular(self, joint: Joint) -> None:
+        """Perpendicular: single dot-product angular constraint."""
+        axis = joint.axis / np.linalg.norm(joint.axis)
+        col_a_start, _ = self._body_cols(joint.body_a)
+        col_b_start, _ = self._body_cols(joint.body_b)
+
+        row = self._make_row()
+        row[col_a_start + 3 : col_a_start + 6] = -axis
+        row[col_b_start + 3 : col_b_start + 6] = axis
+        self.jacobian_rows.append(row)
+        self.row_labels.append(
+            {
+                "joint_id": joint.joint_id,
+                "type": "perpendicular",
+            }
+        )
+
+    # --- Universal (Cardan) joint: 3 translation + 1 rotation ---
+
+    def _build_universal(self, joint: Joint) -> None:
+        """Universal joint: ball + one rotation constraint.
+
+        Allows rotation about two axes, constrains rotation about the third.
+        """
+        self._build_ball(joint)
+
+        axis = joint.axis / np.linalg.norm(joint.axis)
+        col_a_start, _ = self._body_cols(joint.body_a)
+        col_b_start, _ = self._body_cols(joint.body_b)
+
+        row = self._make_row()
+        row[col_a_start + 3 : col_a_start + 6] = -axis
+        row[col_b_start + 3 : col_b_start + 6] = axis
+        self.jacobian_rows.append(row)
+        self.row_labels.append(
+            {
+                "joint_id": joint.joint_id,
+                "type": "universal_rotation",
+            }
+        )
+
+    # --- Screw (helical) joint: 2 translation + 2 rotation + 1 coupled ---
+
+    def _build_screw(self, joint: Joint) -> None:
+        """Screw joint: coupled rotation-translation along axis.
+
+        Like cylindrical but with a coupling constraint:
+        ``v_axial - pitch * w_axial = 0``
+        """
+        self._build_cylindrical(joint)
+
+        axis = joint.axis / np.linalg.norm(joint.axis)
+        col_a_start, _ = self._body_cols(joint.body_a)
+        col_b_start, _ = self._body_cols(joint.body_b)
+
+        row = self._make_row()
+        row[col_a_start : col_a_start + 3] = -axis
+        row[col_b_start : col_b_start + 3] = axis
+        row[col_a_start + 3 : col_a_start + 6] = joint.pitch * axis
+        row[col_b_start + 3 : col_b_start + 6] = -joint.pitch * axis
+        self.jacobian_rows.append(row)
+        self.row_labels.append(
+            {
+                "joint_id": joint.joint_id,
+                "type": "screw_coupling",
+            }
+        )
+
+    # --- Utilities ---
+
+    def _perpendicular_pair(self, axis: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+        """Generate two unit vectors perpendicular to *axis* and each other."""
+        if abs(axis[0]) < 0.9:
+            t1 = np.cross(axis, np.array([1.0, 0, 0]))
+        else:
+            t1 = np.cross(axis, np.array([0, 1.0, 0]))
+        t1 /= np.linalg.norm(t1)
+        t2 = np.cross(axis, t1)
+        t2 /= np.linalg.norm(t2)
+        return t1, t2
+
+    def get_jacobian(self) -> np.ndarray:
+        """Return the full constraint Jacobian matrix."""
+        if not self.jacobian_rows:
+            return np.zeros((0, 6 * self.n_bodies))
+        return np.array(self.jacobian_rows)
+
+    def numerical_rank(self, tol: float = 1e-8) -> int:
+        """Compute the numerical rank of the constraint Jacobian via SVD.
+
+        This is the number of truly independent scalar constraints,
+        accounting for geometric degeneracies that the combinatorial
+        pebble game cannot detect.
+        """
+        j = self.get_jacobian()
+        if j.size == 0:
+            return 0
+        sv = np.linalg.svd(j, compute_uv=False)
+        return int(np.sum(sv > tol))
+
+    def find_dependencies(self, tol: float = 1e-8) -> list[int]:
+        """Identify which constraint rows are numerically dependent.
+
+        Returns indices of rows that can be removed without changing
+        the Jacobian's rank.
+        """
+        j = self.get_jacobian()
+        if j.size == 0:
+            return []
+
+        n_rows = j.shape[0]
+        dependent: list[int] = []
+
+        current = np.zeros((0, j.shape[1]))
+        current_rank = 0
+
+        for i in range(n_rows):
+            candidate = np.vstack([current, j[i : i + 1, :]]) if current.size else j[i : i + 1, :]
+            sv = np.linalg.svd(candidate, compute_uv=False)
+            new_rank = int(np.sum(sv > tol))
+
+            if new_rank > current_rank:
+                current = candidate
+                current_rank = new_rank
+            else:
+                dependent.append(i)
+
+        return dependent

solver/datagen/labeling.py

@@ -0,0 +1,394 @@
+"""Ground truth labeling pipeline for synthetic assemblies.
+
+Produces rich per-constraint, per-joint, per-body, and assembly-level
+labels by running both the pebble game and Jacobian verification and
+correlating their results.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+from solver.datagen.jacobian import JacobianVerifier
+from solver.datagen.pebble_game import PebbleGame3D
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    RigidBody,
+)
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = ["AssemblyLabels", "label_assembly"]
+
+_GROUND_ID = -1
+_SVD_TOL = 1e-8
+
+
+# ---------------------------------------------------------------------------
+# Label dataclasses
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class ConstraintLabel:
+    """Per scalar-constraint label combining both analysis methods."""
+
+    joint_id: int
+    constraint_idx: int
+    pebble_independent: bool
+    jacobian_independent: bool
+
+
+@dataclass
+class JointLabel:
+    """Aggregated constraint counts for a single joint."""
+
+    joint_id: int
+    independent_count: int
+    redundant_count: int
+    total: int
+
+
+@dataclass
+class BodyDofLabel:
+    """Per-body DOF signature from nullspace projection."""
+
+    body_id: int
+    translational_dof: int
+    rotational_dof: int
+
+
+@dataclass
+class AssemblyLabel:
+    """Assembly-wide summary label."""
+
+    classification: str
+    total_dof: int
+    redundant_count: int
+    is_rigid: bool
+    is_minimally_rigid: bool
+    has_degeneracy: bool
+
+
+@dataclass
+class AssemblyLabels:
+    """Complete ground truth labels for an assembly."""
+
+    per_constraint: list[ConstraintLabel]
+    per_joint: list[JointLabel]
+    per_body: list[BodyDofLabel]
+    assembly: AssemblyLabel
+    analysis: ConstraintAnalysis
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "per_constraint": [
+                {
+                    "joint_id": c.joint_id,
+                    "constraint_idx": c.constraint_idx,
+                    "pebble_independent": c.pebble_independent,
+                    "jacobian_independent": c.jacobian_independent,
+                }
+                for c in self.per_constraint
+            ],
+            "per_joint": [
+                {
+                    "joint_id": j.joint_id,
+                    "independent_count": j.independent_count,
+                    "redundant_count": j.redundant_count,
+                    "total": j.total,
+                }
+                for j in self.per_joint
+            ],
+            "per_body": [
+                {
+                    "body_id": b.body_id,
+                    "translational_dof": b.translational_dof,
+                    "rotational_dof": b.rotational_dof,
+                }
+                for b in self.per_body
+            ],
+            "assembly": {
+                "classification": self.assembly.classification,
+                "total_dof": self.assembly.total_dof,
+                "redundant_count": self.assembly.redundant_count,
+                "is_rigid": self.assembly.is_rigid,
+                "is_minimally_rigid": self.assembly.is_minimally_rigid,
+                "has_degeneracy": self.assembly.has_degeneracy,
+            },
+        }
+
+
+# ---------------------------------------------------------------------------
+# Per-body DOF from nullspace projection
+# ---------------------------------------------------------------------------
+
+
+def _compute_per_body_dof(
+    j_reduced: np.ndarray,
+    body_ids: list[int],
+    ground_body: int | None,
+    body_index: dict[int, int],
+) -> list[BodyDofLabel]:
+    """Compute translational and rotational DOF per body.
+
+    Uses SVD nullspace projection: for each body, extract its
+    translational (3 cols) and rotational (3 cols) components
+    from the nullspace basis and compute ranks.
+    """
+    # Build column index mapping for the reduced Jacobian
+    # (ground body columns have been removed)
+    col_map: dict[int, int] = {}
+    col_idx = 0
+    for bid in body_ids:
+        if bid == ground_body:
+            continue
+        col_map[bid] = col_idx
+        col_idx += 1
+
+    results: list[BodyDofLabel] = []
+
+    if j_reduced.size == 0:
+        # No constraints — every body is fully free
+        for bid in body_ids:
+            if bid == ground_body:
+                results.append(BodyDofLabel(body_id=bid, translational_dof=0, rotational_dof=0))
+            else:
+                results.append(BodyDofLabel(body_id=bid, translational_dof=3, rotational_dof=3))
+        return results
+
+    # Full SVD to get nullspace
+    _u, s, vh = np.linalg.svd(j_reduced, full_matrices=True)
+    rank = int(np.sum(s > _SVD_TOL))
+    n_cols = j_reduced.shape[1]
+
+    if rank >= n_cols:
+        # Fully constrained — no nullspace
+        for bid in body_ids:
+            results.append(BodyDofLabel(body_id=bid, translational_dof=0, rotational_dof=0))
+        return results
+
+    # Nullspace basis: rows of Vh beyond the rank
+    nullspace = vh[rank:]  # shape: (n_cols - rank, n_cols)
+
+    for bid in body_ids:
+        if bid == ground_body:
+            results.append(BodyDofLabel(body_id=bid, translational_dof=0, rotational_dof=0))
+            continue
+
+        idx = col_map[bid]
+        trans_cols = nullspace[:, idx * 6 : idx * 6 + 3]
+        rot_cols = nullspace[:, idx * 6 + 3 : idx * 6 + 6]
+
+        # Rank of each block = DOF in that category
+        if trans_cols.size > 0:
+            sv_t = np.linalg.svd(trans_cols, compute_uv=False)
+            t_dof = int(np.sum(sv_t > _SVD_TOL))
+        else:
+            t_dof = 0
+
+        if rot_cols.size > 0:
+            sv_r = np.linalg.svd(rot_cols, compute_uv=False)
+            r_dof = int(np.sum(sv_r > _SVD_TOL))
+        else:
+            r_dof = 0
+
+        results.append(BodyDofLabel(body_id=bid, translational_dof=t_dof, rotational_dof=r_dof))
+
+    return results
+
+
+# ---------------------------------------------------------------------------
+# Main labeling function
+# ---------------------------------------------------------------------------
+
+
+def label_assembly(
+    bodies: list[RigidBody],
+    joints: list[Joint],
+    ground_body: int | None = None,
+) -> AssemblyLabels:
+    """Produce complete ground truth labels for an assembly.
+
+    Runs both the pebble game and Jacobian verification internally,
+    then correlates their results into per-constraint, per-joint,
+    per-body, and assembly-level labels.
+
+    Args:
+        bodies: Rigid bodies in the assembly.
+        joints: Joints connecting the bodies.
+        ground_body: If set, this body is fixed to the world.
+
+    Returns:
+        AssemblyLabels with full label set and embedded ConstraintAnalysis.
+    """
+    # ---- Pebble Game ----
+    pg = PebbleGame3D()
+    all_edge_results: list[dict[str, Any]] = []
+
+    if ground_body is not None:
+        pg.add_body(_GROUND_ID)
+
+    for body in bodies:
+        pg.add_body(body.body_id)
+
+    if ground_body is not None:
+        ground_joint = Joint(
+            joint_id=-1,
+            body_a=ground_body,
+            body_b=_GROUND_ID,
+            joint_type=JointType.FIXED,
+            anchor_a=bodies[0].position if bodies else np.zeros(3),
+            anchor_b=bodies[0].position if bodies else np.zeros(3),
+        )
+        pg.add_joint(ground_joint)
+
+    for joint in joints:
+        results = pg.add_joint(joint)
+        all_edge_results.extend(results)
+
+    grounded = ground_body is not None
+    combinatorial_independent = len(pg.state.independent_edges)
+    raw_dof = pg.get_dof()
+    ground_offset = 6 if grounded else 0
+    effective_dof = raw_dof - ground_offset
+    effective_internal_dof = max(0, effective_dof - (0 if grounded else 6))
+
+    redundant_count = pg.get_redundant_count()
+    if redundant_count > 0 and effective_internal_dof > 0:
+        classification = "mixed"
+    elif redundant_count > 0:
+        classification = "overconstrained"
+    elif effective_internal_dof > 0:
+        classification = "underconstrained"
+    else:
+        classification = "well-constrained"
+
+    # ---- Jacobian Verification ----
+    verifier = JacobianVerifier(bodies)
+
+    for joint in joints:
+        verifier.add_joint_constraints(joint)
+
+    j_full = verifier.get_jacobian()
+    j_reduced = j_full.copy()
+    if ground_body is not None and j_reduced.size > 0:
+        idx = verifier.body_index[ground_body]
+        cols_to_remove = list(range(idx * 6, (idx + 1) * 6))
+        j_reduced = np.delete(j_reduced, cols_to_remove, axis=1)
+
+    if j_reduced.size > 0:
+        sv = np.linalg.svd(j_reduced, compute_uv=False)
+        jacobian_rank = int(np.sum(sv > _SVD_TOL))
+    else:
+        jacobian_rank = 0
+
+    n_cols = j_reduced.shape[1] if j_reduced.size > 0 else 6 * len(bodies)
+    jacobian_nullity = n_cols - jacobian_rank
+    dependent_rows = verifier.find_dependencies()
+    dependent_set = set(dependent_rows)
+
+    trivial_dof = 0 if grounded else 6
+    jacobian_internal_dof = jacobian_nullity - trivial_dof
+    geometric_degeneracies = max(0, combinatorial_independent - jacobian_rank)
+    is_rigid = jacobian_nullity <= trivial_dof
+    is_minimally_rigid = is_rigid and len(dependent_rows) == 0
+
+    # ---- Per-constraint labels ----
+    # Map Jacobian rows to (joint_id, constraint_index).
+    # Rows are added contiguously per joint in the same order as joints.
+    row_to_joint: list[tuple[int, int]] = []
+    for joint in joints:
+        dof = joint.joint_type.dof
+        for ci in range(dof):
+            row_to_joint.append((joint.joint_id, ci))
+
+    per_constraint: list[ConstraintLabel] = []
+    for edge_idx, edge_result in enumerate(all_edge_results):
+        jid = edge_result["joint_id"]
+        ci = edge_result["constraint_index"]
+        pebble_indep = edge_result["independent"]
+
+        # Find matching Jacobian row
+        jacobian_indep = True
+        if edge_idx < len(row_to_joint):
+            row_idx = edge_idx
+            jacobian_indep = row_idx not in dependent_set
+
+        per_constraint.append(
+            ConstraintLabel(
+                joint_id=jid,
+                constraint_idx=ci,
+                pebble_independent=pebble_indep,
+                jacobian_independent=jacobian_indep,
+            )
+        )
+
+    # ---- Per-joint labels ----
+    joint_agg: dict[int, JointLabel] = {}
+    for cl in per_constraint:
+        if cl.joint_id not in joint_agg:
+            joint_agg[cl.joint_id] = JointLabel(
+                joint_id=cl.joint_id,
+                independent_count=0,
+                redundant_count=0,
+                total=0,
+            )
+        jl = joint_agg[cl.joint_id]
+        jl.total += 1
+        if cl.pebble_independent:
+            jl.independent_count += 1
+        else:
+            jl.redundant_count += 1
+
+    per_joint = [joint_agg[j.joint_id] for j in joints if j.joint_id in joint_agg]
+
+    # ---- Per-body DOF labels ----
+    body_ids = [b.body_id for b in bodies]
+    per_body = _compute_per_body_dof(
+        j_reduced,
+        body_ids,
+        ground_body,
+        verifier.body_index,
+    )
+
+    # ---- Assembly label ----
+    assembly_label = AssemblyLabel(
+        classification=classification,
+        total_dof=max(0, jacobian_internal_dof),
+        redundant_count=redundant_count,
+        is_rigid=is_rigid,
+        is_minimally_rigid=is_minimally_rigid,
+        has_degeneracy=geometric_degeneracies > 0,
+    )
+
+    # ---- ConstraintAnalysis (for backward compat) ----
+    analysis = ConstraintAnalysis(
+        combinatorial_dof=effective_dof,
+        combinatorial_internal_dof=effective_internal_dof,
+        combinatorial_redundant=redundant_count,
+        combinatorial_classification=classification,
+        per_edge_results=all_edge_results,
+        jacobian_rank=jacobian_rank,
+        jacobian_nullity=jacobian_nullity,
+        jacobian_internal_dof=max(0, jacobian_internal_dof),
+        numerically_dependent=dependent_rows,
+        geometric_degeneracies=geometric_degeneracies,
+        is_rigid=is_rigid,
+        is_minimally_rigid=is_minimally_rigid,
+    )
+
+    return AssemblyLabels(
+        per_constraint=per_constraint,
+        per_joint=per_joint,
+        per_body=per_body,
+        assembly=assembly_label,
+        analysis=analysis,
+    )

solver/datagen/pebble_game.py

@@ -0,0 +1,258 @@
+"""(6,6)-Pebble game for 3D body-bar-hinge rigidity analysis.
+
+Implements the pebble game algorithm adapted for CAD assembly constraint
+graphs. Each rigid body has 6 DOF (3 translation + 3 rotation). Joints
+between bodies remove DOF according to their type.
+
+The pebble game provides a fast combinatorial *necessary* condition for
+rigidity via Tay's theorem. It does not detect geometric degeneracies —
+use :class:`solver.datagen.jacobian.JacobianVerifier` for the *sufficient*
+condition.
+
+References:
+    - Lee & Streinu, "Pebble Game Algorithms and Sparse Graphs", 2008
+    - Jacobs & Hendrickson, "An Algorithm for Two-Dimensional Rigidity
+      Percolation: The Pebble Game", J. Comput. Phys., 1997
+    - Tay, "Rigidity of Multigraphs I: Linking Rigid Bodies in n-space", 1984
+"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+from solver.datagen.types import Joint, PebbleState
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = ["PebbleGame3D"]
+
+
+class PebbleGame3D:
+    """Implements the (6,6)-pebble game for 3D body-bar-hinge frameworks.
+
+    For body-bar-hinge structures in 3D, Tay's theorem states that a
+    multigraph G on n vertices is generically minimally rigid iff:
+        |E| = 6n - 6  and  |E'| <= 6n' - 6  for all subgraphs (n' >= 2)
+
+    The (6,6)-pebble game tests this sparsity condition incrementally.
+    Each vertex starts with 6 pebbles (representing 6 DOF). To insert
+    an edge, we need to collect 6+1=7 pebbles on its two endpoints.
+    If we can, the edge is independent (removes a DOF). If not, it's
+    redundant (overconstrained).
+
+    In the CAD assembly context:
+        - Vertices = rigid bodies
+        - Edges = scalar constraints from joints
+        - A revolute joint (5 DOF removed) maps to 5 multigraph edges
+        - A fixed joint (6 DOF removed) maps to 6 multigraph edges
+    """
+
+    K = 6  # Pebbles per vertex (DOF per rigid body in 3D)
+    L = 6  # Sparsity parameter: need K+1=7 pebbles to accept edge
+
+    def __init__(self) -> None:
+        self.state = PebbleState()
+        self._edge_counter = 0
+        self._bodies: set[int] = set()
+
+    def add_body(self, body_id: int) -> None:
+        """Register a rigid body (vertex) with K=6 free pebbles."""
+        if body_id in self._bodies:
+            return
+        self._bodies.add(body_id)
+        self.state.free_pebbles[body_id] = self.K
+        self.state.incoming[body_id] = set()
+        self.state.outgoing[body_id] = set()
+
+    def add_joint(self, joint: Joint) -> list[dict[str, Any]]:
+        """Expand a joint into multigraph edges and test each for independence.
+
+        A joint that removes ``d`` DOF becomes ``d`` edges in the multigraph.
+        Each edge is tested individually via the pebble game.
+
+        Returns a list of dicts, one per scalar constraint, with:
+            - edge_id: int
+            - independent: bool
+            - dof_remaining: int (total free pebbles after this edge)
+        """
+        self.add_body(joint.body_a)
+        self.add_body(joint.body_b)
+
+        num_constraints = joint.joint_type.dof
+        results: list[dict[str, Any]] = []
+
+        for i in range(num_constraints):
+            edge_id = self._edge_counter
+            self._edge_counter += 1
+
+            independent = self._try_insert_edge(edge_id, joint.body_a, joint.body_b)
+            total_free = sum(self.state.free_pebbles.values())
+
+            results.append(
+                {
+                    "edge_id": edge_id,
+                    "joint_id": joint.joint_id,
+                    "constraint_index": i,
+                    "independent": independent,
+                    "dof_remaining": total_free,
+                }
+            )
+
+        return results
+
+    def _try_insert_edge(self, edge_id: int, u: int, v: int) -> bool:
+        """Try to insert a directed edge between u and v.
+
+        The edge is accepted (independent) iff we can collect L+1 = 7
+        pebbles on the two endpoints {u, v} combined.
+
+        If accepted, one pebble is consumed and the edge is directed
+        away from the vertex that gives up the pebble.
+        """
+        # Count current free pebbles on u and v
+        available = self.state.free_pebbles[u] + self.state.free_pebbles[v]
+
+        # Try to gather enough pebbles via DFS reachability search
+        if available < self.L + 1:
+            needed = (self.L + 1) - available
+            # Try to free pebbles by searching from u first, then v
+            for target in (u, v):
+                while needed > 0:
+                    found = self._search_and_collect(target, frozenset({u, v}))
+                    if not found:
+                        break
+                    needed -= 1
+
+        # Recheck after collection attempts
+        available = self.state.free_pebbles[u] + self.state.free_pebbles[v]
+
+        if available >= self.L + 1:
+            # Accept: consume a pebble from whichever endpoint has one
+            source = u if self.state.free_pebbles[u] > 0 else v
+
+            self.state.free_pebbles[source] -= 1
+            self.state.directed_edges[edge_id] = (source, v if source == u else u)
+            self.state.outgoing[source].add((edge_id, v if source == u else u))
+            target = v if source == u else u
+            self.state.incoming[target].add((edge_id, source))
+            self.state.independent_edges.add(edge_id)
+            return True
+        else:
+            # Reject: edge is redundant (overconstrained)
+            self.state.redundant_edges.add(edge_id)
+            return False
+
+    def _search_and_collect(self, target: int, forbidden: frozenset[int]) -> bool:
+        """DFS to find a free pebble reachable from *target* and move it.
+
+        Follows directed edges *backwards* (from destination to source)
+        to find a vertex with a free pebble that isn't in *forbidden*.
+        When found, reverses the path to move the pebble to *target*.
+
+        Returns True if a pebble was successfully moved to target.
+        """
+        # BFS/DFS through the directed graph following outgoing edges
+        # from target. An outgoing edge (target -> w) means target spent
+        # a pebble on that edge. If we can find a vertex with a free
+        # pebble, we reverse edges along the path to move it.
+
+        visited: set[int] = set()
+        # Stack: (current_vertex, path_of_edge_ids_to_reverse)
+        stack: list[tuple[int, list[int]]] = [(target, [])]
+
+        while stack:
+            current, path = stack.pop()
+            if current in visited:
+                continue
+            visited.add(current)
+
+            # Check if current vertex (not in forbidden, not target)
+            # has a free pebble
+            if (
+                current != target
+                and current not in forbidden
+                and self.state.free_pebbles[current] > 0
+            ):
+                # Found a pebble — reverse the path
+                self._reverse_path(path, current)
+                return True
+
+            # Follow outgoing edges from current vertex
+            for eid, neighbor in self.state.outgoing.get(current, set()):
+                if neighbor not in visited:
+                    stack.append((neighbor, [*path, eid]))
+
+        return False
+
+    def _reverse_path(self, edge_ids: list[int], pebble_source: int) -> None:
+        """Reverse directed edges along a path, moving a pebble to the start.
+
+        The pebble at *pebble_source* is consumed by the last edge in
+        the path, and a pebble is freed at the path's start vertex.
+        """
+        if not edge_ids:
+            return
+
+        # Reverse each edge in the path
+        for eid in edge_ids:
+            old_source, old_target = self.state.directed_edges[eid]
+
+            # Remove from adjacency
+            self.state.outgoing[old_source].discard((eid, old_target))
+            self.state.incoming[old_target].discard((eid, old_source))
+
+            # Reverse direction
+            self.state.directed_edges[eid] = (old_target, old_source)
+            self.state.outgoing[old_target].add((eid, old_source))
+            self.state.incoming[old_source].add((eid, old_target))
+
+        # Move pebble counts: source loses one, first vertex in path gains one
+        self.state.free_pebbles[pebble_source] -= 1
+
+        # After all reversals, the vertex at the beginning of the
+        # search path gains a pebble
+        _first_src, first_tgt = self.state.directed_edges[edge_ids[0]]
+        self.state.free_pebbles[first_tgt] += 1
+
+    def get_dof(self) -> int:
+        """Total remaining DOF = sum of free pebbles.
+
+        For a fully rigid assembly, this should be 6 (the trivial rigid
+        body motions of the whole assembly). Internal DOF = total - 6.
+        """
+        return sum(self.state.free_pebbles.values())
+
+    def get_internal_dof(self) -> int:
+        """Internal (non-trivial) degrees of freedom."""
+        return max(0, self.get_dof() - 6)
+
+    def is_rigid(self) -> bool:
+        """Combinatorial rigidity check: rigid iff at most 6 pebbles remain."""
+        return self.get_dof() <= self.L
+
+    def get_redundant_count(self) -> int:
+        """Number of redundant (overconstrained) scalar constraints."""
+        return len(self.state.redundant_edges)
+
+    def classify_assembly(self, *, grounded: bool = False) -> str:
+        """Classify the assembly state.
+
+        Args:
+            grounded: If True, the baseline trivial DOF is 0 (not 6),
+                because the ground body's 6 DOF were removed.
+        """
+        total_dof = self.get_dof()
+        redundant = self.get_redundant_count()
+        baseline = 0 if grounded else self.L
+
+        if redundant > 0 and total_dof > baseline:
+            return "mixed"  # Both under and over-constrained regions
+        elif redundant > 0:
+            return "overconstrained"
+        elif total_dof > baseline:
+            return "underconstrained"
+        elif total_dof == baseline:
+            return "well-constrained"
+        else:
+            return "overconstrained"

solver/datagen/types.py

@@ -0,0 +1,144 @@
+"""Shared data types for assembly constraint analysis.
+
+Types ported from the pebble-game synthetic data generator for reuse
+across the solver package (data generation, training, inference).
+"""
+
+from __future__ import annotations
+
+import enum
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "ConstraintAnalysis",
+    "Joint",
+    "JointType",
+    "PebbleState",
+    "RigidBody",
+]
+
+
+# ---------------------------------------------------------------------------
+# Joint definitions: each joint type removes a known number of DOF
+# ---------------------------------------------------------------------------
+
+
+class JointType(enum.Enum):
+    """Standard CAD joint types with their DOF-removal counts.
+
+    Each joint between two 6-DOF rigid bodies removes a specific number
+    of relative degrees of freedom. In the body-bar-hinge multigraph
+    representation, each joint maps to a number of edges equal to the
+    DOF it removes.
+
+    Values are ``(ordinal, dof_removed)`` tuples so that joint types
+    sharing the same DOF count remain distinct enum members. Use the
+    :attr:`dof` property to get the scalar constraint count.
+    """
+
+    FIXED = (0, 6)  # Locks all relative motion
+    REVOLUTE = (1, 5)  # Allows rotation about one axis
+    CYLINDRICAL = (2, 4)  # Allows rotation + translation along one axis
+    SLIDER = (3, 5)  # Allows translation along one axis (prismatic)
+    BALL = (4, 3)  # Allows rotation about a point (spherical)
+    PLANAR = (5, 3)  # Allows 2D translation + rotation normal to plane
+    SCREW = (6, 5)  # Coupled rotation-translation (helical)
+    UNIVERSAL = (7, 4)  # Two rotational DOF (Cardan/U-joint)
+    PARALLEL = (8, 3)  # Forces parallel orientation (3 rotation constraints)
+    PERPENDICULAR = (9, 1)  # Single angular constraint
+    DISTANCE = (10, 1)  # Single scalar distance constraint
+
+    @property
+    def dof(self) -> int:
+        """Number of scalar constraints (DOF removed) by this joint type."""
+        return self.value[1]
+
+
+# ---------------------------------------------------------------------------
+# Data structures
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class RigidBody:
+    """A rigid body in the assembly with pose and geometry info."""
+
+    body_id: int
+    position: np.ndarray = field(default_factory=lambda: np.zeros(3))
+    orientation: np.ndarray = field(default_factory=lambda: np.eye(3))
+
+    # Anchor points for joints, in local frame
+    # Populated when joints reference specific geometry
+    local_anchors: dict[str, np.ndarray] = field(default_factory=dict)
+
+
+@dataclass
+class Joint:
+    """A joint connecting two rigid bodies."""
+
+    joint_id: int
+    body_a: int  # Index of first body
+    body_b: int  # Index of second body
+    joint_type: JointType
+
+    # Joint parameters in world frame
+    anchor_a: np.ndarray = field(default_factory=lambda: np.zeros(3))
+    anchor_b: np.ndarray = field(default_factory=lambda: np.zeros(3))
+    axis: np.ndarray = field(
+        default_factory=lambda: np.array([0.0, 0.0, 1.0]),
+    )
+
+    # For screw joints
+    pitch: float = 0.0
+
+
+@dataclass
+class PebbleState:
+    """Tracks the state of the pebble game on the multigraph."""
+
+    # Number of free pebbles per body (vertex). Starts at 6.
+    free_pebbles: dict[int, int] = field(default_factory=dict)
+
+    # Directed edges: edge_id -> (source_body, target_body)
+    # Edge is directed away from the body that "spent" a pebble.
+    directed_edges: dict[int, tuple[int, int]] = field(default_factory=dict)
+
+    # Track which edges are independent vs redundant
+    independent_edges: set[int] = field(default_factory=set)
+    redundant_edges: set[int] = field(default_factory=set)
+
+    # Adjacency: body_id -> set of (edge_id, neighbor_body_id)
+    # Following directed edges *towards* a body (incoming edges)
+    incoming: dict[int, set[tuple[int, int]]] = field(default_factory=dict)
+
+    # Outgoing edges from a body
+    outgoing: dict[int, set[tuple[int, int]]] = field(default_factory=dict)
+
+
+@dataclass
+class ConstraintAnalysis:
+    """Results of analyzing an assembly's constraint system."""
+
+    # Pebble game (combinatorial) results
+    combinatorial_dof: int
+    combinatorial_internal_dof: int
+    combinatorial_redundant: int
+    combinatorial_classification: str
+    per_edge_results: list[dict[str, Any]]
+
+    # Numerical (Jacobian) results
+    jacobian_rank: int
+    jacobian_nullity: int  # = 6n - rank = total DOF
+    jacobian_internal_dof: int  # = nullity - 6
+    numerically_dependent: list[int]
+
+    # Combined
+    geometric_degeneracies: int  # = combinatorial_independent - jacobian_rank
+    is_rigid: bool
+    is_minimally_rigid: bool

solver/mates/__init__.py

@@ -0,0 +1,47 @@
+"""Mate-level constraint types for assembly analysis."""
+
+from solver.mates.conversion import (
+    MateAnalysisResult,
+    analyze_mate_assembly,
+    convert_mates_to_joints,
+)
+from solver.mates.generator import (
+    SyntheticMateGenerator,
+    generate_mate_training_batch,
+)
+from solver.mates.labeling import (
+    MateAssemblyLabels,
+    MateLabel,
+    label_mate_assembly,
+)
+from solver.mates.patterns import (
+    JointPattern,
+    PatternMatch,
+    recognize_patterns,
+)
+from solver.mates.primitives import (
+    GeometryRef,
+    GeometryType,
+    Mate,
+    MateType,
+    dof_removed,
+)
+
+__all__ = [
+    "GeometryRef",
+    "GeometryType",
+    "JointPattern",
+    "Mate",
+    "MateAnalysisResult",
+    "MateAssemblyLabels",
+    "MateLabel",
+    "MateType",
+    "PatternMatch",
+    "SyntheticMateGenerator",
+    "analyze_mate_assembly",
+    "convert_mates_to_joints",
+    "dof_removed",
+    "generate_mate_training_batch",
+    "label_mate_assembly",
+    "recognize_patterns",
+]

solver/mates/conversion.py

@@ -0,0 +1,276 @@
+"""Mate-to-joint conversion and assembly analysis.
+
+Bridges the mate-level constraint representation to the existing
+joint-based analysis pipeline. Converts recognized mate patterns
+to Joint objects, then runs the pebble game and Jacobian analysis,
+maintaining bidirectional traceability between mates and joints.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+from solver.datagen.labeling import AssemblyLabels, label_assembly
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    RigidBody,
+)
+from solver.mates.patterns import PatternMatch, recognize_patterns
+
+if TYPE_CHECKING:
+    from typing import Any
+
+    from solver.mates.primitives import Mate
+
+__all__ = [
+    "MateAnalysisResult",
+    "analyze_mate_assembly",
+    "convert_mates_to_joints",
+]
+
+
+# ---------------------------------------------------------------------------
+# Result dataclass
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class MateAnalysisResult:
+    """Combined result of mate-based assembly analysis.
+
+    Attributes:
+        patterns: Recognized joint patterns from mate grouping.
+        joints: Joint objects produced by conversion.
+        mate_to_joint: Mapping from mate_id to list of joint_ids.
+        joint_to_mates: Mapping from joint_id to list of mate_ids.
+        analysis: Constraint analysis from pebble game + Jacobian.
+        labels: Full ground truth labels from label_assembly.
+    """
+
+    patterns: list[PatternMatch]
+    joints: list[Joint]
+    mate_to_joint: dict[int, list[int]] = field(default_factory=dict)
+    joint_to_mates: dict[int, list[int]] = field(default_factory=dict)
+    analysis: ConstraintAnalysis | None = None
+    labels: AssemblyLabels | None = None
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "patterns": [p.to_dict() for p in self.patterns],
+            "joints": [
+                {
+                    "joint_id": j.joint_id,
+                    "body_a": j.body_a,
+                    "body_b": j.body_b,
+                    "joint_type": j.joint_type.name,
+                }
+                for j in self.joints
+            ],
+            "mate_to_joint": self.mate_to_joint,
+            "joint_to_mates": self.joint_to_mates,
+            "labels": self.labels.to_dict() if self.labels else None,
+        }
+
+
+# ---------------------------------------------------------------------------
+# Pattern-to-JointType mapping
+# ---------------------------------------------------------------------------
+
+# Maps (JointPattern value) to JointType for known patterns.
+# Used by convert_mates_to_joints when a full pattern is recognized.
+_PATTERN_JOINT_MAP: dict[str, JointType] = {
+    "hinge": JointType.REVOLUTE,
+    "slider": JointType.SLIDER,
+    "cylinder": JointType.CYLINDRICAL,
+    "ball": JointType.BALL,
+    "planar": JointType.PLANAR,
+    "fixed": JointType.FIXED,
+}
+
+# Fallback mapping for individual mate types when no pattern is recognized.
+_MATE_JOINT_FALLBACK: dict[str, JointType] = {
+    "COINCIDENT": JointType.PLANAR,
+    "CONCENTRIC": JointType.CYLINDRICAL,
+    "PARALLEL": JointType.PARALLEL,
+    "PERPENDICULAR": JointType.PERPENDICULAR,
+    "TANGENT": JointType.DISTANCE,
+    "DISTANCE": JointType.DISTANCE,
+    "ANGLE": JointType.PERPENDICULAR,
+    "LOCK": JointType.FIXED,
+}
+
+
+# ---------------------------------------------------------------------------
+# Conversion
+# ---------------------------------------------------------------------------
+
+
+def _compute_joint_params(
+    pattern: PatternMatch,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """Extract anchor and axis from pattern mates.
+
+    Returns:
+        (anchor_a, anchor_b, axis)
+    """
+    anchor_a = np.zeros(3)
+    anchor_b = np.zeros(3)
+    axis = np.array([0.0, 0.0, 1.0])
+
+    for mate in pattern.mates:
+        ref_a = mate.ref_a
+        ref_b = mate.ref_b
+        anchor_a = ref_a.origin.copy()
+        anchor_b = ref_b.origin.copy()
+        if ref_a.direction is not None:
+            axis = ref_a.direction.copy()
+            break
+
+    return anchor_a, anchor_b, axis
+
+
+def _convert_single_mate(
+    mate: Mate,
+    joint_id: int,
+) -> Joint:
+    """Convert a single unmatched mate to a Joint."""
+    joint_type = _MATE_JOINT_FALLBACK.get(mate.mate_type.name, JointType.DISTANCE)
+
+    anchor_a = mate.ref_a.origin.copy()
+    anchor_b = mate.ref_b.origin.copy()
+    axis = np.array([0.0, 0.0, 1.0])
+    if mate.ref_a.direction is not None:
+        axis = mate.ref_a.direction.copy()
+
+    return Joint(
+        joint_id=joint_id,
+        body_a=mate.ref_a.body_id,
+        body_b=mate.ref_b.body_id,
+        joint_type=joint_type,
+        anchor_a=anchor_a,
+        anchor_b=anchor_b,
+        axis=axis,
+    )
+
+
+def convert_mates_to_joints(
+    mates: list[Mate],
+    bodies: list[RigidBody] | None = None,
+) -> tuple[list[Joint], dict[int, list[int]], dict[int, list[int]]]:
+    """Convert mates to Joint objects via pattern recognition.
+
+    For each body pair:
+    - If mates form a recognized pattern, emit the equivalent joint.
+    - Otherwise, emit individual joints for each unmatched mate.
+
+    Args:
+        mates: Mate constraints to convert.
+        bodies: Optional body list (unused currently, reserved for
+            future geometry lookups).
+
+    Returns:
+        (joints, mate_to_joint, joint_to_mates) tuple.
+    """
+    if not mates:
+        return [], {}, {}
+
+    patterns = recognize_patterns(mates)
+    joints: list[Joint] = []
+    mate_to_joint: dict[int, list[int]] = {}
+    joint_to_mates: dict[int, list[int]] = {}
+
+    # Track which mates have been consumed by full-confidence patterns
+    consumed_mate_ids: set[int] = set()
+    next_joint_id = 0
+
+    # First pass: emit joints for full-confidence patterns
+    for pattern in patterns:
+        if pattern.confidence < 1.0:
+            continue
+        if pattern.pattern.value not in _PATTERN_JOINT_MAP:
+            continue
+
+        # Check if any of these mates were already consumed
+        mate_ids = [m.mate_id for m in pattern.mates]
+        if any(mid in consumed_mate_ids for mid in mate_ids):
+            continue
+
+        joint_type = _PATTERN_JOINT_MAP[pattern.pattern.value]
+        anchor_a, anchor_b, axis = _compute_joint_params(pattern)
+
+        joint = Joint(
+            joint_id=next_joint_id,
+            body_a=pattern.body_a,
+            body_b=pattern.body_b,
+            joint_type=joint_type,
+            anchor_a=anchor_a,
+            anchor_b=anchor_b,
+            axis=axis,
+        )
+        joints.append(joint)
+
+        joint_to_mates[next_joint_id] = mate_ids
+        for mid in mate_ids:
+            mate_to_joint.setdefault(mid, []).append(next_joint_id)
+            consumed_mate_ids.add(mid)
+
+        next_joint_id += 1
+
+    # Second pass: emit individual joints for unconsumed mates
+    for mate in mates:
+        if mate.mate_id in consumed_mate_ids:
+            continue
+
+        joint = _convert_single_mate(mate, next_joint_id)
+        joints.append(joint)
+
+        joint_to_mates[next_joint_id] = [mate.mate_id]
+        mate_to_joint.setdefault(mate.mate_id, []).append(next_joint_id)
+
+        next_joint_id += 1
+
+    return joints, mate_to_joint, joint_to_mates
+
+
+# ---------------------------------------------------------------------------
+# Full analysis pipeline
+# ---------------------------------------------------------------------------
+
+
+def analyze_mate_assembly(
+    bodies: list[RigidBody],
+    mates: list[Mate],
+    ground_body: int | None = None,
+) -> MateAnalysisResult:
+    """Run the full analysis pipeline on a mate-based assembly.
+
+    Orchestrates: recognize_patterns -> convert_mates_to_joints ->
+    label_assembly, returning a combined result with full traceability.
+
+    Args:
+        bodies: Rigid bodies in the assembly.
+        mates: Mate constraints between the bodies.
+        ground_body: If set, this body is fixed to the world.
+
+    Returns:
+        MateAnalysisResult with patterns, joints, mappings, and labels.
+    """
+    patterns = recognize_patterns(mates)
+    joints, mate_to_joint, joint_to_mates = convert_mates_to_joints(mates, bodies)
+
+    labels = label_assembly(bodies, joints, ground_body)
+
+    return MateAnalysisResult(
+        patterns=patterns,
+        joints=joints,
+        mate_to_joint=mate_to_joint,
+        joint_to_mates=joint_to_mates,
+        analysis=labels.analysis,
+        labels=labels,
+    )

solver/mates/generator.py

@@ -0,0 +1,315 @@
+"""Mate-based synthetic assembly generator.
+
+Wraps SyntheticAssemblyGenerator to produce mate-level training data.
+Generates joint-based assemblies via the existing generator, then
+reverse-maps joints to plausible mate combinations. Supports noise
+injection (redundant, missing, incompatible mates) for robust training.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+from solver.datagen.generator import SyntheticAssemblyGenerator
+from solver.datagen.types import Joint, JointType, RigidBody
+from solver.mates.conversion import MateAnalysisResult, analyze_mate_assembly
+from solver.mates.primitives import GeometryRef, GeometryType, Mate, MateType
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "SyntheticMateGenerator",
+    "generate_mate_training_batch",
+]
+
+
+# ---------------------------------------------------------------------------
+# Reverse mapping: JointType -> list of (MateType, geom_a, geom_b) combos
+# ---------------------------------------------------------------------------
+
+
+@dataclass(frozen=True)
+class _MateSpec:
+    """Specification for a mate to generate from a joint."""
+
+    mate_type: MateType
+    geom_a: GeometryType
+    geom_b: GeometryType
+
+
+_JOINT_TO_MATES: dict[JointType, list[_MateSpec]] = {
+    JointType.REVOLUTE: [
+        _MateSpec(MateType.CONCENTRIC, GeometryType.AXIS, GeometryType.AXIS),
+        _MateSpec(MateType.COINCIDENT, GeometryType.PLANE, GeometryType.PLANE),
+    ],
+    JointType.CYLINDRICAL: [
+        _MateSpec(MateType.CONCENTRIC, GeometryType.AXIS, GeometryType.AXIS),
+    ],
+    JointType.BALL: [
+        _MateSpec(MateType.COINCIDENT, GeometryType.POINT, GeometryType.POINT),
+    ],
+    JointType.FIXED: [
+        _MateSpec(MateType.LOCK, GeometryType.FACE, GeometryType.FACE),
+    ],
+    JointType.SLIDER: [
+        _MateSpec(MateType.COINCIDENT, GeometryType.PLANE, GeometryType.PLANE),
+        _MateSpec(MateType.PARALLEL, GeometryType.AXIS, GeometryType.AXIS),
+    ],
+    JointType.PLANAR: [
+        _MateSpec(MateType.COINCIDENT, GeometryType.FACE, GeometryType.FACE),
+    ],
+}
+
+
+# ---------------------------------------------------------------------------
+# Generator
+# ---------------------------------------------------------------------------
+
+
+class SyntheticMateGenerator:
+    """Generates mate-based assemblies for training data.
+
+    Wraps SyntheticAssemblyGenerator to produce joint-based assemblies,
+    then reverse-maps each joint to a plausible set of mate constraints.
+
+    Args:
+        seed: Random seed for reproducibility.
+        redundant_prob: Probability of injecting a redundant mate per joint.
+        missing_prob: Probability of dropping a mate from a multi-mate pattern.
+        incompatible_prob: Probability of injecting a mate with wrong geometry.
+    """
+
+    def __init__(
+        self,
+        seed: int = 42,
+        *,
+        redundant_prob: float = 0.0,
+        missing_prob: float = 0.0,
+        incompatible_prob: float = 0.0,
+    ) -> None:
+        self._joint_gen = SyntheticAssemblyGenerator(seed=seed)
+        self._rng = np.random.default_rng(seed)
+        self.redundant_prob = redundant_prob
+        self.missing_prob = missing_prob
+        self.incompatible_prob = incompatible_prob
+
+    def _make_geometry_ref(
+        self,
+        body_id: int,
+        geom_type: GeometryType,
+        joint: Joint,
+        *,
+        is_ref_a: bool = True,
+    ) -> GeometryRef:
+        """Create a GeometryRef from joint geometry.
+
+        Uses joint anchor, axis, and body_id to produce a ref
+        with realistic geometry for the given type.
+        """
+        origin = joint.anchor_a if is_ref_a else joint.anchor_b
+
+        direction: np.ndarray | None = None
+        if geom_type in {GeometryType.AXIS, GeometryType.PLANE, GeometryType.FACE}:
+            direction = joint.axis.copy()
+
+        geom_id = f"{geom_type.value.capitalize()}001"
+
+        return GeometryRef(
+            body_id=body_id,
+            geometry_type=geom_type,
+            geometry_id=geom_id,
+            origin=origin.copy(),
+            direction=direction,
+        )
+
+    def _reverse_map_joint(
+        self,
+        joint: Joint,
+        next_mate_id: int,
+    ) -> list[Mate]:
+        """Convert a joint to its mate representation."""
+        specs = _JOINT_TO_MATES.get(joint.joint_type, [])
+        if not specs:
+            # Fallback: emit a single DISTANCE mate
+            specs = [_MateSpec(MateType.DISTANCE, GeometryType.POINT, GeometryType.POINT)]
+
+        mates: list[Mate] = []
+        for spec in specs:
+            ref_a = self._make_geometry_ref(joint.body_a, spec.geom_a, joint, is_ref_a=True)
+            ref_b = self._make_geometry_ref(joint.body_b, spec.geom_b, joint, is_ref_a=False)
+            mates.append(
+                Mate(
+                    mate_id=next_mate_id + len(mates),
+                    mate_type=spec.mate_type,
+                    ref_a=ref_a,
+                    ref_b=ref_b,
+                )
+            )
+        return mates
+
+    def _inject_noise(
+        self,
+        mates: list[Mate],
+        next_mate_id: int,
+    ) -> list[Mate]:
+        """Apply noise injection to the mate list.
+
+        Modifies the list in-place and may add new mates.
+        Returns the (possibly extended) list.
+        """
+        result = list(mates)
+        extra: list[Mate] = []
+
+        for mate in mates:
+            # Redundant: duplicate a mate
+            if self._rng.random() < self.redundant_prob:
+                dup = Mate(
+                    mate_id=next_mate_id + len(extra),
+                    mate_type=mate.mate_type,
+                    ref_a=mate.ref_a,
+                    ref_b=mate.ref_b,
+                    value=mate.value,
+                    tolerance=mate.tolerance,
+                )
+                extra.append(dup)
+
+            # Incompatible: wrong geometry type
+            if self._rng.random() < self.incompatible_prob:
+                bad_geom = GeometryType.POINT
+                bad_ref = GeometryRef(
+                    body_id=mate.ref_a.body_id,
+                    geometry_type=bad_geom,
+                    geometry_id="BadGeom001",
+                    origin=mate.ref_a.origin.copy(),
+                    direction=None,
+                )
+                extra.append(
+                    Mate(
+                        mate_id=next_mate_id + len(extra),
+                        mate_type=MateType.CONCENTRIC,
+                        ref_a=bad_ref,
+                        ref_b=mate.ref_b,
+                    )
+                )
+
+        result.extend(extra)
+
+        # Missing: drop mates from multi-mate patterns (only if > 1 mate
+        # for same body pair)
+        if self.missing_prob > 0:
+            filtered: list[Mate] = []
+            for mate in result:
+                if self._rng.random() < self.missing_prob:
+                    continue
+                filtered.append(mate)
+            # Ensure at least one mate remains
+            if not filtered and result:
+                filtered = [result[0]]
+            result = filtered
+
+        return result
+
+    def generate(
+        self,
+        n_bodies: int = 4,
+        *,
+        grounded: bool = False,
+    ) -> tuple[list[RigidBody], list[Mate], MateAnalysisResult]:
+        """Generate a mate-based assembly.
+
+        Args:
+            n_bodies: Number of rigid bodies.
+            grounded: Whether to ground the first body.
+
+        Returns:
+            (bodies, mates, analysis_result) tuple.
+        """
+        bodies, joints, _analysis = self._joint_gen.generate_chain_assembly(
+            n_bodies,
+            joint_type=JointType.REVOLUTE,
+            grounded=grounded,
+        )
+
+        mates: list[Mate] = []
+        next_id = 0
+        for joint in joints:
+            joint_mates = self._reverse_map_joint(joint, next_id)
+            mates.extend(joint_mates)
+            next_id += len(joint_mates)
+
+        # Apply noise
+        mates = self._inject_noise(mates, next_id)
+
+        ground_body = bodies[0].body_id if grounded else None
+        result = analyze_mate_assembly(bodies, mates, ground_body)
+
+        return bodies, mates, result
+
+
+# ---------------------------------------------------------------------------
+# Batch generation
+# ---------------------------------------------------------------------------
+
+
+def generate_mate_training_batch(
+    batch_size: int = 100,
+    n_bodies_range: tuple[int, int] = (3, 8),
+    seed: int = 42,
+    *,
+    redundant_prob: float = 0.0,
+    missing_prob: float = 0.0,
+    incompatible_prob: float = 0.0,
+    grounded_ratio: float = 1.0,
+) -> list[dict[str, Any]]:
+    """Produce a batch of mate-level training examples.
+
+    Args:
+        batch_size: Number of assemblies to generate.
+        n_bodies_range: (min, max_exclusive) body count.
+        seed: Random seed.
+        redundant_prob: Probability of redundant mate injection.
+        missing_prob: Probability of missing mate injection.
+        incompatible_prob: Probability of incompatible mate injection.
+        grounded_ratio: Fraction of assemblies that are grounded.
+
+    Returns:
+        List of dicts with bodies, mates, patterns, and labels.
+    """
+    rng = np.random.default_rng(seed)
+    examples: list[dict[str, Any]] = []
+
+    for i in range(batch_size):
+        gen = SyntheticMateGenerator(
+            seed=seed + i,
+            redundant_prob=redundant_prob,
+            missing_prob=missing_prob,
+            incompatible_prob=incompatible_prob,
+        )
+        n = int(rng.integers(*n_bodies_range))
+        grounded = bool(rng.random() < grounded_ratio)
+
+        bodies, mates, result = gen.generate(n, grounded=grounded)
+
+        examples.append(
+            {
+                "bodies": [
+                    {
+                        "body_id": b.body_id,
+                        "position": b.position.tolist(),
+                    }
+                    for b in bodies
+                ],
+                "mates": [m.to_dict() for m in mates],
+                "patterns": [p.to_dict() for p in result.patterns],
+                "labels": result.labels.to_dict() if result.labels else None,
+                "n_bodies": len(bodies),
+                "n_mates": len(mates),
+                "n_joints": len(result.joints),
+            }
+        )
+
+    return examples

solver/mates/labeling.py

@@ -0,0 +1,224 @@
+"""Mate-level ground truth labels for assembly analysis.
+
+Back-attributes joint-level independence results to originating mates
+via the mate-to-joint mapping from conversion.py. Produces per-mate
+labels indicating whether each mate is independent, redundant, or
+degenerate.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import TYPE_CHECKING
+
+from solver.mates.conversion import analyze_mate_assembly
+
+if TYPE_CHECKING:
+    from typing import Any
+
+    from solver.datagen.labeling import AssemblyLabel
+    from solver.datagen.types import ConstraintAnalysis, RigidBody
+    from solver.mates.conversion import MateAnalysisResult
+    from solver.mates.patterns import JointPattern, PatternMatch
+    from solver.mates.primitives import Mate
+
+__all__ = [
+    "MateAssemblyLabels",
+    "MateLabel",
+    "label_mate_assembly",
+]
+
+
+# ---------------------------------------------------------------------------
+# Label dataclasses
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class MateLabel:
+    """Per-mate ground truth label.
+
+    Attributes:
+        mate_id: The mate this label refers to.
+        is_independent: Contributes non-redundant DOF removal.
+        is_redundant: Fully redundant (removable without DOF change).
+        is_degenerate: Combinatorially independent but geometrically dependent.
+        pattern: Which joint pattern this mate belongs to, if any.
+        issue: Detected issue type, if any.
+    """
+
+    mate_id: int
+    is_independent: bool = True
+    is_redundant: bool = False
+    is_degenerate: bool = False
+    pattern: JointPattern | None = None
+    issue: str | None = None
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "mate_id": self.mate_id,
+            "is_independent": self.is_independent,
+            "is_redundant": self.is_redundant,
+            "is_degenerate": self.is_degenerate,
+            "pattern": self.pattern.value if self.pattern else None,
+            "issue": self.issue,
+        }
+
+
+@dataclass
+class MateAssemblyLabels:
+    """Complete mate-level ground truth labels for an assembly.
+
+    Attributes:
+        per_mate: Per-mate labels.
+        patterns: Recognized joint patterns.
+        assembly: Assembly-wide summary label.
+        analysis: Constraint analysis from pebble game + Jacobian.
+    """
+
+    per_mate: list[MateLabel]
+    patterns: list[PatternMatch]
+    assembly: AssemblyLabel
+    analysis: ConstraintAnalysis
+    mate_analysis: MateAnalysisResult | None = None
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "per_mate": [ml.to_dict() for ml in self.per_mate],
+            "patterns": [p.to_dict() for p in self.patterns],
+            "assembly": {
+                "classification": self.assembly.classification,
+                "total_dof": self.assembly.total_dof,
+                "redundant_count": self.assembly.redundant_count,
+                "is_rigid": self.assembly.is_rigid,
+                "is_minimally_rigid": self.assembly.is_minimally_rigid,
+                "has_degeneracy": self.assembly.has_degeneracy,
+            },
+        }
+
+
+# ---------------------------------------------------------------------------
+# Labeling logic
+# ---------------------------------------------------------------------------
+
+
+def _build_mate_pattern_map(
+    patterns: list[PatternMatch],
+) -> dict[int, JointPattern]:
+    """Map mate_ids to the pattern they belong to (best match)."""
+    result: dict[int, JointPattern] = {}
+    # Sort by confidence descending so best matches win
+    sorted_patterns = sorted(patterns, key=lambda p: -p.confidence)
+    for pm in sorted_patterns:
+        if pm.confidence < 1.0:
+            continue
+        for mate in pm.mates:
+            if mate.mate_id not in result:
+                result[mate.mate_id] = pm.pattern
+    return result
+
+
+def label_mate_assembly(
+    bodies: list[RigidBody],
+    mates: list[Mate],
+    ground_body: int | None = None,
+) -> MateAssemblyLabels:
+    """Produce mate-level ground truth labels for an assembly.
+
+    Runs analyze_mate_assembly() internally, then back-attributes
+    joint-level independence to originating mates via the mate_to_joint
+    mapping.
+
+    A mate is:
+    - **redundant** if ALL joints it contributes to are fully redundant
+    - **degenerate** if any joint it contributes to is geometrically
+      dependent but combinatorially independent
+    - **independent** otherwise
+
+    Args:
+        bodies: Rigid bodies in the assembly.
+        mates: Mate constraints between the bodies.
+        ground_body: If set, this body is fixed to the world.
+
+    Returns:
+        MateAssemblyLabels with per-mate labels and assembly summary.
+    """
+    mate_result = analyze_mate_assembly(bodies, mates, ground_body)
+
+    # Build per-joint redundancy from labels
+    joint_redundant: dict[int, bool] = {}
+    joint_degenerate: dict[int, bool] = {}
+
+    if mate_result.labels is not None:
+        for jl in mate_result.labels.per_joint:
+            # A joint is fully redundant if all its constraints are redundant
+            joint_redundant[jl.joint_id] = jl.redundant_count == jl.total and jl.total > 0
+            # Joint is degenerate if it has more independent constraints
+            # than Jacobian rank would suggest (geometric degeneracy)
+            joint_degenerate[jl.joint_id] = False
+
+        # Check for geometric degeneracy via per-constraint labels
+        for cl in mate_result.labels.per_constraint:
+            if cl.pebble_independent and not cl.jacobian_independent:
+                joint_degenerate[cl.joint_id] = True
+
+    # Build pattern membership map
+    pattern_map = _build_mate_pattern_map(mate_result.patterns)
+
+    # Back-attribute to mates
+    per_mate: list[MateLabel] = []
+    for mate in mates:
+        mate_joint_ids = mate_result.mate_to_joint.get(mate.mate_id, [])
+
+        if not mate_joint_ids:
+            # Mate wasn't converted to any joint (shouldn't happen, but safe)
+            per_mate.append(
+                MateLabel(
+                    mate_id=mate.mate_id,
+                    is_independent=False,
+                    is_redundant=True,
+                    issue="unmapped",
+                )
+            )
+            continue
+
+        # Redundant if ALL contributed joints are redundant
+        all_redundant = all(joint_redundant.get(jid, False) for jid in mate_joint_ids)
+
+        # Degenerate if ANY contributed joint is degenerate
+        any_degenerate = any(joint_degenerate.get(jid, False) for jid in mate_joint_ids)
+
+        is_independent = not all_redundant
+        pattern = pattern_map.get(mate.mate_id)
+
+        # Determine issue string
+        issue: str | None = None
+        if all_redundant:
+            issue = "redundant"
+        elif any_degenerate:
+            issue = "degenerate"
+
+        per_mate.append(
+            MateLabel(
+                mate_id=mate.mate_id,
+                is_independent=is_independent,
+                is_redundant=all_redundant,
+                is_degenerate=any_degenerate,
+                pattern=pattern,
+                issue=issue,
+            )
+        )
+
+    # Assembly label
+    assert mate_result.labels is not None
+    assembly_label = mate_result.labels.assembly
+
+    return MateAssemblyLabels(
+        per_mate=per_mate,
+        patterns=mate_result.patterns,
+        assembly=assembly_label,
+        analysis=mate_result.labels.analysis,
+        mate_analysis=mate_result,
+    )

solver/mates/patterns.py

@@ -0,0 +1,284 @@
+"""Joint pattern recognition from mate combinations.
+
+Groups mates by body pair and matches them against canonical joint
+patterns (hinge, slider, ball, etc.). Each pattern is a known
+combination of mate types that together constrain motion equivalently
+to a single mechanical joint.
+"""
+
+from __future__ import annotations
+
+import enum
+from collections import defaultdict
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING
+
+from solver.datagen.types import JointType
+from solver.mates.primitives import GeometryType, Mate, MateType
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "JointPattern",
+    "PatternMatch",
+    "recognize_patterns",
+]
+
+
+# ---------------------------------------------------------------------------
+# Enums
+# ---------------------------------------------------------------------------
+
+
+class JointPattern(enum.Enum):
+    """Canonical joint patterns formed by mate combinations."""
+
+    HINGE = "hinge"
+    SLIDER = "slider"
+    CYLINDER = "cylinder"
+    BALL = "ball"
+    PLANAR = "planar"
+    FIXED = "fixed"
+    GEAR = "gear"
+    RACK_PINION = "rack_pinion"
+    UNKNOWN = "unknown"
+
+
+# ---------------------------------------------------------------------------
+# Pattern match result
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class PatternMatch:
+    """Result of matching a group of mates to a joint pattern.
+
+    Attributes:
+        pattern: The identified joint pattern.
+        mates: The mates that form this pattern.
+        body_a: First body in the pair.
+        body_b: Second body in the pair.
+        confidence: How well the mates match the canonical pattern (0-1).
+        equivalent_joint_type: The JointType this pattern maps to.
+        missing_mates: Descriptions of mates absent for a full match.
+    """
+
+    pattern: JointPattern
+    mates: list[Mate]
+    body_a: int
+    body_b: int
+    confidence: float
+    equivalent_joint_type: JointType
+    missing_mates: list[str] = field(default_factory=list)
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "pattern": self.pattern.value,
+            "body_a": self.body_a,
+            "body_b": self.body_b,
+            "confidence": self.confidence,
+            "equivalent_joint_type": self.equivalent_joint_type.name,
+            "mate_ids": [m.mate_id for m in self.mates],
+            "missing_mates": self.missing_mates,
+        }
+
+
+# ---------------------------------------------------------------------------
+# Pattern rules (data-driven)
+# ---------------------------------------------------------------------------
+
+
+@dataclass(frozen=True)
+class _MateRequirement:
+    """A single mate requirement within a pattern rule."""
+
+    mate_type: MateType
+    geometry_a: GeometryType | None = None
+    geometry_b: GeometryType | None = None
+
+
+@dataclass(frozen=True)
+class _PatternRule:
+    """Defines a canonical pattern as a set of required mates."""
+
+    pattern: JointPattern
+    joint_type: JointType
+    required: tuple[_MateRequirement, ...]
+    description: str = ""
+
+
+_PATTERN_RULES: list[_PatternRule] = [
+    _PatternRule(
+        pattern=JointPattern.HINGE,
+        joint_type=JointType.REVOLUTE,
+        required=(
+            _MateRequirement(MateType.CONCENTRIC, GeometryType.AXIS, GeometryType.AXIS),
+            _MateRequirement(MateType.COINCIDENT, GeometryType.PLANE, GeometryType.PLANE),
+        ),
+        description="Concentric axes + coincident plane",
+    ),
+    _PatternRule(
+        pattern=JointPattern.SLIDER,
+        joint_type=JointType.SLIDER,
+        required=(
+            _MateRequirement(MateType.COINCIDENT, GeometryType.PLANE, GeometryType.PLANE),
+            _MateRequirement(MateType.PARALLEL, GeometryType.AXIS, GeometryType.AXIS),
+        ),
+        description="Coincident plane + parallel axis",
+    ),
+    _PatternRule(
+        pattern=JointPattern.CYLINDER,
+        joint_type=JointType.CYLINDRICAL,
+        required=(_MateRequirement(MateType.CONCENTRIC, GeometryType.AXIS, GeometryType.AXIS),),
+        description="Concentric axes only",
+    ),
+    _PatternRule(
+        pattern=JointPattern.BALL,
+        joint_type=JointType.BALL,
+        required=(_MateRequirement(MateType.COINCIDENT, GeometryType.POINT, GeometryType.POINT),),
+        description="Coincident points",
+    ),
+    _PatternRule(
+        pattern=JointPattern.PLANAR,
+        joint_type=JointType.PLANAR,
+        required=(_MateRequirement(MateType.COINCIDENT, GeometryType.FACE, GeometryType.FACE),),
+        description="Coincident faces",
+    ),
+    _PatternRule(
+        pattern=JointPattern.PLANAR,
+        joint_type=JointType.PLANAR,
+        required=(_MateRequirement(MateType.COINCIDENT, GeometryType.PLANE, GeometryType.PLANE),),
+        description="Coincident planes (alternate planar)",
+    ),
+    _PatternRule(
+        pattern=JointPattern.FIXED,
+        joint_type=JointType.FIXED,
+        required=(_MateRequirement(MateType.LOCK),),
+        description="Lock mate",
+    ),
+]
+
+
+# ---------------------------------------------------------------------------
+# Matching logic
+# ---------------------------------------------------------------------------
+
+
+def _mate_matches_requirement(mate: Mate, req: _MateRequirement) -> bool:
+    """Check if a mate satisfies a requirement."""
+    if mate.mate_type is not req.mate_type:
+        return False
+    if req.geometry_a is not None and mate.ref_a.geometry_type is not req.geometry_a:
+        return False
+    return not (req.geometry_b is not None and mate.ref_b.geometry_type is not req.geometry_b)
+
+
+def _try_match_rule(
+    rule: _PatternRule,
+    mates: list[Mate],
+) -> tuple[float, list[Mate], list[str]]:
+    """Try to match a rule against a group of mates.
+
+    Returns:
+        (confidence, matched_mates, missing_descriptions)
+    """
+    matched: list[Mate] = []
+    missing: list[str] = []
+
+    for req in rule.required:
+        found = False
+        for mate in mates:
+            if mate in matched:
+                continue
+            if _mate_matches_requirement(mate, req):
+                matched.append(mate)
+                found = True
+                break
+        if not found:
+            geom_desc = ""
+            if req.geometry_a is not None:
+                geom_b = req.geometry_b.value if req.geometry_b else "*"
+                geom_desc = f" ({req.geometry_a.value}-{geom_b})"
+            missing.append(f"{req.mate_type.name}{geom_desc}")
+
+    total_required = len(rule.required)
+    if total_required == 0:
+        return 0.0, [], []
+
+    matched_count = len(matched)
+    confidence = matched_count / total_required
+
+    return confidence, matched, missing
+
+
+def _normalize_body_pair(body_a: int, body_b: int) -> tuple[int, int]:
+    """Normalize a body pair so the smaller ID comes first."""
+    return (min(body_a, body_b), max(body_a, body_b))
+
+
+def recognize_patterns(mates: list[Mate]) -> list[PatternMatch]:
+    """Identify joint patterns from a list of mates.
+
+    Groups mates by body pair, then checks each group against
+    canonical pattern rules. Returns matches sorted by confidence
+    descending.
+
+    Args:
+        mates: List of mate constraints to analyze.
+
+    Returns:
+        List of PatternMatch results, highest confidence first.
+    """
+    if not mates:
+        return []
+
+    # Group mates by normalized body pair
+    groups: dict[tuple[int, int], list[Mate]] = defaultdict(list)
+    for mate in mates:
+        pair = _normalize_body_pair(mate.ref_a.body_id, mate.ref_b.body_id)
+        groups[pair].append(mate)
+
+    results: list[PatternMatch] = []
+
+    for (body_a, body_b), group_mates in groups.items():
+        group_matches: list[PatternMatch] = []
+
+        for rule in _PATTERN_RULES:
+            confidence, matched, missing = _try_match_rule(rule, group_mates)
+
+            if confidence > 0:
+                group_matches.append(
+                    PatternMatch(
+                        pattern=rule.pattern,
+                        mates=matched if matched else group_mates,
+                        body_a=body_a,
+                        body_b=body_b,
+                        confidence=confidence,
+                        equivalent_joint_type=rule.joint_type,
+                        missing_mates=missing,
+                    )
+                )
+
+        if group_matches:
+            # Sort by confidence descending, prefer more-specific patterns
+            group_matches.sort(key=lambda m: (-m.confidence, -len(m.mates)))
+            results.extend(group_matches)
+        else:
+            # No pattern matched at all
+            results.append(
+                PatternMatch(
+                    pattern=JointPattern.UNKNOWN,
+                    mates=group_mates,
+                    body_a=body_a,
+                    body_b=body_b,
+                    confidence=0.0,
+                    equivalent_joint_type=JointType.DISTANCE,
+                    missing_mates=[],
+                )
+            )
+
+    # Global sort by confidence descending
+    results.sort(key=lambda m: -m.confidence)
+    return results

solver/mates/primitives.py

@@ -0,0 +1,279 @@
+"""Mate type definitions and geometry references for assembly constraints.
+
+Mates are the user-facing constraint primitives in CAD (e.g. SolidWorks-style
+Coincident, Concentric, Parallel). Each mate references geometry on two bodies
+and removes a context-dependent number of degrees of freedom.
+"""
+
+from __future__ import annotations
+
+import enum
+from dataclasses import dataclass, field
+from typing import TYPE_CHECKING
+
+import numpy as np
+
+if TYPE_CHECKING:
+    from typing import Any
+
+__all__ = [
+    "GeometryRef",
+    "GeometryType",
+    "Mate",
+    "MateType",
+    "dof_removed",
+]
+
+
+# ---------------------------------------------------------------------------
+# Enums
+# ---------------------------------------------------------------------------
+
+
+class MateType(enum.Enum):
+    """CAD mate types with default DOF-removal counts.
+
+    Values are ``(ordinal, default_dof)`` tuples so that mate types
+    sharing the same DOF count remain distinct enum members. Use the
+    :attr:`default_dof` property to get the scalar constraint count.
+
+    The actual DOF removed can be context-dependent (e.g. COINCIDENT
+    removes 3 DOF for face-face but only 1 for face-point). Use
+    :func:`dof_removed` for the context-aware count.
+    """
+
+    COINCIDENT = (0, 3)
+    CONCENTRIC = (1, 2)
+    PARALLEL = (2, 2)
+    PERPENDICULAR = (3, 1)
+    TANGENT = (4, 1)
+    DISTANCE = (5, 1)
+    ANGLE = (6, 1)
+    LOCK = (7, 6)
+
+    @property
+    def default_dof(self) -> int:
+        """Default number of DOF removed by this mate type."""
+        return self.value[1]
+
+
+class GeometryType(enum.Enum):
+    """Types of geometric references used by mates."""
+
+    FACE = "face"
+    EDGE = "edge"
+    POINT = "point"
+    AXIS = "axis"
+    PLANE = "plane"
+
+
+# Geometry types that require a direction vector.
+_DIRECTIONAL_TYPES = frozenset(
+    {
+        GeometryType.FACE,
+        GeometryType.AXIS,
+        GeometryType.PLANE,
+    }
+)
+
+
+# ---------------------------------------------------------------------------
+# Dataclasses
+# ---------------------------------------------------------------------------
+
+
+@dataclass
+class GeometryRef:
+    """A reference to a specific geometric entity on a body.
+
+    Attributes:
+        body_id: Index of the body this geometry belongs to.
+        geometry_type: What kind of geometry (face, edge, etc.).
+        geometry_id: CAD identifier string (e.g. ``"Face001"``).
+        origin: 3D position of the geometry reference point.
+        direction: Unit direction vector. Required for FACE, AXIS, PLANE;
+            ``None`` for POINT.
+    """
+
+    body_id: int
+    geometry_type: GeometryType
+    geometry_id: str
+    origin: np.ndarray = field(default_factory=lambda: np.zeros(3))
+    direction: np.ndarray | None = None
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "body_id": self.body_id,
+            "geometry_type": self.geometry_type.value,
+            "geometry_id": self.geometry_id,
+            "origin": self.origin.tolist(),
+            "direction": self.direction.tolist() if self.direction is not None else None,
+        }
+
+    @classmethod
+    def from_dict(cls, data: dict[str, Any]) -> GeometryRef:
+        """Construct from a dict produced by :meth:`to_dict`."""
+        direction_raw = data.get("direction")
+        return cls(
+            body_id=data["body_id"],
+            geometry_type=GeometryType(data["geometry_type"]),
+            geometry_id=data["geometry_id"],
+            origin=np.asarray(data["origin"], dtype=np.float64),
+            direction=(
+                np.asarray(direction_raw, dtype=np.float64) if direction_raw is not None else None
+            ),
+        )
+
+
+@dataclass
+class Mate:
+    """A mate constraint between geometry on two bodies.
+
+    Attributes:
+        mate_id: Unique identifier for this mate.
+        mate_type: The type of constraint (Coincident, Concentric, etc.).
+        ref_a: Geometry reference on the first body.
+        ref_b: Geometry reference on the second body.
+        value: Scalar parameter for DISTANCE and ANGLE mates (0 otherwise).
+        tolerance: Numeric tolerance for constraint satisfaction.
+    """
+
+    mate_id: int
+    mate_type: MateType
+    ref_a: GeometryRef
+    ref_b: GeometryRef
+    value: float = 0.0
+    tolerance: float = 1e-6
+
+    def validate(self) -> None:
+        """Raise ``ValueError`` if this mate has incompatible geometry.
+
+        Checks:
+        - Self-mate (both refs on same body)
+        - CONCENTRIC requires AXIS geometry on both refs
+        - PARALLEL requires directional geometry (not POINT)
+        - TANGENT requires surface geometry (FACE or EDGE)
+        - Directional geometry types must have a direction vector
+        """
+        if self.ref_a.body_id == self.ref_b.body_id:
+            msg = f"Self-mate: ref_a and ref_b both reference body {self.ref_a.body_id}"
+            raise ValueError(msg)
+
+        for label, ref in [("ref_a", self.ref_a), ("ref_b", self.ref_b)]:
+            if ref.geometry_type in _DIRECTIONAL_TYPES and ref.direction is None:
+                msg = (
+                    f"{label}: geometry type {ref.geometry_type.value} requires a direction vector"
+                )
+                raise ValueError(msg)
+
+        if self.mate_type is MateType.CONCENTRIC:
+            for label, ref in [("ref_a", self.ref_a), ("ref_b", self.ref_b)]:
+                if ref.geometry_type is not GeometryType.AXIS:
+                    msg = (
+                        f"CONCENTRIC mate requires AXIS geometry, "
+                        f"got {ref.geometry_type.value} on {label}"
+                    )
+                    raise ValueError(msg)
+
+        if self.mate_type is MateType.PARALLEL:
+            for label, ref in [("ref_a", self.ref_a), ("ref_b", self.ref_b)]:
+                if ref.geometry_type is GeometryType.POINT:
+                    msg = f"PARALLEL mate requires directional geometry, got POINT on {label}"
+                    raise ValueError(msg)
+
+        if self.mate_type is MateType.TANGENT:
+            _surface = frozenset({GeometryType.FACE, GeometryType.EDGE})
+            for label, ref in [("ref_a", self.ref_a), ("ref_b", self.ref_b)]:
+                if ref.geometry_type not in _surface:
+                    msg = (
+                        f"TANGENT mate requires surface geometry "
+                        f"(FACE or EDGE), got {ref.geometry_type.value} "
+                        f"on {label}"
+                    )
+                    raise ValueError(msg)
+
+    def to_dict(self) -> dict[str, Any]:
+        """Return a JSON-serializable dict."""
+        return {
+            "mate_id": self.mate_id,
+            "mate_type": self.mate_type.name,
+            "ref_a": self.ref_a.to_dict(),
+            "ref_b": self.ref_b.to_dict(),
+            "value": self.value,
+            "tolerance": self.tolerance,
+        }
+
+    @classmethod
+    def from_dict(cls, data: dict[str, Any]) -> Mate:
+        """Construct from a dict produced by :meth:`to_dict`."""
+        return cls(
+            mate_id=data["mate_id"],
+            mate_type=MateType[data["mate_type"]],
+            ref_a=GeometryRef.from_dict(data["ref_a"]),
+            ref_b=GeometryRef.from_dict(data["ref_b"]),
+            value=data.get("value", 0.0),
+            tolerance=data.get("tolerance", 1e-6),
+        )
+
+
+# ---------------------------------------------------------------------------
+# Context-dependent DOF removal
+# ---------------------------------------------------------------------------
+
+# Lookup table: (MateType, ref_a GeometryType, ref_b GeometryType) -> DOF removed.
+# Entries with None match any geometry type for that position.
+_DOF_TABLE: dict[tuple[MateType, GeometryType | None, GeometryType | None], int] = {
+    # COINCIDENT — context-dependent
+    (MateType.COINCIDENT, GeometryType.FACE, GeometryType.FACE): 3,
+    (MateType.COINCIDENT, GeometryType.POINT, GeometryType.POINT): 3,
+    (MateType.COINCIDENT, GeometryType.PLANE, GeometryType.PLANE): 3,
+    (MateType.COINCIDENT, GeometryType.EDGE, GeometryType.EDGE): 2,
+    (MateType.COINCIDENT, GeometryType.FACE, GeometryType.POINT): 1,
+    (MateType.COINCIDENT, GeometryType.POINT, GeometryType.FACE): 1,
+    # CONCENTRIC
+    (MateType.CONCENTRIC, GeometryType.AXIS, GeometryType.AXIS): 2,
+    # PARALLEL
+    (MateType.PARALLEL, GeometryType.AXIS, GeometryType.AXIS): 2,
+    (MateType.PARALLEL, GeometryType.FACE, GeometryType.FACE): 2,
+    (MateType.PARALLEL, GeometryType.PLANE, GeometryType.PLANE): 2,
+    # TANGENT
+    (MateType.TANGENT, GeometryType.FACE, GeometryType.FACE): 1,
+    (MateType.TANGENT, GeometryType.FACE, GeometryType.EDGE): 1,
+    (MateType.TANGENT, GeometryType.EDGE, GeometryType.FACE): 1,
+    # Types where DOF is always the same regardless of geometry
+    (MateType.PERPENDICULAR, None, None): 1,
+    (MateType.DISTANCE, None, None): 1,
+    (MateType.ANGLE, None, None): 1,
+    (MateType.LOCK, None, None): 6,
+}
+
+
+def dof_removed(
+    mate_type: MateType,
+    ref_a: GeometryRef,
+    ref_b: GeometryRef,
+) -> int:
+    """Return the number of DOF removed by a mate given its geometry context.
+
+    Looks up the exact ``(mate_type, ref_a.geometry_type, ref_b.geometry_type)``
+    combination first, then falls back to a wildcard ``(mate_type, None, None)``
+    entry, and finally to :attr:`MateType.default_dof`.
+
+    Args:
+        mate_type: The mate constraint type.
+        ref_a: Geometry reference on the first body.
+        ref_b: Geometry reference on the second body.
+
+    Returns:
+        Number of scalar DOF removed by this mate.
+    """
+    key = (mate_type, ref_a.geometry_type, ref_b.geometry_type)
+    if key in _DOF_TABLE:
+        return _DOF_TABLE[key]
+
+    wildcard = (mate_type, None, None)
+    if wildcard in _DOF_TABLE:
+        return _DOF_TABLE[wildcard]
+
+    return mate_type.default_dof

tests/datagen/test_analysis.py

@@ -0,0 +1,240 @@
+"""Tests for solver.datagen.analysis -- combined analysis function."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from solver.datagen.analysis import analyze_assembly
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    RigidBody,
+)
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _two_bodies() -> list[RigidBody]:
+    return [
+        RigidBody(0, position=np.array([0.0, 0.0, 0.0])),
+        RigidBody(1, position=np.array([2.0, 0.0, 0.0])),
+    ]
+
+
+def _triangle_bodies() -> list[RigidBody]:
+    return [
+        RigidBody(0, position=np.array([0.0, 0.0, 0.0])),
+        RigidBody(1, position=np.array([2.0, 0.0, 0.0])),
+        RigidBody(2, position=np.array([1.0, 1.7, 0.0])),
+    ]
+
+
+# ---------------------------------------------------------------------------
+# Scenario 1: Two bodies + revolute (underconstrained, 1 internal DOF)
+# ---------------------------------------------------------------------------
+
+
+class TestTwoBodiesRevolute:
+    """Demo scenario 1: two bodies connected by a revolute joint."""
+
+    @pytest.fixture()
+    def result(self) -> ConstraintAnalysis:
+        bodies = _two_bodies()
+        joints = [
+            Joint(
+                0,
+                body_a=0,
+                body_b=1,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array([1.0, 0.0, 0.0]),
+                anchor_b=np.array([1.0, 0.0, 0.0]),
+                axis=np.array([0.0, 0.0, 1.0]),
+            ),
+        ]
+        return analyze_assembly(bodies, joints, ground_body=0)
+
+    def test_internal_dof(self, result: ConstraintAnalysis) -> None:
+        assert result.jacobian_internal_dof == 1
+
+    def test_not_rigid(self, result: ConstraintAnalysis) -> None:
+        assert not result.is_rigid
+
+    def test_classification(self, result: ConstraintAnalysis) -> None:
+        assert result.combinatorial_classification == "underconstrained"
+
+    def test_no_redundant(self, result: ConstraintAnalysis) -> None:
+        assert result.combinatorial_redundant == 0
+
+
+# ---------------------------------------------------------------------------
+# Scenario 2: Two bodies + fixed (well-constrained, 0 internal DOF)
+# ---------------------------------------------------------------------------
+
+
+class TestTwoBodiesFixed:
+    """Demo scenario 2: two bodies connected by a fixed joint."""
+
+    @pytest.fixture()
+    def result(self) -> ConstraintAnalysis:
+        bodies = _two_bodies()
+        joints = [
+            Joint(
+                0,
+                body_a=0,
+                body_b=1,
+                joint_type=JointType.FIXED,
+                anchor_a=np.array([1.0, 0.0, 0.0]),
+                anchor_b=np.array([1.0, 0.0, 0.0]),
+            ),
+        ]
+        return analyze_assembly(bodies, joints, ground_body=0)
+
+    def test_internal_dof(self, result: ConstraintAnalysis) -> None:
+        assert result.jacobian_internal_dof == 0
+
+    def test_rigid(self, result: ConstraintAnalysis) -> None:
+        assert result.is_rigid
+
+    def test_minimally_rigid(self, result: ConstraintAnalysis) -> None:
+        assert result.is_minimally_rigid
+
+    def test_classification(self, result: ConstraintAnalysis) -> None:
+        assert result.combinatorial_classification == "well-constrained"
+
+
+# ---------------------------------------------------------------------------
+# Scenario 3: Triangle with revolute joints (overconstrained)
+# ---------------------------------------------------------------------------
+
+
+class TestTriangleRevolute:
+    """Demo scenario 3: triangle of 3 bodies + 3 revolute joints."""
+
+    @pytest.fixture()
+    def result(self) -> ConstraintAnalysis:
+        bodies = _triangle_bodies()
+        joints = [
+            Joint(
+                0,
+                body_a=0,
+                body_b=1,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array([1.0, 0.0, 0.0]),
+                anchor_b=np.array([1.0, 0.0, 0.0]),
+                axis=np.array([0.0, 0.0, 1.0]),
+            ),
+            Joint(
+                1,
+                body_a=1,
+                body_b=2,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array([1.5, 0.85, 0.0]),
+                anchor_b=np.array([1.5, 0.85, 0.0]),
+                axis=np.array([0.0, 0.0, 1.0]),
+            ),
+            Joint(
+                2,
+                body_a=2,
+                body_b=0,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array([0.5, 0.85, 0.0]),
+                anchor_b=np.array([0.5, 0.85, 0.0]),
+                axis=np.array([0.0, 0.0, 1.0]),
+            ),
+        ]
+        return analyze_assembly(bodies, joints, ground_body=0)
+
+    def test_has_redundant(self, result: ConstraintAnalysis) -> None:
+        assert result.combinatorial_redundant > 0
+
+    def test_classification(self, result: ConstraintAnalysis) -> None:
+        assert result.combinatorial_classification in ("overconstrained", "mixed")
+
+    def test_rigid(self, result: ConstraintAnalysis) -> None:
+        assert result.is_rigid
+
+    def test_numerically_dependent(self, result: ConstraintAnalysis) -> None:
+        assert len(result.numerically_dependent) > 0
+
+
+# ---------------------------------------------------------------------------
+# Scenario 4: Parallel revolute axes (geometric degeneracy)
+# ---------------------------------------------------------------------------
+
+
+class TestParallelRevoluteAxes:
+    """Demo scenario 4: parallel revolute axes create geometric degeneracies."""
+
+    @pytest.fixture()
+    def result(self) -> ConstraintAnalysis:
+        bodies = [
+            RigidBody(0, position=np.array([0.0, 0.0, 0.0])),
+            RigidBody(1, position=np.array([2.0, 0.0, 0.0])),
+            RigidBody(2, position=np.array([4.0, 0.0, 0.0])),
+        ]
+        joints = [
+            Joint(
+                0,
+                body_a=0,
+                body_b=1,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array([1.0, 0.0, 0.0]),
+                anchor_b=np.array([1.0, 0.0, 0.0]),
+                axis=np.array([0.0, 0.0, 1.0]),
+            ),
+            Joint(
+                1,
+                body_a=1,
+                body_b=2,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array([3.0, 0.0, 0.0]),
+                anchor_b=np.array([3.0, 0.0, 0.0]),
+                axis=np.array([0.0, 0.0, 1.0]),
+            ),
+        ]
+        return analyze_assembly(bodies, joints, ground_body=0)
+
+    def test_geometric_degeneracies_detected(self, result: ConstraintAnalysis) -> None:
+        """Parallel axes produce at least one geometric degeneracy."""
+        assert result.geometric_degeneracies > 0
+
+
+# ---------------------------------------------------------------------------
+# Edge cases
+# ---------------------------------------------------------------------------
+
+
+class TestNoJoints:
+    """Assembly with bodies but no joints."""
+
+    def test_all_dof_free(self) -> None:
+        bodies = _two_bodies()
+        result = analyze_assembly(bodies, [], ground_body=0)
+        # Body 1 is completely free (6 DOF), body 0 is grounded
+        assert result.jacobian_internal_dof > 0
+        assert not result.is_rigid
+
+    def test_ungrounded(self) -> None:
+        bodies = _two_bodies()
+        result = analyze_assembly(bodies, [])
+        assert result.combinatorial_classification == "underconstrained"
+
+
+class TestReturnType:
+    """Verify the return object is a proper ConstraintAnalysis."""
+
+    def test_instance(self) -> None:
+        bodies = _two_bodies()
+        joints = [Joint(0, 0, 1, JointType.FIXED)]
+        result = analyze_assembly(bodies, joints)
+        assert isinstance(result, ConstraintAnalysis)
+
+    def test_per_edge_results_populated(self) -> None:
+        bodies = _two_bodies()
+        joints = [Joint(0, 0, 1, JointType.REVOLUTE)]
+        result = analyze_assembly(bodies, joints)
+        assert len(result.per_edge_results) == 5

tests/datagen/test_dataset.py

@@ -0,0 +1,337 @@
+"""Tests for solver.datagen.dataset — dataset generation orchestration."""
+
+from __future__ import annotations
+
+import json
+import os
+import subprocess
+import sys
+from typing import TYPE_CHECKING
+
+from solver.datagen.dataset import (
+    DatasetConfig,
+    DatasetGenerator,
+    _derive_shard_seed,
+    _parse_scalar,
+    parse_simple_yaml,
+)
+
+if TYPE_CHECKING:
+    from pathlib import Path
+    from typing import Any
+
+
+# ---------------------------------------------------------------------------
+# DatasetConfig
+# ---------------------------------------------------------------------------
+
+
+class TestDatasetConfig:
+    """DatasetConfig construction and defaults."""
+
+    def test_defaults(self) -> None:
+        cfg = DatasetConfig()
+        assert cfg.num_assemblies == 100_000
+        assert cfg.seed == 42
+        assert cfg.shard_size == 1000
+        assert cfg.num_workers == 4
+
+    def test_from_dict_flat(self) -> None:
+        d: dict[str, Any] = {"num_assemblies": 500, "seed": 123}
+        cfg = DatasetConfig.from_dict(d)
+        assert cfg.num_assemblies == 500
+        assert cfg.seed == 123
+
+    def test_from_dict_nested_body_count(self) -> None:
+        d: dict[str, Any] = {"body_count": {"min": 3, "max": 20}}
+        cfg = DatasetConfig.from_dict(d)
+        assert cfg.body_count_min == 3
+        assert cfg.body_count_max == 20
+
+    def test_from_dict_flat_body_count(self) -> None:
+        d: dict[str, Any] = {"body_count_min": 5, "body_count_max": 30}
+        cfg = DatasetConfig.from_dict(d)
+        assert cfg.body_count_min == 5
+        assert cfg.body_count_max == 30
+
+    def test_from_dict_complexity_distribution(self) -> None:
+        d: dict[str, Any] = {"complexity_distribution": {"simple": 0.6, "complex": 0.4}}
+        cfg = DatasetConfig.from_dict(d)
+        assert cfg.complexity_distribution == {"simple": 0.6, "complex": 0.4}
+
+    def test_from_dict_templates(self) -> None:
+        d: dict[str, Any] = {"templates": ["chain", "tree"]}
+        cfg = DatasetConfig.from_dict(d)
+        assert cfg.templates == ["chain", "tree"]
+
+
+# ---------------------------------------------------------------------------
+# Minimal YAML parser
+# ---------------------------------------------------------------------------
+
+
+class TestParseScalar:
+    """_parse_scalar handles different value types."""
+
+    def test_int(self) -> None:
+        assert _parse_scalar("42") == 42
+
+    def test_float(self) -> None:
+        assert _parse_scalar("3.14") == 3.14
+
+    def test_bool_true(self) -> None:
+        assert _parse_scalar("true") is True
+
+    def test_bool_false(self) -> None:
+        assert _parse_scalar("false") is False
+
+    def test_string(self) -> None:
+        assert _parse_scalar("hello") == "hello"
+
+    def test_inline_comment(self) -> None:
+        assert _parse_scalar("0.4  # some comment") == 0.4
+
+
+class TestParseSimpleYaml:
+    """parse_simple_yaml handles the synthetic.yaml format."""
+
+    def test_flat_scalars(self, tmp_path: Path) -> None:
+        yaml_file = tmp_path / "test.yaml"
+        yaml_file.write_text("name: test\nnum: 42\nratio: 0.5\n")
+        result = parse_simple_yaml(str(yaml_file))
+        assert result["name"] == "test"
+        assert result["num"] == 42
+        assert result["ratio"] == 0.5
+
+    def test_nested_dict(self, tmp_path: Path) -> None:
+        yaml_file = tmp_path / "test.yaml"
+        yaml_file.write_text("body_count:\n  min: 2\n  max: 50\n")
+        result = parse_simple_yaml(str(yaml_file))
+        assert result["body_count"] == {"min": 2, "max": 50}
+
+    def test_list(self, tmp_path: Path) -> None:
+        yaml_file = tmp_path / "test.yaml"
+        yaml_file.write_text("templates:\n  - chain\n  - tree\n  - loop\n")
+        result = parse_simple_yaml(str(yaml_file))
+        assert result["templates"] == ["chain", "tree", "loop"]
+
+    def test_inline_comments(self, tmp_path: Path) -> None:
+        yaml_file = tmp_path / "test.yaml"
+        yaml_file.write_text("dist:\n  simple: 0.4  # comment\n")
+        result = parse_simple_yaml(str(yaml_file))
+        assert result["dist"]["simple"] == 0.4
+
+    def test_synthetic_yaml(self) -> None:
+        """Parse the actual project config."""
+        result = parse_simple_yaml("configs/dataset/synthetic.yaml")
+        assert result["name"] == "synthetic"
+        assert result["num_assemblies"] == 100000
+        assert isinstance(result["complexity_distribution"], dict)
+        assert isinstance(result["templates"], list)
+        assert result["shard_size"] == 1000
+
+
+# ---------------------------------------------------------------------------
+# Shard seed derivation
+# ---------------------------------------------------------------------------
+
+
+class TestShardSeedDerivation:
+    """_derive_shard_seed is deterministic and unique per shard."""
+
+    def test_deterministic(self) -> None:
+        s1 = _derive_shard_seed(42, 0)
+        s2 = _derive_shard_seed(42, 0)
+        assert s1 == s2
+
+    def test_different_shards(self) -> None:
+        s1 = _derive_shard_seed(42, 0)
+        s2 = _derive_shard_seed(42, 1)
+        assert s1 != s2
+
+    def test_different_global_seeds(self) -> None:
+        s1 = _derive_shard_seed(42, 0)
+        s2 = _derive_shard_seed(99, 0)
+        assert s1 != s2
+
+
+# ---------------------------------------------------------------------------
+# DatasetGenerator — small end-to-end tests
+# ---------------------------------------------------------------------------
+
+
+class TestDatasetGenerator:
+    """End-to-end tests with small datasets."""
+
+    def test_small_generation(self, tmp_path: Path) -> None:
+        """Generate 10 examples in a single shard."""
+        cfg = DatasetConfig(
+            num_assemblies=10,
+            output_dir=str(tmp_path / "output"),
+            shard_size=10,
+            seed=42,
+            num_workers=1,
+        )
+        DatasetGenerator(cfg).run()
+
+        shards_dir = tmp_path / "output" / "shards"
+        assert shards_dir.exists()
+        shard_files = sorted(shards_dir.glob("shard_*"))
+        assert len(shard_files) == 1
+
+        index_file = tmp_path / "output" / "index.json"
+        assert index_file.exists()
+        index = json.loads(index_file.read_text())
+        assert index["total_assemblies"] == 10
+
+        stats_file = tmp_path / "output" / "stats.json"
+        assert stats_file.exists()
+
+    def test_multi_shard(self, tmp_path: Path) -> None:
+        """Generate 20 examples across 2 shards."""
+        cfg = DatasetConfig(
+            num_assemblies=20,
+            output_dir=str(tmp_path / "output"),
+            shard_size=10,
+            seed=42,
+            num_workers=1,
+        )
+        DatasetGenerator(cfg).run()
+
+        shards_dir = tmp_path / "output" / "shards"
+        shard_files = sorted(shards_dir.glob("shard_*"))
+        assert len(shard_files) == 2
+
+    def test_resume_skips_completed(self, tmp_path: Path) -> None:
+        """Resume skips already-completed shards."""
+        cfg = DatasetConfig(
+            num_assemblies=20,
+            output_dir=str(tmp_path / "output"),
+            shard_size=10,
+            seed=42,
+            num_workers=1,
+        )
+        DatasetGenerator(cfg).run()
+
+        # Record shard modification times
+        shards_dir = tmp_path / "output" / "shards"
+        mtimes = {p.name: p.stat().st_mtime for p in shards_dir.glob("shard_*")}
+
+        # Remove stats (simulate incomplete) and re-run
+        (tmp_path / "output" / "stats.json").unlink()
+
+        DatasetGenerator(cfg).run()
+
+        # Shards should NOT have been regenerated
+        for p in shards_dir.glob("shard_*"):
+            assert p.stat().st_mtime == mtimes[p.name]
+
+        # Stats should be regenerated
+        assert (tmp_path / "output" / "stats.json").exists()
+
+    def test_checkpoint_removed(self, tmp_path: Path) -> None:
+        """Checkpoint file is cleaned up after completion."""
+        cfg = DatasetConfig(
+            num_assemblies=5,
+            output_dir=str(tmp_path / "output"),
+            shard_size=5,
+            seed=42,
+            num_workers=1,
+        )
+        DatasetGenerator(cfg).run()
+        checkpoint = tmp_path / "output" / ".checkpoint.json"
+        assert not checkpoint.exists()
+
+    def test_stats_structure(self, tmp_path: Path) -> None:
+        """stats.json has expected top-level keys."""
+        cfg = DatasetConfig(
+            num_assemblies=10,
+            output_dir=str(tmp_path / "output"),
+            shard_size=10,
+            seed=42,
+            num_workers=1,
+        )
+        DatasetGenerator(cfg).run()
+
+        stats = json.loads((tmp_path / "output" / "stats.json").read_text())
+        assert stats["total_examples"] == 10
+        assert "classification_distribution" in stats
+        assert "body_count_histogram" in stats
+        assert "joint_type_distribution" in stats
+        assert "dof_statistics" in stats
+        assert "geometric_degeneracy" in stats
+        assert "rigidity" in stats
+
+    def test_index_structure(self, tmp_path: Path) -> None:
+        """index.json has expected format."""
+        cfg = DatasetConfig(
+            num_assemblies=15,
+            output_dir=str(tmp_path / "output"),
+            shard_size=10,
+            seed=42,
+            num_workers=1,
+        )
+        DatasetGenerator(cfg).run()
+
+        index = json.loads((tmp_path / "output" / "index.json").read_text())
+        assert index["format_version"] == 1
+        assert index["total_assemblies"] == 15
+        assert index["total_shards"] == 2
+        assert "shards" in index
+        for _name, info in index["shards"].items():
+            assert "start_id" in info
+            assert "count" in info
+
+    def test_deterministic_output(self, tmp_path: Path) -> None:
+        """Same seed produces same results."""
+        for run_dir in ("run1", "run2"):
+            cfg = DatasetConfig(
+                num_assemblies=5,
+                output_dir=str(tmp_path / run_dir),
+                shard_size=5,
+                seed=42,
+                num_workers=1,
+            )
+            DatasetGenerator(cfg).run()
+
+        s1 = json.loads((tmp_path / "run1" / "stats.json").read_text())
+        s2 = json.loads((tmp_path / "run2" / "stats.json").read_text())
+        assert s1["total_examples"] == s2["total_examples"]
+        assert s1["classification_distribution"] == s2["classification_distribution"]
+
+
+# ---------------------------------------------------------------------------
+# CLI integration test
+# ---------------------------------------------------------------------------
+
+
+class TestCLI:
+    """Run the script via subprocess."""
+
+    def test_argparse_mode(self, tmp_path: Path) -> None:
+        result = subprocess.run(
+            [
+                sys.executable,
+                "scripts/generate_synthetic.py",
+                "--num-assemblies",
+                "5",
+                "--output-dir",
+                str(tmp_path / "cli_out"),
+                "--shard-size",
+                "5",
+                "--num-workers",
+                "1",
+                "--seed",
+                "42",
+            ],
+            capture_output=True,
+            text=True,
+            cwd="/home/developer",
+            timeout=120,
+            env={**os.environ, "PYTHONPATH": "/home/developer"},
+        )
+        assert result.returncode == 0, (
+            f"CLI failed:\nstdout: {result.stdout}\nstderr: {result.stderr}"
+        )
+        assert (tmp_path / "cli_out" / "index.json").exists()
+        assert (tmp_path / "cli_out" / "stats.json").exists()

tests/datagen/test_generator.py

@@ -0,0 +1,682 @@
+"""Tests for solver.datagen.generator -- synthetic assembly generation."""
+
+from __future__ import annotations
+
+from typing import ClassVar
+
+import numpy as np
+import pytest
+
+from solver.datagen.generator import COMPLEXITY_RANGES, SyntheticAssemblyGenerator
+from solver.datagen.types import JointType
+
+# ---------------------------------------------------------------------------
+# Original generators (chain / rigid / overconstrained)
+# ---------------------------------------------------------------------------
+
+
+class TestChainAssembly:
+    """generate_chain_assembly produces valid underconstrained chains."""
+
+    def test_returns_three_tuple(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        bodies, joints, _analysis = gen.generate_chain_assembly(4)
+        assert len(bodies) == 4
+        assert len(joints) == 3
+
+    def test_chain_underconstrained(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        _, _, analysis = gen.generate_chain_assembly(4)
+        assert analysis.combinatorial_classification == "underconstrained"
+
+    def test_chain_body_ids(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        bodies, _, _ = gen.generate_chain_assembly(5)
+        ids = [b.body_id for b in bodies]
+        assert ids == [0, 1, 2, 3, 4]
+
+    def test_chain_joint_connectivity(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        _, joints, _ = gen.generate_chain_assembly(4)
+        for i, j in enumerate(joints):
+            assert j.body_a == i
+            assert j.body_b == i + 1
+
+    def test_chain_custom_joint_type(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        _, joints, _ = gen.generate_chain_assembly(
+            3,
+            joint_type=JointType.BALL,
+        )
+        assert all(j.joint_type is JointType.BALL for j in joints)
+
+
+class TestRigidAssembly:
+    """generate_rigid_assembly produces rigid assemblies."""
+
+    def test_rigid(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_rigid_assembly(4)
+        assert analysis.is_rigid
+
+    def test_spanning_tree_structure(self) -> None:
+        """n bodies should have at least n-1 joints (spanning tree)."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, joints, _ = gen.generate_rigid_assembly(5)
+        assert len(joints) >= len(bodies) - 1
+
+    def test_deterministic(self) -> None:
+        """Same seed produces same results."""
+        g1 = SyntheticAssemblyGenerator(seed=99)
+        g2 = SyntheticAssemblyGenerator(seed=99)
+        _, j1, a1 = g1.generate_rigid_assembly(4)
+        _, j2, a2 = g2.generate_rigid_assembly(4)
+        assert a1.jacobian_rank == a2.jacobian_rank
+        assert len(j1) == len(j2)
+
+
+class TestOverconstrainedAssembly:
+    """generate_overconstrained_assembly adds redundant constraints."""
+
+    def test_has_redundant(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_overconstrained_assembly(
+            4,
+            extra_joints=2,
+        )
+        assert analysis.combinatorial_redundant > 0
+
+    def test_extra_joints_added(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints_base, _ = gen.generate_rigid_assembly(4)
+
+        gen2 = SyntheticAssemblyGenerator(seed=42)
+        _, joints_over, _ = gen2.generate_overconstrained_assembly(
+            4,
+            extra_joints=3,
+        )
+        # Overconstrained has base joints + extra
+        assert len(joints_over) > len(joints_base)
+
+
+# ---------------------------------------------------------------------------
+# New topology generators
+# ---------------------------------------------------------------------------
+
+
+class TestTreeAssembly:
+    """generate_tree_assembly produces tree-structured assemblies."""
+
+    def test_body_and_joint_counts(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, joints, _ = gen.generate_tree_assembly(6)
+        assert len(bodies) == 6
+        assert len(joints) == 5  # n - 1
+
+    def test_underconstrained(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_tree_assembly(6)
+        assert analysis.combinatorial_classification == "underconstrained"
+
+    def test_branching_factor(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, joints, _ = gen.generate_tree_assembly(
+            10,
+            branching_factor=2,
+        )
+        assert len(bodies) == 10
+        assert len(joints) == 9
+
+    def test_mixed_joint_types(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        types = [JointType.REVOLUTE, JointType.BALL, JointType.FIXED]
+        _, joints, _ = gen.generate_tree_assembly(10, joint_types=types)
+        used = {j.joint_type for j in joints}
+        # With 9 joints and 3 types, very likely to use at least 2
+        assert len(used) >= 2
+
+    def test_single_joint_type(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_tree_assembly(
+            5,
+            joint_types=JointType.BALL,
+        )
+        assert all(j.joint_type is JointType.BALL for j in joints)
+
+    def test_sequential_body_ids(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, _, _ = gen.generate_tree_assembly(7)
+        assert [b.body_id for b in bodies] == list(range(7))
+
+
+class TestLoopAssembly:
+    """generate_loop_assembly produces closed-loop assemblies."""
+
+    def test_body_and_joint_counts(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, joints, _ = gen.generate_loop_assembly(5)
+        assert len(bodies) == 5
+        assert len(joints) == 5  # n joints for n bodies
+
+    def test_has_redundancy(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_loop_assembly(5)
+        assert analysis.combinatorial_redundant > 0
+
+    def test_wrap_around_connectivity(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_loop_assembly(4)
+        edges = {(j.body_a, j.body_b) for j in joints}
+        assert (0, 1) in edges
+        assert (1, 2) in edges
+        assert (2, 3) in edges
+        assert (3, 0) in edges  # wrap-around
+
+    def test_minimum_bodies_error(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        with pytest.raises(ValueError, match="at least 3"):
+            gen.generate_loop_assembly(2)
+
+    def test_mixed_joint_types(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        types = [JointType.REVOLUTE, JointType.FIXED]
+        _, joints, _ = gen.generate_loop_assembly(8, joint_types=types)
+        used = {j.joint_type for j in joints}
+        assert len(used) >= 2
+
+
+class TestStarAssembly:
+    """generate_star_assembly produces hub-and-spoke assemblies."""
+
+    def test_body_and_joint_counts(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, joints, _ = gen.generate_star_assembly(6)
+        assert len(bodies) == 6
+        assert len(joints) == 5  # n - 1
+
+    def test_all_joints_connect_to_hub(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_star_assembly(6)
+        for j in joints:
+            assert j.body_a == 0 or j.body_b == 0
+
+    def test_underconstrained(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_star_assembly(5)
+        assert analysis.combinatorial_classification == "underconstrained"
+
+    def test_minimum_bodies_error(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        with pytest.raises(ValueError, match="at least 2"):
+            gen.generate_star_assembly(1)
+
+    def test_hub_at_origin(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, _, _ = gen.generate_star_assembly(4)
+        np.testing.assert_array_equal(bodies[0].position, np.zeros(3))
+
+
+class TestMixedAssembly:
+    """generate_mixed_assembly produces tree+loop hybrid assemblies."""
+
+    def test_more_joints_than_tree(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, joints, _ = gen.generate_mixed_assembly(
+            8,
+            edge_density=0.3,
+        )
+        assert len(joints) > len(bodies) - 1
+
+    def test_density_zero_is_tree(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _bodies, joints, _ = gen.generate_mixed_assembly(
+            5,
+            edge_density=0.0,
+        )
+        assert len(joints) == 4  # spanning tree only
+
+    def test_density_validation(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        with pytest.raises(ValueError, match="must be in"):
+            gen.generate_mixed_assembly(5, edge_density=1.5)
+        with pytest.raises(ValueError, match="must be in"):
+            gen.generate_mixed_assembly(5, edge_density=-0.1)
+
+    def test_no_duplicate_edges(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_mixed_assembly(6, edge_density=0.5)
+        edges = [frozenset([j.body_a, j.body_b]) for j in joints]
+        assert len(edges) == len(set(edges))
+
+    def test_high_density(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _bodies, joints, _ = gen.generate_mixed_assembly(
+            5,
+            edge_density=1.0,
+        )
+        # Fully connected: 5*(5-1)/2 = 10 edges
+        assert len(joints) == 10
+
+
+# ---------------------------------------------------------------------------
+# Axis sampling strategies
+# ---------------------------------------------------------------------------
+
+
+class TestAxisStrategy:
+    """Axis sampling strategies produce valid unit vectors."""
+
+    def test_cardinal_axis_from_six(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        axes = {tuple(gen._cardinal_axis()) for _ in range(200)}
+        expected = {
+            (1, 0, 0),
+            (-1, 0, 0),
+            (0, 1, 0),
+            (0, -1, 0),
+            (0, 0, 1),
+            (0, 0, -1),
+        }
+        assert axes == expected
+
+    def test_random_axis_unit_norm(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        for _ in range(50):
+            axis = gen._sample_axis("random")
+            assert abs(np.linalg.norm(axis) - 1.0) < 1e-10
+
+    def test_near_parallel_close_to_base(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        base = np.array([0.0, 0.0, 1.0])
+        for _ in range(50):
+            axis = gen._near_parallel_axis(base)
+            assert abs(np.linalg.norm(axis) - 1.0) < 1e-10
+            assert np.dot(axis, base) > 0.95
+
+    def test_sample_axis_cardinal(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        axis = gen._sample_axis("cardinal")
+        cardinals = [
+            np.array(v, dtype=float)
+            for v in [(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1)]
+        ]
+        assert any(np.allclose(axis, c) for c in cardinals)
+
+    def test_sample_axis_near_parallel(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=0)
+        axis = gen._sample_axis("near_parallel")
+        z = np.array([0.0, 0.0, 1.0])
+        assert np.dot(axis, z) > 0.95
+
+
+# ---------------------------------------------------------------------------
+# Geometric diversity: orientations
+# ---------------------------------------------------------------------------
+
+
+class TestRandomOrientations:
+    """Bodies should have non-identity orientations."""
+
+    def test_bodies_have_orientations(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, _, _ = gen.generate_tree_assembly(5)
+        non_identity = sum(1 for b in bodies if not np.allclose(b.orientation, np.eye(3)))
+        assert non_identity >= 3
+
+    def test_orientations_are_valid_rotations(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        bodies, _, _ = gen.generate_star_assembly(6)
+        for b in bodies:
+            r = b.orientation
+            # R^T R == I
+            np.testing.assert_allclose(r.T @ r, np.eye(3), atol=1e-10)
+            # det(R) == 1
+            assert abs(np.linalg.det(r) - 1.0) < 1e-10
+
+    def test_all_generators_set_orientations(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        # Chain
+        bodies, _, _ = gen.generate_chain_assembly(3)
+        assert not np.allclose(bodies[1].orientation, np.eye(3))
+        # Loop
+        bodies, _, _ = gen.generate_loop_assembly(4)
+        assert not np.allclose(bodies[1].orientation, np.eye(3))
+        # Mixed
+        bodies, _, _ = gen.generate_mixed_assembly(4)
+        assert not np.allclose(bodies[1].orientation, np.eye(3))
+
+
+# ---------------------------------------------------------------------------
+# Geometric diversity: grounded parameter
+# ---------------------------------------------------------------------------
+
+
+class TestGroundedParameter:
+    """Grounded parameter controls ground_body in analysis."""
+
+    def test_chain_grounded_default(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_chain_assembly(4)
+        assert analysis.combinatorial_dof >= 0
+
+    def test_chain_floating(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, _, analysis = gen.generate_chain_assembly(
+            4,
+            grounded=False,
+        )
+        # Floating: 6 trivial DOF not subtracted by ground
+        assert analysis.combinatorial_dof >= 6
+
+    def test_floating_vs_grounded_dof_difference(self) -> None:
+        gen1 = SyntheticAssemblyGenerator(seed=42)
+        _, _, a_grounded = gen1.generate_chain_assembly(4, grounded=True)
+        gen2 = SyntheticAssemblyGenerator(seed=42)
+        _, _, a_floating = gen2.generate_chain_assembly(4, grounded=False)
+        # Floating should have higher DOF due to missing ground constraint
+        assert a_floating.combinatorial_dof > a_grounded.combinatorial_dof
+
+    @pytest.mark.parametrize(
+        "gen_method",
+        [
+            "generate_chain_assembly",
+            "generate_rigid_assembly",
+            "generate_tree_assembly",
+            "generate_loop_assembly",
+            "generate_star_assembly",
+            "generate_mixed_assembly",
+        ],
+    )
+    def test_all_generators_accept_grounded(
+        self,
+        gen_method: str,
+    ) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        method = getattr(gen, gen_method)
+        n = 4
+        # Should not raise
+        if gen_method in ("generate_chain_assembly", "generate_rigid_assembly"):
+            method(n, grounded=False)
+        else:
+            method(n, grounded=False)
+
+
+# ---------------------------------------------------------------------------
+# Geometric diversity: parallel axis injection
+# ---------------------------------------------------------------------------
+
+
+class TestParallelAxisInjection:
+    """parallel_axis_prob causes shared axis direction."""
+
+    def test_parallel_axes_similar(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_chain_assembly(
+            6,
+            parallel_axis_prob=1.0,
+        )
+        base = joints[0].axis
+        for j in joints[1:]:
+            # Near-parallel: |dot| close to 1
+            assert abs(np.dot(j.axis, base)) > 0.9
+
+    def test_zero_prob_no_forced_parallel(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_chain_assembly(
+            6,
+            parallel_axis_prob=0.0,
+        )
+        base = joints[0].axis
+        dots = [abs(np.dot(j.axis, base)) for j in joints[1:]]
+        # With 5 random axes, extremely unlikely all are parallel
+        assert min(dots) < 0.95
+
+    def test_parallel_on_loop(self) -> None:
+        """Parallel axes on a loop assembly."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_loop_assembly(
+            5,
+            parallel_axis_prob=1.0,
+        )
+        base = joints[0].axis
+        for j in joints[1:]:
+            assert abs(np.dot(j.axis, base)) > 0.9
+
+    def test_parallel_on_star(self) -> None:
+        """Parallel axes on a star assembly."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        _, joints, _ = gen.generate_star_assembly(
+            5,
+            parallel_axis_prob=1.0,
+        )
+        base = joints[0].axis
+        for j in joints[1:]:
+            assert abs(np.dot(j.axis, base)) > 0.9
+
+
+# ---------------------------------------------------------------------------
+# Complexity tiers
+# ---------------------------------------------------------------------------
+
+
+class TestComplexityTiers:
+    """Complexity tier parameter on batch generation."""
+
+    def test_simple_range(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(20, complexity_tier="simple")
+        lo, hi = COMPLEXITY_RANGES["simple"]
+        for ex in batch:
+            assert lo <= ex["n_bodies"] < hi
+
+    def test_medium_range(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(20, complexity_tier="medium")
+        lo, hi = COMPLEXITY_RANGES["medium"]
+        for ex in batch:
+            assert lo <= ex["n_bodies"] < hi
+
+    def test_complex_range(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(3, complexity_tier="complex")
+        lo, hi = COMPLEXITY_RANGES["complex"]
+        for ex in batch:
+            assert lo <= ex["n_bodies"] < hi
+
+    def test_tier_overrides_range(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(
+            10,
+            n_bodies_range=(2, 3),
+            complexity_tier="medium",
+        )
+        lo, hi = COMPLEXITY_RANGES["medium"]
+        for ex in batch:
+            assert lo <= ex["n_bodies"] < hi
+
+
+# ---------------------------------------------------------------------------
+# Training batch
+# ---------------------------------------------------------------------------
+
+
+class TestTrainingBatch:
+    """generate_training_batch produces well-structured examples."""
+
+    EXPECTED_KEYS: ClassVar[set[str]] = {
+        "example_id",
+        "generator_type",
+        "grounded",
+        "n_bodies",
+        "n_joints",
+        "body_positions",
+        "body_orientations",
+        "joints",
+        "joint_labels",
+        "labels",
+        "assembly_classification",
+        "is_rigid",
+        "is_minimally_rigid",
+        "internal_dof",
+        "geometric_degeneracies",
+    }
+
+    VALID_GEN_TYPES: ClassVar[set[str]] = {
+        "chain",
+        "rigid",
+        "overconstrained",
+        "tree",
+        "loop",
+        "star",
+        "mixed",
+    }
+
+    def test_batch_size(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(20)
+        assert len(batch) == 20
+
+    def test_example_keys(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(10)
+        for ex in batch:
+            assert set(ex.keys()) == self.EXPECTED_KEYS
+
+    def test_example_ids_sequential(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(15)
+        assert [ex["example_id"] for ex in batch] == list(range(15))
+
+    def test_generator_type_valid(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(50)
+        for ex in batch:
+            assert ex["generator_type"] in self.VALID_GEN_TYPES
+
+    def test_generator_type_diversity(self) -> None:
+        """100-sample batch should use at least 5 of 7 generator types."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(100)
+        types = {ex["generator_type"] for ex in batch}
+        assert len(types) >= 5
+
+    def test_default_body_range(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(30)
+        for ex in batch:
+            # default (3, 8), but loop/star may clamp
+            assert 2 <= ex["n_bodies"] <= 7
+
+    def test_joint_label_consistency(self) -> None:
+        """independent + redundant == total for every joint."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(30)
+        for ex in batch:
+            for label in ex["joint_labels"].values():
+                total = label["independent_constraints"] + label["redundant_constraints"]
+                assert total == label["total_constraints"]
+
+    def test_body_orientations_present(self) -> None:
+        """Each example includes body_orientations as 3x3 lists."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(10)
+        for ex in batch:
+            orients = ex["body_orientations"]
+            assert len(orients) == ex["n_bodies"]
+            for o in orients:
+                assert len(o) == 3
+                assert len(o[0]) == 3
+
+    def test_labels_structure(self) -> None:
+        """Each example has labels dict with expected sub-keys."""
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(10)
+        for ex in batch:
+            labels = ex["labels"]
+            assert "per_constraint" in labels
+            assert "per_joint" in labels
+            assert "per_body" in labels
+            assert "assembly" in labels
+
+    def test_grounded_field_present(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(10)
+        for ex in batch:
+            assert isinstance(ex["grounded"], bool)
+
+
+# ---------------------------------------------------------------------------
+# Batch grounded ratio
+# ---------------------------------------------------------------------------
+
+
+class TestBatchGroundedRatio:
+    """grounded_ratio controls the mix in batch generation."""
+
+    def test_all_grounded(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(20, grounded_ratio=1.0)
+        assert all(ex["grounded"] for ex in batch)
+
+    def test_none_grounded(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(20, grounded_ratio=0.0)
+        assert not any(ex["grounded"] for ex in batch)
+
+    def test_mixed_ratio(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(100, grounded_ratio=0.5)
+        grounded_count = sum(1 for ex in batch if ex["grounded"])
+        # With 100 samples and p=0.5, should be roughly 50 +/- 20
+        assert 20 < grounded_count < 80
+
+    def test_batch_axis_strategy_cardinal(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(
+            10,
+            axis_strategy="cardinal",
+        )
+        assert len(batch) == 10
+
+    def test_batch_parallel_axis_prob(self) -> None:
+        gen = SyntheticAssemblyGenerator(seed=42)
+        batch = gen.generate_training_batch(
+            10,
+            parallel_axis_prob=0.5,
+        )
+        assert len(batch) == 10
+
+
+# ---------------------------------------------------------------------------
+# Seed reproducibility
+# ---------------------------------------------------------------------------
+
+
+class TestSeedReproducibility:
+    """Different seeds produce different results."""
+
+    def test_different_seeds_differ(self) -> None:
+        g1 = SyntheticAssemblyGenerator(seed=1)
+        g2 = SyntheticAssemblyGenerator(seed=2)
+        b1 = g1.generate_training_batch(
+            batch_size=5,
+            n_bodies_range=(3, 6),
+        )
+        b2 = g2.generate_training_batch(
+            batch_size=5,
+            n_bodies_range=(3, 6),
+        )
+        c1 = [ex["assembly_classification"] for ex in b1]
+        c2 = [ex["assembly_classification"] for ex in b2]
+        r1 = [ex["is_rigid"] for ex in b1]
+        r2 = [ex["is_rigid"] for ex in b2]
+        assert c1 != c2 or r1 != r2
+
+    def test_same_seed_identical(self) -> None:
+        g1 = SyntheticAssemblyGenerator(seed=123)
+        g2 = SyntheticAssemblyGenerator(seed=123)
+        b1, j1, _ = g1.generate_tree_assembly(5)
+        b2, j2, _ = g2.generate_tree_assembly(5)
+        for a, b in zip(b1, b2, strict=True):
+            np.testing.assert_array_almost_equal(a.position, b.position)
+        assert len(j1) == len(j2)

tests/datagen/test_jacobian.py

@@ -0,0 +1,267 @@
+"""Tests for solver.datagen.jacobian -- Jacobian rank verification."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from solver.datagen.jacobian import JacobianVerifier
+from solver.datagen.types import Joint, JointType, RigidBody
+
+# ---------------------------------------------------------------------------
+# Fixtures
+# ---------------------------------------------------------------------------
+
+
+def _two_bodies() -> list[RigidBody]:
+    return [
+        RigidBody(0, position=np.array([0.0, 0.0, 0.0])),
+        RigidBody(1, position=np.array([2.0, 0.0, 0.0])),
+    ]
+
+
+def _three_bodies() -> list[RigidBody]:
+    return [
+        RigidBody(0, position=np.array([0.0, 0.0, 0.0])),
+        RigidBody(1, position=np.array([2.0, 0.0, 0.0])),
+        RigidBody(2, position=np.array([4.0, 0.0, 0.0])),
+    ]
+
+
+# ---------------------------------------------------------------------------
+# Tests
+# ---------------------------------------------------------------------------
+
+
+class TestJacobianShape:
+    """Verify Jacobian matrix dimensions for each joint type."""
+
+    @pytest.mark.parametrize(
+        "joint_type,expected_rows",
+        [
+            (JointType.FIXED, 6),
+            (JointType.REVOLUTE, 5),
+            (JointType.CYLINDRICAL, 4),
+            (JointType.SLIDER, 5),
+            (JointType.BALL, 3),
+            (JointType.PLANAR, 3),
+            (JointType.SCREW, 5),
+            (JointType.UNIVERSAL, 4),
+            (JointType.PARALLEL, 3),
+            (JointType.PERPENDICULAR, 1),
+            (JointType.DISTANCE, 1),
+        ],
+    )
+    def test_row_count(self, joint_type: JointType, expected_rows: int) -> None:
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        joint = Joint(
+            joint_id=0,
+            body_a=0,
+            body_b=1,
+            joint_type=joint_type,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([1.0, 0.0, 0.0]),
+            axis=np.array([0.0, 0.0, 1.0]),
+        )
+        n_added = v.add_joint_constraints(joint)
+        assert n_added == expected_rows
+
+        j = v.get_jacobian()
+        assert j.shape == (expected_rows, 12)  # 2 bodies * 6 cols
+
+
+class TestNumericalRank:
+    """Numerical rank checks for known configurations."""
+
+    def test_fixed_joint_rank_six(self) -> None:
+        """Fixed joint between 2 bodies: rank = 6."""
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        j = Joint(
+            joint_id=0,
+            body_a=0,
+            body_b=1,
+            joint_type=JointType.FIXED,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([1.0, 0.0, 0.0]),
+        )
+        v.add_joint_constraints(j)
+        assert v.numerical_rank() == 6
+
+    def test_revolute_joint_rank_five(self) -> None:
+        """Revolute joint between 2 bodies: rank = 5."""
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        j = Joint(
+            joint_id=0,
+            body_a=0,
+            body_b=1,
+            joint_type=JointType.REVOLUTE,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([1.0, 0.0, 0.0]),
+            axis=np.array([0.0, 0.0, 1.0]),
+        )
+        v.add_joint_constraints(j)
+        assert v.numerical_rank() == 5
+
+    def test_ball_joint_rank_three(self) -> None:
+        """Ball joint between 2 bodies: rank = 3."""
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        j = Joint(
+            joint_id=0,
+            body_a=0,
+            body_b=1,
+            joint_type=JointType.BALL,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([1.0, 0.0, 0.0]),
+        )
+        v.add_joint_constraints(j)
+        assert v.numerical_rank() == 3
+
+    def test_empty_jacobian_rank_zero(self) -> None:
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        assert v.numerical_rank() == 0
+
+
+class TestParallelAxesDegeneracy:
+    """Parallel revolute axes create geometric dependencies."""
+
+    def _four_body_loop(self) -> list[RigidBody]:
+        return [
+            RigidBody(0, position=np.array([0.0, 0.0, 0.0])),
+            RigidBody(1, position=np.array([2.0, 0.0, 0.0])),
+            RigidBody(2, position=np.array([2.0, 2.0, 0.0])),
+            RigidBody(3, position=np.array([0.0, 2.0, 0.0])),
+        ]
+
+    def _loop_joints(self, axes: list[np.ndarray]) -> list[Joint]:
+        pairs = [(0, 1, [1, 0, 0]), (1, 2, [2, 1, 0]), (2, 3, [1, 2, 0]), (3, 0, [0, 1, 0])]
+        return [
+            Joint(
+                joint_id=i,
+                body_a=a,
+                body_b=b,
+                joint_type=JointType.REVOLUTE,
+                anchor_a=np.array(anc, dtype=float),
+                anchor_b=np.array(anc, dtype=float),
+                axis=axes[i],
+            )
+            for i, (a, b, anc) in enumerate(pairs)
+        ]
+
+    def test_parallel_has_lower_rank(self) -> None:
+        """4-body closed loop: all-parallel revolute axes produce lower
+        Jacobian rank than mixed axes due to geometric dependency."""
+        bodies = self._four_body_loop()
+        z_axis = np.array([0.0, 0.0, 1.0])
+
+        # All axes parallel to Z
+        v_par = JacobianVerifier(bodies)
+        for j in self._loop_joints([z_axis] * 4):
+            v_par.add_joint_constraints(j)
+        rank_par = v_par.numerical_rank()
+
+        # Mixed axes
+        mixed = [
+            np.array([0.0, 0.0, 1.0]),
+            np.array([0.0, 1.0, 0.0]),
+            np.array([0.0, 0.0, 1.0]),
+            np.array([1.0, 0.0, 0.0]),
+        ]
+        v_mix = JacobianVerifier(bodies)
+        for j in self._loop_joints(mixed):
+            v_mix.add_joint_constraints(j)
+        rank_mix = v_mix.numerical_rank()
+
+        assert rank_par < rank_mix
+
+
+class TestFindDependencies:
+    """Dependency detection."""
+
+    def test_fixed_joint_no_dependencies(self) -> None:
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        j = Joint(
+            joint_id=0,
+            body_a=0,
+            body_b=1,
+            joint_type=JointType.FIXED,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([1.0, 0.0, 0.0]),
+        )
+        v.add_joint_constraints(j)
+        assert v.find_dependencies() == []
+
+    def test_duplicate_fixed_has_dependencies(self) -> None:
+        """Two fixed joints on same pair: second is fully dependent."""
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        for jid in range(2):
+            v.add_joint_constraints(
+                Joint(
+                    joint_id=jid,
+                    body_a=0,
+                    body_b=1,
+                    joint_type=JointType.FIXED,
+                    anchor_a=np.array([1.0, 0.0, 0.0]),
+                    anchor_b=np.array([1.0, 0.0, 0.0]),
+                )
+            )
+        deps = v.find_dependencies()
+        assert len(deps) == 6  # Second fixed joint entirely redundant
+
+    def test_empty_no_dependencies(self) -> None:
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        assert v.find_dependencies() == []
+
+
+class TestRowLabels:
+    """Row label metadata."""
+
+    def test_labels_match_rows(self) -> None:
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        j = Joint(
+            joint_id=7,
+            body_a=0,
+            body_b=1,
+            joint_type=JointType.REVOLUTE,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([1.0, 0.0, 0.0]),
+            axis=np.array([0.0, 0.0, 1.0]),
+        )
+        v.add_joint_constraints(j)
+        assert len(v.row_labels) == 5
+        assert all(lab["joint_id"] == 7 for lab in v.row_labels)
+
+
+class TestPerpendicularPair:
+    """Internal _perpendicular_pair utility."""
+
+    @pytest.mark.parametrize(
+        "axis",
+        [
+            np.array([1.0, 0.0, 0.0]),
+            np.array([0.0, 1.0, 0.0]),
+            np.array([0.0, 0.0, 1.0]),
+            np.array([1.0, 1.0, 1.0]) / np.sqrt(3),
+        ],
+    )
+    def test_orthonormal(self, axis: np.ndarray) -> None:
+        bodies = _two_bodies()
+        v = JacobianVerifier(bodies)
+        t1, t2 = v._perpendicular_pair(axis)
+
+        # All unit length
+        np.testing.assert_allclose(np.linalg.norm(t1), 1.0, atol=1e-12)
+        np.testing.assert_allclose(np.linalg.norm(t2), 1.0, atol=1e-12)
+
+        # Mutually perpendicular
+        np.testing.assert_allclose(np.dot(axis, t1), 0.0, atol=1e-12)
+        np.testing.assert_allclose(np.dot(axis, t2), 0.0, atol=1e-12)
+        np.testing.assert_allclose(np.dot(t1, t2), 0.0, atol=1e-12)

tests/datagen/test_labeling.py

@@ -0,0 +1,346 @@
+"""Tests for solver.datagen.labeling -- ground truth labeling pipeline."""
+
+from __future__ import annotations
+
+import json
+
+import numpy as np
+
+from solver.datagen.labeling import (
+    label_assembly,
+)
+from solver.datagen.types import Joint, JointType, RigidBody
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _make_bodies(*positions: tuple[float, ...]) -> list[RigidBody]:
+    return [RigidBody(body_id=i, position=np.array(pos)) for i, pos in enumerate(positions)]
+
+
+def _make_joint(
+    jid: int,
+    a: int,
+    b: int,
+    jtype: JointType,
+    axis: tuple[float, ...] = (0.0, 0.0, 1.0),
+) -> Joint:
+    return Joint(
+        joint_id=jid,
+        body_a=a,
+        body_b=b,
+        joint_type=jtype,
+        anchor_a=np.zeros(3),
+        anchor_b=np.zeros(3),
+        axis=np.array(axis),
+    )
+
+
+# ---------------------------------------------------------------------------
+# Per-constraint labels
+# ---------------------------------------------------------------------------
+
+
+class TestConstraintLabels:
+    """Per-constraint labels combine pebble game and Jacobian results."""
+
+    def test_fixed_joint_all_independent(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.FIXED)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert len(labels.per_constraint) == 6
+        for cl in labels.per_constraint:
+            assert cl.pebble_independent is True
+            assert cl.jacobian_independent is True
+
+    def test_revolute_joint_all_independent(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert len(labels.per_constraint) == 5
+        for cl in labels.per_constraint:
+            assert cl.pebble_independent is True
+            assert cl.jacobian_independent is True
+
+    def test_chain_constraint_count(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (4, 0, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.REVOLUTE),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert len(labels.per_constraint) == 10  # 5 + 5
+
+    def test_constraint_joint_ids(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (4, 0, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.BALL),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        j0_constraints = [c for c in labels.per_constraint if c.joint_id == 0]
+        j1_constraints = [c for c in labels.per_constraint if c.joint_id == 1]
+        assert len(j0_constraints) == 5  # revolute
+        assert len(j1_constraints) == 3  # ball
+
+    def test_overconstrained_has_pebble_redundant(self) -> None:
+        """Triangle with revolute joints: some constraints redundant."""
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (1, 2, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.REVOLUTE),
+            _make_joint(2, 2, 0, JointType.REVOLUTE),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        pebble_redundant = sum(1 for c in labels.per_constraint if not c.pebble_independent)
+        assert pebble_redundant > 0
+
+
+# ---------------------------------------------------------------------------
+# Per-joint labels
+# ---------------------------------------------------------------------------
+
+
+class TestJointLabels:
+    """Per-joint aggregated labels."""
+
+    def test_fixed_joint_counts(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.FIXED)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert len(labels.per_joint) == 1
+        jl = labels.per_joint[0]
+        assert jl.joint_id == 0
+        assert jl.independent_count == 6
+        assert jl.redundant_count == 0
+        assert jl.total == 6
+
+    def test_overconstrained_has_redundant_joints(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (1, 2, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.REVOLUTE),
+            _make_joint(2, 2, 0, JointType.REVOLUTE),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        total_redundant = sum(jl.redundant_count for jl in labels.per_joint)
+        assert total_redundant > 0
+
+    def test_joint_total_equals_dof(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.BALL)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        jl = labels.per_joint[0]
+        assert jl.total == 3  # ball has 3 DOF
+
+
+# ---------------------------------------------------------------------------
+# Per-body DOF labels
+# ---------------------------------------------------------------------------
+
+
+class TestBodyDofLabels:
+    """Per-body DOF signatures from nullspace projection."""
+
+    def test_fixed_joint_grounded_both_zero(self) -> None:
+        """Two bodies + fixed joint + grounded: both fully constrained."""
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.FIXED)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        for bl in labels.per_body:
+            assert bl.translational_dof == 0
+            assert bl.rotational_dof == 0
+
+    def test_revolute_has_rotational_dof(self) -> None:
+        """Two bodies + revolute + grounded: body 1 has rotational DOF."""
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        b1 = next(b for b in labels.per_body if b.body_id == 1)
+        # Revolute allows 1 rotation DOF
+        assert b1.rotational_dof >= 1
+
+    def test_dof_bounds(self) -> None:
+        """All DOF values should be in [0, 3]."""
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (4, 0, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.REVOLUTE),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        for bl in labels.per_body:
+            assert 0 <= bl.translational_dof <= 3
+            assert 0 <= bl.rotational_dof <= 3
+
+    def test_floating_more_dof_than_grounded(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        grounded = label_assembly(bodies, joints, ground_body=0)
+        floating = label_assembly(bodies, joints, ground_body=None)
+        g_total = sum(b.translational_dof + b.rotational_dof for b in grounded.per_body)
+        f_total = sum(b.translational_dof + b.rotational_dof for b in floating.per_body)
+        assert f_total > g_total
+
+    def test_grounded_body_zero_dof(self) -> None:
+        """The grounded body should have 0 DOF."""
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        b0 = next(b for b in labels.per_body if b.body_id == 0)
+        assert b0.translational_dof == 0
+        assert b0.rotational_dof == 0
+
+    def test_body_count_matches(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (4, 0, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.BALL),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert len(labels.per_body) == 3
+
+
+# ---------------------------------------------------------------------------
+# Assembly label
+# ---------------------------------------------------------------------------
+
+
+class TestAssemblyLabel:
+    """Assembly-wide summary labels."""
+
+    def test_underconstrained_chain(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (4, 0, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.REVOLUTE),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert labels.assembly.classification == "underconstrained"
+        assert labels.assembly.is_rigid is False
+
+    def test_well_constrained(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.FIXED)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert labels.assembly.classification == "well-constrained"
+        assert labels.assembly.is_rigid is True
+        assert labels.assembly.is_minimally_rigid is True
+
+    def test_overconstrained(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (1, 2, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE),
+            _make_joint(1, 1, 2, JointType.REVOLUTE),
+            _make_joint(2, 2, 0, JointType.REVOLUTE),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert labels.assembly.redundant_count > 0
+
+    def test_has_degeneracy_with_parallel_axes(self) -> None:
+        """Parallel revolute axes in a loop create geometric degeneracy."""
+        z_axis = (0.0, 0.0, 1.0)
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0), (2, 2, 0), (0, 2, 0))
+        joints = [
+            _make_joint(0, 0, 1, JointType.REVOLUTE, axis=z_axis),
+            _make_joint(1, 1, 2, JointType.REVOLUTE, axis=z_axis),
+            _make_joint(2, 2, 3, JointType.REVOLUTE, axis=z_axis),
+            _make_joint(3, 3, 0, JointType.REVOLUTE, axis=z_axis),
+        ]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        assert labels.assembly.has_degeneracy is True
+
+
+# ---------------------------------------------------------------------------
+# Serialization
+# ---------------------------------------------------------------------------
+
+
+class TestToDict:
+    """to_dict produces JSON-serializable output."""
+
+    def test_top_level_keys(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        d = labels.to_dict()
+        assert set(d.keys()) == {
+            "per_constraint",
+            "per_joint",
+            "per_body",
+            "assembly",
+        }
+
+    def test_per_constraint_keys(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        d = labels.to_dict()
+        for item in d["per_constraint"]:
+            assert set(item.keys()) == {
+                "joint_id",
+                "constraint_idx",
+                "pebble_independent",
+                "jacobian_independent",
+            }
+
+    def test_assembly_keys(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        d = labels.to_dict()
+        assert set(d["assembly"].keys()) == {
+            "classification",
+            "total_dof",
+            "redundant_count",
+            "is_rigid",
+            "is_minimally_rigid",
+            "has_degeneracy",
+        }
+
+    def test_json_serializable(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        d = labels.to_dict()
+        # Should not raise
+        serialized = json.dumps(d)
+        assert isinstance(serialized, str)
+
+
+# ---------------------------------------------------------------------------
+# Edge cases
+# ---------------------------------------------------------------------------
+
+
+class TestLabelAssemblyEdgeCases:
+    """Edge cases for label_assembly."""
+
+    def test_no_joints(self) -> None:
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        labels = label_assembly(bodies, [], ground_body=0)
+        assert len(labels.per_constraint) == 0
+        assert len(labels.per_joint) == 0
+        assert labels.assembly.classification == "underconstrained"
+        # Non-ground body should be fully free
+        b1 = next(b for b in labels.per_body if b.body_id == 1)
+        assert b1.translational_dof == 3
+        assert b1.rotational_dof == 3
+
+    def test_no_joints_floating(self) -> None:
+        bodies = _make_bodies((0, 0, 0))
+        labels = label_assembly(bodies, [], ground_body=None)
+        assert len(labels.per_body) == 1
+        assert labels.per_body[0].translational_dof == 3
+        assert labels.per_body[0].rotational_dof == 3
+
+    def test_analysis_embedded(self) -> None:
+        """AssemblyLabels.analysis should be a valid ConstraintAnalysis."""
+        bodies = _make_bodies((0, 0, 0), (2, 0, 0))
+        joints = [_make_joint(0, 0, 1, JointType.REVOLUTE)]
+        labels = label_assembly(bodies, joints, ground_body=0)
+        analysis = labels.analysis
+        assert hasattr(analysis, "combinatorial_classification")
+        assert hasattr(analysis, "jacobian_rank")
+        assert hasattr(analysis, "is_rigid")

tests/datagen/test_pebble_game.py

@@ -0,0 +1,206 @@
+"""Tests for solver.datagen.pebble_game -- (6,6)-pebble game."""
+
+from __future__ import annotations
+
+import itertools
+
+import numpy as np
+import pytest
+
+from solver.datagen.pebble_game import PebbleGame3D
+from solver.datagen.types import Joint, JointType
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _revolute(jid: int, a: int, b: int, axis: np.ndarray | None = None) -> Joint:
+    """Shorthand for a revolute joint between bodies *a* and *b*."""
+    if axis is None:
+        axis = np.array([0.0, 0.0, 1.0])
+    return Joint(
+        joint_id=jid,
+        body_a=a,
+        body_b=b,
+        joint_type=JointType.REVOLUTE,
+        axis=axis,
+    )
+
+
+def _fixed(jid: int, a: int, b: int) -> Joint:
+    return Joint(joint_id=jid, body_a=a, body_b=b, joint_type=JointType.FIXED)
+
+
+# ---------------------------------------------------------------------------
+# Tests
+# ---------------------------------------------------------------------------
+
+
+class TestAddBody:
+    """Body registration basics."""
+
+    def test_single_body_six_pebbles(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_body(0)
+        assert pg.state.free_pebbles[0] == 6
+
+    def test_duplicate_body_no_op(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_body(0)
+        pg.add_body(0)
+        assert pg.state.free_pebbles[0] == 6
+
+    def test_multiple_bodies(self) -> None:
+        pg = PebbleGame3D()
+        for i in range(5):
+            pg.add_body(i)
+        assert pg.get_dof() == 30  # 5 * 6
+
+
+class TestAddJoint:
+    """Joint insertion and DOF accounting."""
+
+    def test_revolute_removes_five_dof(self) -> None:
+        pg = PebbleGame3D()
+        results = pg.add_joint(_revolute(0, 0, 1))
+        assert len(results) == 5  # 5 scalar constraints
+        assert all(r["independent"] for r in results)
+        # 2 bodies * 6 = 12, minus 5 independent = 7 free pebbles
+        assert pg.get_dof() == 7
+
+    def test_fixed_removes_six_dof(self) -> None:
+        pg = PebbleGame3D()
+        results = pg.add_joint(_fixed(0, 0, 1))
+        assert len(results) == 6
+        assert all(r["independent"] for r in results)
+        assert pg.get_dof() == 6
+
+    def test_ball_removes_three_dof(self) -> None:
+        pg = PebbleGame3D()
+        j = Joint(joint_id=0, body_a=0, body_b=1, joint_type=JointType.BALL)
+        results = pg.add_joint(j)
+        assert len(results) == 3
+        assert all(r["independent"] for r in results)
+        assert pg.get_dof() == 9
+
+
+class TestTwoBodiesRevolute:
+    """Two bodies connected by a revolute -- demo scenario 1."""
+
+    def test_internal_dof(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_joint(_revolute(0, 0, 1))
+        # Total DOF = 7, internal = 7 - 6 = 1
+        assert pg.get_internal_dof() == 1
+
+    def test_not_rigid(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_joint(_revolute(0, 0, 1))
+        assert not pg.is_rigid()
+
+    def test_classification(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_joint(_revolute(0, 0, 1))
+        assert pg.classify_assembly() == "underconstrained"
+
+
+class TestTwoBodiesFixed:
+    """Two bodies + fixed joint -- demo scenario 2."""
+
+    def test_zero_internal_dof(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_joint(_fixed(0, 0, 1))
+        assert pg.get_internal_dof() == 0
+
+    def test_rigid(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_joint(_fixed(0, 0, 1))
+        assert pg.is_rigid()
+
+    def test_well_constrained(self) -> None:
+        pg = PebbleGame3D()
+        pg.add_joint(_fixed(0, 0, 1))
+        assert pg.classify_assembly() == "well-constrained"
+
+
+class TestTriangleRevolute:
+    """Triangle of 3 bodies with revolute joints -- demo scenario 3."""
+
+    @pytest.fixture()
+    def pg(self) -> PebbleGame3D:
+        pg = PebbleGame3D()
+        pg.add_joint(_revolute(0, 0, 1))
+        pg.add_joint(_revolute(1, 1, 2))
+        pg.add_joint(_revolute(2, 2, 0))
+        return pg
+
+    def test_has_redundant_edges(self, pg: PebbleGame3D) -> None:
+        assert pg.get_redundant_count() > 0
+
+    def test_classification_overconstrained(self, pg: PebbleGame3D) -> None:
+        # 15 constraints on 3 bodies (Maxwell: 6*3-6=12 needed)
+        assert pg.classify_assembly() in ("overconstrained", "mixed")
+
+    def test_rigid(self, pg: PebbleGame3D) -> None:
+        assert pg.is_rigid()
+
+
+class TestChainNotRigid:
+    """A serial chain of 4 bodies with revolute joints is never rigid."""
+
+    def test_chain_underconstrained(self) -> None:
+        pg = PebbleGame3D()
+        for i in range(3):
+            pg.add_joint(_revolute(i, i, i + 1))
+        assert not pg.is_rigid()
+        assert pg.classify_assembly() == "underconstrained"
+
+    def test_chain_internal_dof(self) -> None:
+        pg = PebbleGame3D()
+        for i in range(3):
+            pg.add_joint(_revolute(i, i, i + 1))
+        # 4 bodies * 6 = 24, minus 15 independent = 9 free, internal = 3
+        assert pg.get_internal_dof() == 3
+
+
+class TestEdgeResults:
+    """Result dicts returned by add_joint."""
+
+    def test_result_keys(self) -> None:
+        pg = PebbleGame3D()
+        results = pg.add_joint(_revolute(0, 0, 1))
+        expected_keys = {"edge_id", "joint_id", "constraint_index", "independent", "dof_remaining"}
+        for r in results:
+            assert set(r.keys()) == expected_keys
+
+    def test_edge_ids_sequential(self) -> None:
+        pg = PebbleGame3D()
+        r1 = pg.add_joint(_revolute(0, 0, 1))
+        r2 = pg.add_joint(_revolute(1, 1, 2))
+        all_ids = [r["edge_id"] for r in r1 + r2]
+        assert all_ids == list(range(10))
+
+    def test_dof_remaining_monotonic(self) -> None:
+        pg = PebbleGame3D()
+        results = pg.add_joint(_revolute(0, 0, 1))
+        dofs = [r["dof_remaining"] for r in results]
+        # Should be non-increasing (each independent edge removes a pebble)
+        for a, b in itertools.pairwise(dofs):
+            assert a >= b
+
+
+class TestGroundedClassification:
+    """classify_assembly with grounded=True."""
+
+    def test_grounded_baseline_zero(self) -> None:
+        """With grounded=True the baseline is 0 (not 6)."""
+        pg = PebbleGame3D()
+        pg.add_joint(_fixed(0, 0, 1))
+        # Ungrounded: well-constrained (6 pebbles = baseline 6)
+        assert pg.classify_assembly(grounded=False) == "well-constrained"
+        # Grounded: the 6 remaining pebbles on body 1 exceed baseline 0,
+        # so the raw pebble game (without a virtual ground body) sees this
+        # as underconstrained. The analysis function handles this properly
+        # by adding a virtual ground body.
+        assert pg.classify_assembly(grounded=True) == "underconstrained"

tests/datagen/test_types.py

@@ -0,0 +1,163 @@
+"""Tests for solver.datagen.types -- shared data types."""
+
+from __future__ import annotations
+
+from typing import ClassVar
+
+import numpy as np
+import pytest
+
+from solver.datagen.types import (
+    ConstraintAnalysis,
+    Joint,
+    JointType,
+    PebbleState,
+    RigidBody,
+)
+
+
+class TestJointType:
+    """JointType enum construction and DOF values."""
+
+    EXPECTED_DOF: ClassVar[dict[str, int]] = {
+        "FIXED": 6,
+        "REVOLUTE": 5,
+        "CYLINDRICAL": 4,
+        "SLIDER": 5,
+        "BALL": 3,
+        "PLANAR": 3,
+        "SCREW": 5,
+        "UNIVERSAL": 4,
+        "PARALLEL": 3,
+        "PERPENDICULAR": 1,
+        "DISTANCE": 1,
+    }
+
+    def test_member_count(self) -> None:
+        assert len(JointType) == 11
+
+    @pytest.mark.parametrize("name,dof", EXPECTED_DOF.items())
+    def test_dof_values(self, name: str, dof: int) -> None:
+        assert JointType[name].dof == dof
+
+    def test_access_by_name(self) -> None:
+        assert JointType["REVOLUTE"] is JointType.REVOLUTE
+
+    def test_value_is_tuple(self) -> None:
+        assert JointType.REVOLUTE.value == (1, 5)
+        assert JointType.REVOLUTE.dof == 5
+
+
+class TestRigidBody:
+    """RigidBody dataclass defaults and construction."""
+
+    def test_defaults(self) -> None:
+        body = RigidBody(body_id=0)
+        np.testing.assert_array_equal(body.position, np.zeros(3))
+        np.testing.assert_array_equal(body.orientation, np.eye(3))
+        assert body.local_anchors == {}
+
+    def test_custom_position(self) -> None:
+        pos = np.array([1.0, 2.0, 3.0])
+        body = RigidBody(body_id=7, position=pos)
+        np.testing.assert_array_equal(body.position, pos)
+        assert body.body_id == 7
+
+    def test_local_anchors_mutable(self) -> None:
+        body = RigidBody(body_id=0)
+        body.local_anchors["top"] = np.array([0.0, 0.0, 1.0])
+        assert "top" in body.local_anchors
+
+    def test_default_factory_isolation(self) -> None:
+        """Each instance gets its own default containers."""
+        b1 = RigidBody(body_id=0)
+        b2 = RigidBody(body_id=1)
+        b1.local_anchors["x"] = np.zeros(3)
+        assert "x" not in b2.local_anchors
+
+
+class TestJoint:
+    """Joint dataclass defaults and construction."""
+
+    def test_defaults(self) -> None:
+        j = Joint(joint_id=0, body_a=0, body_b=1, joint_type=JointType.REVOLUTE)
+        np.testing.assert_array_equal(j.anchor_a, np.zeros(3))
+        np.testing.assert_array_equal(j.anchor_b, np.zeros(3))
+        np.testing.assert_array_equal(j.axis, np.array([0.0, 0.0, 1.0]))
+        assert j.pitch == 0.0
+
+    def test_full_construction(self) -> None:
+        j = Joint(
+            joint_id=5,
+            body_a=2,
+            body_b=3,
+            joint_type=JointType.SCREW,
+            anchor_a=np.array([1.0, 0.0, 0.0]),
+            anchor_b=np.array([2.0, 0.0, 0.0]),
+            axis=np.array([1.0, 0.0, 0.0]),
+            pitch=0.5,
+        )
+        assert j.joint_id == 5
+        assert j.joint_type is JointType.SCREW
+        assert j.pitch == 0.5
+
+
+class TestPebbleState:
+    """PebbleState dataclass defaults."""
+
+    def test_defaults(self) -> None:
+        s = PebbleState()
+        assert s.free_pebbles == {}
+        assert s.directed_edges == {}
+        assert s.independent_edges == set()
+        assert s.redundant_edges == set()
+        assert s.incoming == {}
+        assert s.outgoing == {}
+
+    def test_default_factory_isolation(self) -> None:
+        s1 = PebbleState()
+        s2 = PebbleState()
+        s1.free_pebbles[0] = 6
+        assert 0 not in s2.free_pebbles
+
+
+class TestConstraintAnalysis:
+    """ConstraintAnalysis dataclass construction."""
+
+    def test_construction(self) -> None:
+        ca = ConstraintAnalysis(
+            combinatorial_dof=6,
+            combinatorial_internal_dof=0,
+            combinatorial_redundant=0,
+            combinatorial_classification="well-constrained",
+            per_edge_results=[],
+            jacobian_rank=6,
+            jacobian_nullity=0,
+            jacobian_internal_dof=0,
+            numerically_dependent=[],
+            geometric_degeneracies=0,
+            is_rigid=True,
+            is_minimally_rigid=True,
+        )
+        assert ca.is_rigid is True
+        assert ca.is_minimally_rigid is True
+        assert ca.combinatorial_classification == "well-constrained"
+
+    def test_per_edge_results_typing(self) -> None:
+        """per_edge_results accepts list[dict[str, Any]]."""
+        ca = ConstraintAnalysis(
+            combinatorial_dof=7,
+            combinatorial_internal_dof=1,
+            combinatorial_redundant=0,
+            combinatorial_classification="underconstrained",
+            per_edge_results=[{"edge_id": 0, "independent": True}],
+            jacobian_rank=5,
+            jacobian_nullity=1,
+            jacobian_internal_dof=1,
+            numerically_dependent=[],
+            geometric_degeneracies=0,
+            is_rigid=False,
+            is_minimally_rigid=False,
+        )
+        assert len(ca.per_edge_results) == 1
+        assert ca.per_edge_results[0]["edge_id"] == 0

tests/mates/test_conversion.py

@@ -0,0 +1,287 @@
+"""Tests for solver.mates.conversion -- mate-to-joint conversion."""
+
+from __future__ import annotations
+
+import numpy as np
+
+from solver.datagen.types import JointType, RigidBody
+from solver.mates.conversion import (
+    MateAnalysisResult,
+    analyze_mate_assembly,
+    convert_mates_to_joints,
+)
+from solver.mates.primitives import GeometryRef, GeometryType, Mate, MateType
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _make_ref(
+    body_id: int,
+    geom_type: GeometryType,
+    *,
+    origin: np.ndarray | None = None,
+    direction: np.ndarray | None = None,
+) -> GeometryRef:
+    """Factory for GeometryRef with sensible defaults."""
+    if origin is None:
+        origin = np.zeros(3)
+    if direction is None and geom_type in {
+        GeometryType.FACE,
+        GeometryType.AXIS,
+        GeometryType.PLANE,
+    }:
+        direction = np.array([0.0, 0.0, 1.0])
+    return GeometryRef(
+        body_id=body_id,
+        geometry_type=geom_type,
+        geometry_id="Geom001",
+        origin=origin,
+        direction=direction,
+    )
+
+
+def _make_bodies(n: int) -> list[RigidBody]:
+    """Create n bodies at distinct positions."""
+    return [RigidBody(body_id=i, position=np.array([float(i), 0.0, 0.0])) for i in range(n)]
+
+
+# ---------------------------------------------------------------------------
+# convert_mates_to_joints
+# ---------------------------------------------------------------------------
+
+
+class TestConvertMatesToJoints:
+    """convert_mates_to_joints function."""
+
+    def test_empty_input(self) -> None:
+        joints, m2j, j2m = convert_mates_to_joints([])
+        assert joints == []
+        assert m2j == {}
+        assert j2m == {}
+
+    def test_hinge_pattern(self) -> None:
+        """Concentric + Coincident(plane) -> single REVOLUTE joint."""
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.CONCENTRIC,
+                ref_a=_make_ref(0, GeometryType.AXIS),
+                ref_b=_make_ref(1, GeometryType.AXIS),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.COINCIDENT,
+                ref_a=_make_ref(0, GeometryType.PLANE),
+                ref_b=_make_ref(1, GeometryType.PLANE),
+            ),
+        ]
+        joints, m2j, j2m = convert_mates_to_joints(mates)
+        assert len(joints) == 1
+        assert joints[0].joint_type is JointType.REVOLUTE
+        assert joints[0].body_a == 0
+        assert joints[0].body_b == 1
+        # Both mates map to the single joint
+        assert 0 in m2j
+        assert 1 in m2j
+        assert j2m[joints[0].joint_id] == [0, 1]
+
+    def test_lock_pattern(self) -> None:
+        """Lock -> FIXED joint."""
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        joints, _m2j, _j2m = convert_mates_to_joints(mates)
+        assert len(joints) == 1
+        assert joints[0].joint_type is JointType.FIXED
+
+    def test_unmatched_mate_fallback(self) -> None:
+        """A single ANGLE mate with no pattern -> individual joint."""
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.ANGLE,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        joints, _m2j, _j2m = convert_mates_to_joints(mates)
+        assert len(joints) == 1
+        assert joints[0].joint_type is JointType.PERPENDICULAR
+
+    def test_mapping_consistency(self) -> None:
+        """mate_to_joint and joint_to_mates are consistent."""
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.CONCENTRIC,
+                ref_a=_make_ref(0, GeometryType.AXIS),
+                ref_b=_make_ref(1, GeometryType.AXIS),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.COINCIDENT,
+                ref_a=_make_ref(0, GeometryType.PLANE),
+                ref_b=_make_ref(1, GeometryType.PLANE),
+            ),
+            Mate(
+                mate_id=2,
+                mate_type=MateType.DISTANCE,
+                ref_a=_make_ref(2, GeometryType.POINT),
+                ref_b=_make_ref(3, GeometryType.POINT),
+            ),
+        ]
+        joints, m2j, j2m = convert_mates_to_joints(mates)
+        # Every mate should be in m2j
+        for mate in mates:
+            assert mate.mate_id in m2j
+        # Every joint should be in j2m
+        for joint in joints:
+            assert joint.joint_id in j2m
+
+    def test_joint_axis_from_geometry(self) -> None:
+        """Joint axis should come from mate geometry direction."""
+        axis_dir = np.array([1.0, 0.0, 0.0])
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.CONCENTRIC,
+                ref_a=_make_ref(0, GeometryType.AXIS, direction=axis_dir),
+                ref_b=_make_ref(1, GeometryType.AXIS, direction=axis_dir),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.COINCIDENT,
+                ref_a=_make_ref(0, GeometryType.PLANE),
+                ref_b=_make_ref(1, GeometryType.PLANE),
+            ),
+        ]
+        joints, _, _ = convert_mates_to_joints(mates)
+        np.testing.assert_array_almost_equal(joints[0].axis, axis_dir)
+
+
+# ---------------------------------------------------------------------------
+# MateAnalysisResult
+# ---------------------------------------------------------------------------
+
+
+class TestMateAnalysisResult:
+    """MateAnalysisResult dataclass."""
+
+    def test_to_dict(self) -> None:
+        result = MateAnalysisResult(
+            patterns=[],
+            joints=[],
+        )
+        d = result.to_dict()
+        assert d["patterns"] == []
+        assert d["joints"] == []
+        assert d["labels"] is None
+
+
+# ---------------------------------------------------------------------------
+# analyze_mate_assembly
+# ---------------------------------------------------------------------------
+
+
+class TestAnalyzeMateAssembly:
+    """Full pipeline: mates -> joints -> analysis."""
+
+    def test_two_bodies_hinge(self) -> None:
+        """Two bodies connected by hinge mates -> underconstrained (1 DOF)."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.CONCENTRIC,
+                ref_a=_make_ref(0, GeometryType.AXIS),
+                ref_b=_make_ref(1, GeometryType.AXIS),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.COINCIDENT,
+                ref_a=_make_ref(0, GeometryType.PLANE),
+                ref_b=_make_ref(1, GeometryType.PLANE),
+            ),
+        ]
+        result = analyze_mate_assembly(bodies, mates)
+        assert result.analysis is not None
+        assert result.labels is not None
+        # A revolute joint removes 5 DOF, leaving 1 internal DOF
+        assert result.analysis.combinatorial_internal_dof == 1
+        assert len(result.joints) == 1
+        assert result.joints[0].joint_type is JointType.REVOLUTE
+
+    def test_two_bodies_fixed(self) -> None:
+        """Two bodies with lock mate -> well-constrained."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        result = analyze_mate_assembly(bodies, mates)
+        assert result.analysis is not None
+        assert result.analysis.combinatorial_internal_dof == 0
+        assert result.analysis.is_rigid
+
+    def test_grounded_assembly(self) -> None:
+        """Grounded assembly analysis works."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        result = analyze_mate_assembly(bodies, mates, ground_body=0)
+        assert result.analysis is not None
+        assert result.analysis.is_rigid
+
+    def test_no_mates(self) -> None:
+        """Assembly with no mates should be fully underconstrained."""
+        bodies = _make_bodies(2)
+        result = analyze_mate_assembly(bodies, [])
+        assert result.analysis is not None
+        assert result.analysis.combinatorial_internal_dof == 6
+        assert len(result.joints) == 0
+
+    def test_single_body(self) -> None:
+        """Single body, no mates."""
+        bodies = _make_bodies(1)
+        result = analyze_mate_assembly(bodies, [])
+        assert result.analysis is not None
+        assert len(result.joints) == 0
+
+    def test_result_traceability(self) -> None:
+        """mate_to_joint and joint_to_mates populated in result."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.CONCENTRIC,
+                ref_a=_make_ref(0, GeometryType.AXIS),
+                ref_b=_make_ref(1, GeometryType.AXIS),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.COINCIDENT,
+                ref_a=_make_ref(0, GeometryType.PLANE),
+                ref_b=_make_ref(1, GeometryType.PLANE),
+            ),
+        ]
+        result = analyze_mate_assembly(bodies, mates)
+        assert 0 in result.mate_to_joint
+        assert 1 in result.mate_to_joint
+        assert len(result.joint_to_mates) > 0

tests/mates/test_generator.py

@@ -0,0 +1,155 @@
+"""Tests for solver.mates.generator -- synthetic mate generator."""
+
+from __future__ import annotations
+
+from solver.mates.generator import SyntheticMateGenerator, generate_mate_training_batch
+from solver.mates.primitives import MateType
+
+# ---------------------------------------------------------------------------
+# SyntheticMateGenerator
+# ---------------------------------------------------------------------------
+
+
+class TestSyntheticMateGenerator:
+    """SyntheticMateGenerator core functionality."""
+
+    def test_generate_basic(self) -> None:
+        """Generate a simple assembly with mates."""
+        gen = SyntheticMateGenerator(seed=42)
+        bodies, mates, result = gen.generate(3)
+        assert len(bodies) == 3
+        assert len(mates) > 0
+        assert result.analysis is not None
+
+    def test_deterministic_with_seed(self) -> None:
+        """Same seed produces same output."""
+        gen1 = SyntheticMateGenerator(seed=123)
+        _, mates1, _ = gen1.generate(3)
+
+        gen2 = SyntheticMateGenerator(seed=123)
+        _, mates2, _ = gen2.generate(3)
+
+        assert len(mates1) == len(mates2)
+        for m1, m2 in zip(mates1, mates2, strict=True):
+            assert m1.mate_type == m2.mate_type
+            assert m1.ref_a.body_id == m2.ref_a.body_id
+
+    def test_grounded(self) -> None:
+        """Grounded assembly should work."""
+        gen = SyntheticMateGenerator(seed=42)
+        bodies, _mates, result = gen.generate(3, grounded=True)
+        assert len(bodies) == 3
+        assert result.analysis is not None
+
+    def test_revolute_produces_two_mates(self) -> None:
+        """A revolute joint should reverse-map to 2 mates."""
+        gen = SyntheticMateGenerator(seed=42)
+        _bodies, mates, _result = gen.generate(2)
+        # 2 bodies -> 1 revolute joint -> 2 mates (concentric + coincident)
+        assert len(mates) == 2
+        mate_types = {m.mate_type for m in mates}
+        assert MateType.CONCENTRIC in mate_types
+        assert MateType.COINCIDENT in mate_types
+
+
+class TestReverseMapping:
+    """Reverse mapping from joints to mates."""
+
+    def test_revolute_mapping(self) -> None:
+        """REVOLUTE -> Concentric + Coincident."""
+        gen = SyntheticMateGenerator(seed=42)
+        _bodies, mates, _result = gen.generate(2)
+        types = [m.mate_type for m in mates]
+        assert MateType.CONCENTRIC in types
+        assert MateType.COINCIDENT in types
+
+    def test_round_trip_analysis(self) -> None:
+        """Generated mates round-trip through analysis successfully."""
+        gen = SyntheticMateGenerator(seed=42)
+        _bodies, _mates, result = gen.generate(4)
+        assert result.analysis is not None
+        assert result.labels is not None
+        # Should produce joints from the mates
+        assert len(result.joints) > 0
+
+
+class TestNoiseInjection:
+    """Noise injection mechanisms."""
+
+    def test_redundant_injection(self) -> None:
+        """Redundant prob > 0 produces more mates than clean version."""
+        gen_clean = SyntheticMateGenerator(seed=42, redundant_prob=0.0)
+        _, mates_clean, _ = gen_clean.generate(4)
+
+        gen_noisy = SyntheticMateGenerator(seed=42, redundant_prob=1.0)
+        _, mates_noisy, _ = gen_noisy.generate(4)
+
+        assert len(mates_noisy) > len(mates_clean)
+
+    def test_missing_injection(self) -> None:
+        """Missing prob > 0 produces fewer mates than clean version."""
+        gen_clean = SyntheticMateGenerator(seed=42, missing_prob=0.0)
+        _, mates_clean, _ = gen_clean.generate(4)
+
+        gen_noisy = SyntheticMateGenerator(seed=42, missing_prob=0.5)
+        _, mates_noisy, _ = gen_noisy.generate(4)
+
+        # With 50% drop rate on 6 mates, very likely to drop at least one
+        assert len(mates_noisy) <= len(mates_clean)
+
+    def test_incompatible_injection(self) -> None:
+        """Incompatible prob > 0 adds mates with wrong geometry."""
+        gen = SyntheticMateGenerator(seed=42, incompatible_prob=1.0)
+        _, mates, _ = gen.generate(3)
+        # Should have extra mates beyond the clean count
+        gen_clean = SyntheticMateGenerator(seed=42)
+        _, mates_clean, _ = gen_clean.generate(3)
+        assert len(mates) > len(mates_clean)
+
+
+# ---------------------------------------------------------------------------
+# generate_mate_training_batch
+# ---------------------------------------------------------------------------
+
+
+class TestGenerateMateTrainingBatch:
+    """Batch generation function."""
+
+    def test_batch_structure(self) -> None:
+        """Each example has required keys."""
+        examples = generate_mate_training_batch(batch_size=3, seed=42)
+        assert len(examples) == 3
+        for ex in examples:
+            assert "bodies" in ex
+            assert "mates" in ex
+            assert "patterns" in ex
+            assert "labels" in ex
+            assert "n_bodies" in ex
+            assert "n_mates" in ex
+            assert "n_joints" in ex
+
+    def test_batch_deterministic(self) -> None:
+        """Same seed produces same batch."""
+        batch1 = generate_mate_training_batch(batch_size=5, seed=99)
+        batch2 = generate_mate_training_batch(batch_size=5, seed=99)
+        for ex1, ex2 in zip(batch1, batch2, strict=True):
+            assert ex1["n_bodies"] == ex2["n_bodies"]
+            assert ex1["n_mates"] == ex2["n_mates"]
+
+    def test_batch_grounded_ratio(self) -> None:
+        """Batch respects grounded_ratio parameter."""
+        # All grounded
+        examples = generate_mate_training_batch(batch_size=5, seed=42, grounded_ratio=1.0)
+        assert len(examples) == 5
+
+    def test_batch_with_noise(self) -> None:
+        """Batch with noise injection runs without error."""
+        examples = generate_mate_training_batch(
+            batch_size=3,
+            seed=42,
+            redundant_prob=0.3,
+            missing_prob=0.1,
+        )
+        assert len(examples) == 3
+        for ex in examples:
+            assert ex["n_mates"] >= 0

tests/mates/test_labeling.py

@@ -0,0 +1,224 @@
+"""Tests for solver.mates.labeling -- mate-level ground truth labels."""
+
+from __future__ import annotations
+
+import numpy as np
+
+from solver.datagen.types import RigidBody
+from solver.mates.labeling import MateAssemblyLabels, MateLabel, label_mate_assembly
+from solver.mates.patterns import JointPattern
+from solver.mates.primitives import GeometryRef, GeometryType, Mate, MateType
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _make_ref(
+    body_id: int,
+    geom_type: GeometryType,
+    *,
+    origin: np.ndarray | None = None,
+    direction: np.ndarray | None = None,
+) -> GeometryRef:
+    """Factory for GeometryRef with sensible defaults."""
+    if origin is None:
+        origin = np.zeros(3)
+    if direction is None and geom_type in {
+        GeometryType.FACE,
+        GeometryType.AXIS,
+        GeometryType.PLANE,
+    }:
+        direction = np.array([0.0, 0.0, 1.0])
+    return GeometryRef(
+        body_id=body_id,
+        geometry_type=geom_type,
+        geometry_id="Geom001",
+        origin=origin,
+        direction=direction,
+    )
+
+
+def _make_bodies(n: int) -> list[RigidBody]:
+    """Create n bodies at distinct positions."""
+    return [RigidBody(body_id=i, position=np.array([float(i), 0.0, 0.0])) for i in range(n)]
+
+
+# ---------------------------------------------------------------------------
+# MateLabel
+# ---------------------------------------------------------------------------
+
+
+class TestMateLabel:
+    """MateLabel dataclass."""
+
+    def test_defaults(self) -> None:
+        ml = MateLabel(mate_id=0)
+        assert ml.is_independent is True
+        assert ml.is_redundant is False
+        assert ml.is_degenerate is False
+        assert ml.pattern is None
+        assert ml.issue is None
+
+    def test_to_dict(self) -> None:
+        ml = MateLabel(
+            mate_id=5,
+            is_independent=False,
+            is_redundant=True,
+            pattern=JointPattern.HINGE,
+            issue="redundant",
+        )
+        d = ml.to_dict()
+        assert d["mate_id"] == 5
+        assert d["is_redundant"] is True
+        assert d["pattern"] == "hinge"
+        assert d["issue"] == "redundant"
+
+    def test_to_dict_none_pattern(self) -> None:
+        ml = MateLabel(mate_id=0)
+        d = ml.to_dict()
+        assert d["pattern"] is None
+
+
+# ---------------------------------------------------------------------------
+# MateAssemblyLabels
+# ---------------------------------------------------------------------------
+
+
+class TestMateAssemblyLabels:
+    """MateAssemblyLabels dataclass."""
+
+    def test_to_dict_structure(self) -> None:
+        """to_dict produces expected keys."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        result = label_mate_assembly(bodies, mates)
+        d = result.to_dict()
+        assert "per_mate" in d
+        assert "patterns" in d
+        assert "assembly" in d
+        assert isinstance(d["per_mate"], list)
+
+
+# ---------------------------------------------------------------------------
+# label_mate_assembly
+# ---------------------------------------------------------------------------
+
+
+class TestLabelMateAssembly:
+    """Full labeling pipeline."""
+
+    def test_clean_assembly_no_redundancy(self) -> None:
+        """Two bodies with lock mate -> clean, no redundancy."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        result = label_mate_assembly(bodies, mates)
+        assert isinstance(result, MateAssemblyLabels)
+        assert len(result.per_mate) == 1
+        ml = result.per_mate[0]
+        assert ml.mate_id == 0
+        assert ml.is_independent is True
+        assert ml.is_redundant is False
+        assert ml.issue is None
+
+    def test_redundant_assembly(self) -> None:
+        """Two lock mates on same body pair -> one is redundant."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE, origin=np.array([1.0, 0.0, 0.0])),
+                ref_b=_make_ref(1, GeometryType.FACE, origin=np.array([1.0, 0.0, 0.0])),
+            ),
+        ]
+        result = label_mate_assembly(bodies, mates)
+        assert len(result.per_mate) == 2
+        redundant_count = sum(1 for ml in result.per_mate if ml.is_redundant)
+        # At least one should be redundant
+        assert redundant_count >= 1
+        assert result.assembly.redundant_count > 0
+
+    def test_hinge_pattern_labeling(self) -> None:
+        """Hinge mates get pattern membership."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.CONCENTRIC,
+                ref_a=_make_ref(0, GeometryType.AXIS),
+                ref_b=_make_ref(1, GeometryType.AXIS),
+            ),
+            Mate(
+                mate_id=1,
+                mate_type=MateType.COINCIDENT,
+                ref_a=_make_ref(0, GeometryType.PLANE),
+                ref_b=_make_ref(1, GeometryType.PLANE),
+            ),
+        ]
+        result = label_mate_assembly(bodies, mates)
+        assert len(result.per_mate) == 2
+        # Both mates should be part of the hinge pattern
+        for ml in result.per_mate:
+            assert ml.pattern is JointPattern.HINGE
+            assert ml.is_independent is True
+
+    def test_grounded_assembly(self) -> None:
+        """Grounded assembly labeling works."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        result = label_mate_assembly(bodies, mates, ground_body=0)
+        assert result.assembly.is_rigid
+
+    def test_empty_mates(self) -> None:
+        """No mates -> no per_mate labels, underconstrained."""
+        bodies = _make_bodies(2)
+        result = label_mate_assembly(bodies, [])
+        assert len(result.per_mate) == 0
+        assert result.assembly.classification == "underconstrained"
+
+    def test_assembly_classification(self) -> None:
+        """Assembly classification is present."""
+        bodies = _make_bodies(2)
+        mates = [
+            Mate(
+                mate_id=0,
+                mate_type=MateType.LOCK,
+                ref_a=_make_ref(0, GeometryType.FACE),
+                ref_b=_make_ref(1, GeometryType.FACE),
+            ),
+        ]
+        result = label_mate_assembly(bodies, mates)
+        assert result.assembly.classification in {
+            "well-constrained",
+            "overconstrained",
+            "underconstrained",
+            "mixed",
+        }

tests/mates/test_patterns.py

@@ -0,0 +1,285 @@
+"""Tests for solver.mates.patterns -- joint pattern recognition."""
+
+from __future__ import annotations
+
+import numpy as np
+
+from solver.datagen.types import JointType
+from solver.mates.patterns import JointPattern, PatternMatch, recognize_patterns
+from solver.mates.primitives import GeometryRef, GeometryType, Mate, MateType
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _make_ref(
+    body_id: int,
+    geom_type: GeometryType,
+    *,
+    geometry_id: str = "Geom001",
+    origin: np.ndarray | None = None,
+    direction: np.ndarray | None = None,
+) -> GeometryRef:
+    """Factory for GeometryRef with sensible defaults."""
+    if origin is None:
+        origin = np.zeros(3)
+    if direction is None and geom_type in {
+        GeometryType.FACE,
+        GeometryType.AXIS,
+        GeometryType.PLANE,
+    }:
+        direction = np.array([0.0, 0.0, 1.0])
+    return GeometryRef(
+        body_id=body_id,
+        geometry_type=geom_type,
+        geometry_id=geometry_id,
+        origin=origin,
+        direction=direction,
+    )
+
+
+def _make_mate(
+    mate_id: int,
+    mate_type: MateType,
+    body_a: int,
+    body_b: int,
+    geom_a: GeometryType = GeometryType.FACE,
+    geom_b: GeometryType = GeometryType.FACE,
+) -> Mate:
+    """Factory for Mate with body pair and geometry types."""
+    return Mate(
+        mate_id=mate_id,
+        mate_type=mate_type,
+        ref_a=_make_ref(body_a, geom_a),
+        ref_b=_make_ref(body_b, geom_b),
+    )
+
+
+# ---------------------------------------------------------------------------
+# JointPattern enum
+# ---------------------------------------------------------------------------
+
+
+class TestJointPattern:
+    """JointPattern enum."""
+
+    def test_member_count(self) -> None:
+        assert len(JointPattern) == 9
+
+    def test_string_values(self) -> None:
+        for jp in JointPattern:
+            assert isinstance(jp.value, str)
+
+    def test_access_by_name(self) -> None:
+        assert JointPattern["HINGE"] is JointPattern.HINGE
+
+
+# ---------------------------------------------------------------------------
+# PatternMatch
+# ---------------------------------------------------------------------------
+
+
+class TestPatternMatch:
+    """PatternMatch dataclass."""
+
+    def test_construction(self) -> None:
+        mate = _make_mate(0, MateType.LOCK, 0, 1)
+        pm = PatternMatch(
+            pattern=JointPattern.FIXED,
+            mates=[mate],
+            body_a=0,
+            body_b=1,
+            confidence=1.0,
+            equivalent_joint_type=JointType.FIXED,
+        )
+        assert pm.pattern is JointPattern.FIXED
+        assert pm.confidence == 1.0
+        assert pm.missing_mates == []
+
+    def test_to_dict(self) -> None:
+        mate = _make_mate(5, MateType.LOCK, 0, 1)
+        pm = PatternMatch(
+            pattern=JointPattern.FIXED,
+            mates=[mate],
+            body_a=0,
+            body_b=1,
+            confidence=1.0,
+            equivalent_joint_type=JointType.FIXED,
+        )
+        d = pm.to_dict()
+        assert d["pattern"] == "fixed"
+        assert d["mate_ids"] == [5]
+        assert d["equivalent_joint_type"] == "FIXED"
+
+
+# ---------------------------------------------------------------------------
+# recognize_patterns — canonical patterns
+# ---------------------------------------------------------------------------
+
+
+class TestRecognizeCanonical:
+    """Full-confidence canonical pattern recognition."""
+
+    def test_empty_input(self) -> None:
+        assert recognize_patterns([]) == []
+
+    def test_hinge(self) -> None:
+        """Concentric(axis) + Coincident(plane) -> Hinge."""
+        mates = [
+            _make_mate(0, MateType.CONCENTRIC, 0, 1, GeometryType.AXIS, GeometryType.AXIS),
+            _make_mate(1, MateType.COINCIDENT, 0, 1, GeometryType.PLANE, GeometryType.PLANE),
+        ]
+        results = recognize_patterns(mates)
+        top = results[0]
+        assert top.pattern is JointPattern.HINGE
+        assert top.confidence == 1.0
+        assert top.equivalent_joint_type is JointType.REVOLUTE
+        assert top.missing_mates == []
+
+    def test_slider(self) -> None:
+        """Coincident(plane) + Parallel(axis) -> Slider."""
+        mates = [
+            _make_mate(0, MateType.COINCIDENT, 0, 1, GeometryType.PLANE, GeometryType.PLANE),
+            _make_mate(1, MateType.PARALLEL, 0, 1, GeometryType.AXIS, GeometryType.AXIS),
+        ]
+        results = recognize_patterns(mates)
+        top = results[0]
+        assert top.pattern is JointPattern.SLIDER
+        assert top.confidence == 1.0
+        assert top.equivalent_joint_type is JointType.SLIDER
+
+    def test_cylinder(self) -> None:
+        """Concentric(axis) only -> Cylinder."""
+        mates = [
+            _make_mate(0, MateType.CONCENTRIC, 0, 1, GeometryType.AXIS, GeometryType.AXIS),
+        ]
+        results = recognize_patterns(mates)
+        # Should match cylinder at confidence 1.0
+        cylinder = [r for r in results if r.pattern is JointPattern.CYLINDER]
+        assert len(cylinder) >= 1
+        assert cylinder[0].confidence == 1.0
+        assert cylinder[0].equivalent_joint_type is JointType.CYLINDRICAL
+
+    def test_ball(self) -> None:
+        """Coincident(point) -> Ball."""
+        mates = [
+            _make_mate(0, MateType.COINCIDENT, 0, 1, GeometryType.POINT, GeometryType.POINT),
+        ]
+        results = recognize_patterns(mates)
+        top = results[0]
+        assert top.pattern is JointPattern.BALL
+        assert top.confidence == 1.0
+        assert top.equivalent_joint_type is JointType.BALL
+
+    def test_planar_face(self) -> None:
+        """Coincident(face) -> Planar."""
+        mates = [
+            _make_mate(0, MateType.COINCIDENT, 0, 1, GeometryType.FACE, GeometryType.FACE),
+        ]
+        results = recognize_patterns(mates)
+        top = results[0]
+        assert top.pattern is JointPattern.PLANAR
+        assert top.confidence == 1.0
+        assert top.equivalent_joint_type is JointType.PLANAR
+
+    def test_fixed(self) -> None:
+        """Lock -> Fixed."""
+        mates = [
+            _make_mate(0, MateType.LOCK, 0, 1, GeometryType.FACE, GeometryType.FACE),
+        ]
+        results = recognize_patterns(mates)
+        top = results[0]
+        assert top.pattern is JointPattern.FIXED
+        assert top.confidence == 1.0
+        assert top.equivalent_joint_type is JointType.FIXED
+
+
+# ---------------------------------------------------------------------------
+# recognize_patterns — partial matches
+# ---------------------------------------------------------------------------
+
+
+class TestRecognizePartial:
+    """Partial pattern matches and hints."""
+
+    def test_concentric_without_plane_hints_hinge(self) -> None:
+        """Concentric alone matches hinge at 0.5 confidence with missing hint."""
+        mates = [
+            _make_mate(0, MateType.CONCENTRIC, 0, 1, GeometryType.AXIS, GeometryType.AXIS),
+        ]
+        results = recognize_patterns(mates)
+        hinge_matches = [r for r in results if r.pattern is JointPattern.HINGE]
+        assert len(hinge_matches) >= 1
+        hinge = hinge_matches[0]
+        assert hinge.confidence == 0.5
+        assert len(hinge.missing_mates) > 0
+
+    def test_coincident_plane_without_parallel_hints_slider(self) -> None:
+        """Coincident(plane) alone matches slider at 0.5 confidence."""
+        mates = [
+            _make_mate(0, MateType.COINCIDENT, 0, 1, GeometryType.PLANE, GeometryType.PLANE),
+        ]
+        results = recognize_patterns(mates)
+        slider_matches = [r for r in results if r.pattern is JointPattern.SLIDER]
+        assert len(slider_matches) >= 1
+        assert slider_matches[0].confidence == 0.5
+
+
+# ---------------------------------------------------------------------------
+# recognize_patterns — ambiguous / multi-body
+# ---------------------------------------------------------------------------
+
+
+class TestRecognizeAmbiguous:
+    """Ambiguous patterns and multi-body-pair assemblies."""
+
+    def test_concentric_matches_both_hinge_and_cylinder(self) -> None:
+        """A single concentric mate produces both hinge (partial) and cylinder matches."""
+        mates = [
+            _make_mate(0, MateType.CONCENTRIC, 0, 1, GeometryType.AXIS, GeometryType.AXIS),
+        ]
+        results = recognize_patterns(mates)
+        patterns = {r.pattern for r in results}
+        assert JointPattern.HINGE in patterns
+        assert JointPattern.CYLINDER in patterns
+
+    def test_multiple_body_pairs(self) -> None:
+        """Mates across different body pairs produce separate pattern matches."""
+        mates = [
+            _make_mate(0, MateType.LOCK, 0, 1),
+            _make_mate(1, MateType.COINCIDENT, 2, 3, GeometryType.POINT, GeometryType.POINT),
+        ]
+        results = recognize_patterns(mates)
+        pairs = {(r.body_a, r.body_b) for r in results}
+        assert (0, 1) in pairs
+        assert (2, 3) in pairs
+
+    def test_results_sorted_by_confidence(self) -> None:
+        """All results should be sorted by confidence descending."""
+        mates = [
+            _make_mate(0, MateType.CONCENTRIC, 0, 1, GeometryType.AXIS, GeometryType.AXIS),
+            _make_mate(1, MateType.LOCK, 2, 3),
+        ]
+        results = recognize_patterns(mates)
+        confidences = [r.confidence for r in results]
+        assert confidences == sorted(confidences, reverse=True)
+
+    def test_unknown_pattern(self) -> None:
+        """A mate type that matches no rule returns UNKNOWN."""
+        mates = [
+            _make_mate(0, MateType.ANGLE, 0, 1, GeometryType.FACE, GeometryType.FACE),
+        ]
+        results = recognize_patterns(mates)
+        assert any(r.pattern is JointPattern.UNKNOWN for r in results)
+
+    def test_body_pair_normalization(self) -> None:
+        """Mates with reversed body order should be grouped together."""
+        mates = [
+            _make_mate(0, MateType.CONCENTRIC, 1, 0, GeometryType.AXIS, GeometryType.AXIS),
+            _make_mate(1, MateType.COINCIDENT, 0, 1, GeometryType.PLANE, GeometryType.PLANE),
+        ]
+        results = recognize_patterns(mates)
+        hinge_matches = [r for r in results if r.pattern is JointPattern.HINGE]
+        assert len(hinge_matches) >= 1
+        assert hinge_matches[0].confidence == 1.0

tests/mates/test_primitives.py

@@ -0,0 +1,329 @@
+"""Tests for solver.mates.primitives -- mate type definitions."""
+
+from __future__ import annotations
+
+from typing import ClassVar
+
+import numpy as np
+import pytest
+
+from solver.mates.primitives import (
+    GeometryRef,
+    GeometryType,
+    Mate,
+    MateType,
+    dof_removed,
+)
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def _make_ref(
+    body_id: int,
+    geom_type: GeometryType,
+    *,
+    geometry_id: str = "Geom001",
+    origin: np.ndarray | None = None,
+    direction: np.ndarray | None = None,
+) -> GeometryRef:
+    """Factory for GeometryRef with sensible defaults."""
+    if origin is None:
+        origin = np.zeros(3)
+    if direction is None and geom_type in {
+        GeometryType.FACE,
+        GeometryType.AXIS,
+        GeometryType.PLANE,
+    }:
+        direction = np.array([0.0, 0.0, 1.0])
+    return GeometryRef(
+        body_id=body_id,
+        geometry_type=geom_type,
+        geometry_id=geometry_id,
+        origin=origin,
+        direction=direction,
+    )
+
+
+# ---------------------------------------------------------------------------
+# MateType
+# ---------------------------------------------------------------------------
+
+
+class TestMateType:
+    """MateType enum construction and DOF values."""
+
+    EXPECTED_DOF: ClassVar[dict[str, int]] = {
+        "COINCIDENT": 3,
+        "CONCENTRIC": 2,
+        "PARALLEL": 2,
+        "PERPENDICULAR": 1,
+        "TANGENT": 1,
+        "DISTANCE": 1,
+        "ANGLE": 1,
+        "LOCK": 6,
+    }
+
+    def test_member_count(self) -> None:
+        assert len(MateType) == 8
+
+    @pytest.mark.parametrize("name,dof", EXPECTED_DOF.items())
+    def test_default_dof_values(self, name: str, dof: int) -> None:
+        assert MateType[name].default_dof == dof
+
+    def test_value_is_tuple(self) -> None:
+        assert MateType.COINCIDENT.value == (0, 3)
+        assert MateType.COINCIDENT.default_dof == 3
+
+    def test_access_by_name(self) -> None:
+        assert MateType["LOCK"] is MateType.LOCK
+
+    def test_no_alias_collision(self) -> None:
+        ordinals = [m.value[0] for m in MateType]
+        assert len(ordinals) == len(set(ordinals))
+
+
+# ---------------------------------------------------------------------------
+# GeometryType
+# ---------------------------------------------------------------------------
+
+
+class TestGeometryType:
+    """GeometryType enum."""
+
+    def test_member_count(self) -> None:
+        assert len(GeometryType) == 5
+
+    def test_string_values(self) -> None:
+        for gt in GeometryType:
+            assert isinstance(gt.value, str)
+            assert gt.value == gt.name.lower()
+
+    def test_access_by_name(self) -> None:
+        assert GeometryType["FACE"] is GeometryType.FACE
+
+
+# ---------------------------------------------------------------------------
+# GeometryRef
+# ---------------------------------------------------------------------------
+
+
+class TestGeometryRef:
+    """GeometryRef dataclass."""
+
+    def test_construction(self) -> None:
+        ref = _make_ref(0, GeometryType.AXIS, geometry_id="Axis001")
+        assert ref.body_id == 0
+        assert ref.geometry_type is GeometryType.AXIS
+        assert ref.geometry_id == "Axis001"
+        np.testing.assert_array_equal(ref.origin, np.zeros(3))
+        assert ref.direction is not None
+
+    def test_default_direction_none(self) -> None:
+        ref = GeometryRef(
+            body_id=0,
+            geometry_type=GeometryType.POINT,
+            geometry_id="Point001",
+        )
+        assert ref.direction is None
+
+    def test_to_dict_round_trip(self) -> None:
+        ref = _make_ref(
+            1,
+            GeometryType.FACE,
+            origin=np.array([1.0, 2.0, 3.0]),
+            direction=np.array([0.0, 1.0, 0.0]),
+        )
+        d = ref.to_dict()
+        restored = GeometryRef.from_dict(d)
+        assert restored.body_id == ref.body_id
+        assert restored.geometry_type is ref.geometry_type
+        assert restored.geometry_id == ref.geometry_id
+        np.testing.assert_array_almost_equal(restored.origin, ref.origin)
+        assert restored.direction is not None
+        np.testing.assert_array_almost_equal(restored.direction, ref.direction)
+
+    def test_to_dict_with_none_direction(self) -> None:
+        ref = GeometryRef(
+            body_id=2,
+            geometry_type=GeometryType.POINT,
+            geometry_id="Point002",
+            origin=np.array([5.0, 6.0, 7.0]),
+        )
+        d = ref.to_dict()
+        assert d["direction"] is None
+        restored = GeometryRef.from_dict(d)
+        assert restored.direction is None
+
+
+# ---------------------------------------------------------------------------
+# Mate
+# ---------------------------------------------------------------------------
+
+
+class TestMate:
+    """Mate dataclass."""
+
+    def test_construction(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.FACE)
+        m = Mate(mate_id=0, mate_type=MateType.COINCIDENT, ref_a=ref_a, ref_b=ref_b)
+        assert m.mate_id == 0
+        assert m.mate_type is MateType.COINCIDENT
+
+    def test_value_default_zero(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.FACE)
+        m = Mate(mate_id=0, mate_type=MateType.COINCIDENT, ref_a=ref_a, ref_b=ref_b)
+        assert m.value == 0.0
+
+    def test_tolerance_default(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.FACE)
+        m = Mate(mate_id=0, mate_type=MateType.COINCIDENT, ref_a=ref_a, ref_b=ref_b)
+        assert m.tolerance == 1e-6
+
+    def test_to_dict_round_trip(self) -> None:
+        ref_a = _make_ref(0, GeometryType.AXIS, origin=np.array([1.0, 0.0, 0.0]))
+        ref_b = _make_ref(1, GeometryType.AXIS, origin=np.array([2.0, 0.0, 0.0]))
+        m = Mate(
+            mate_id=5,
+            mate_type=MateType.CONCENTRIC,
+            ref_a=ref_a,
+            ref_b=ref_b,
+            value=0.0,
+            tolerance=1e-8,
+        )
+        d = m.to_dict()
+        restored = Mate.from_dict(d)
+        assert restored.mate_id == m.mate_id
+        assert restored.mate_type is m.mate_type
+        assert restored.ref_a.body_id == m.ref_a.body_id
+        assert restored.ref_b.body_id == m.ref_b.body_id
+        assert restored.value == m.value
+        assert restored.tolerance == m.tolerance
+
+    def test_from_dict_missing_optional(self) -> None:
+        d = {
+            "mate_id": 1,
+            "mate_type": "DISTANCE",
+            "ref_a": _make_ref(0, GeometryType.POINT).to_dict(),
+            "ref_b": _make_ref(1, GeometryType.POINT).to_dict(),
+        }
+        m = Mate.from_dict(d)
+        assert m.value == 0.0
+        assert m.tolerance == 1e-6
+
+
+# ---------------------------------------------------------------------------
+# dof_removed
+# ---------------------------------------------------------------------------
+
+
+class TestDofRemoved:
+    """Context-dependent DOF removal counts."""
+
+    def test_coincident_face_face(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.FACE)
+        assert dof_removed(MateType.COINCIDENT, ref_a, ref_b) == 3
+
+    def test_coincident_point_point(self) -> None:
+        ref_a = _make_ref(0, GeometryType.POINT)
+        ref_b = _make_ref(1, GeometryType.POINT)
+        assert dof_removed(MateType.COINCIDENT, ref_a, ref_b) == 3
+
+    def test_coincident_edge_edge(self) -> None:
+        ref_a = _make_ref(0, GeometryType.EDGE)
+        ref_b = _make_ref(1, GeometryType.EDGE)
+        assert dof_removed(MateType.COINCIDENT, ref_a, ref_b) == 2
+
+    def test_coincident_face_point(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.POINT)
+        assert dof_removed(MateType.COINCIDENT, ref_a, ref_b) == 1
+
+    def test_concentric_axis_axis(self) -> None:
+        ref_a = _make_ref(0, GeometryType.AXIS)
+        ref_b = _make_ref(1, GeometryType.AXIS)
+        assert dof_removed(MateType.CONCENTRIC, ref_a, ref_b) == 2
+
+    def test_lock_any(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.POINT)
+        assert dof_removed(MateType.LOCK, ref_a, ref_b) == 6
+
+    def test_distance_any(self) -> None:
+        ref_a = _make_ref(0, GeometryType.POINT)
+        ref_b = _make_ref(1, GeometryType.EDGE)
+        assert dof_removed(MateType.DISTANCE, ref_a, ref_b) == 1
+
+    def test_unknown_combo_uses_default(self) -> None:
+        """Unlisted geometry combos fall back to default_dof."""
+        ref_a = _make_ref(0, GeometryType.EDGE)
+        ref_b = _make_ref(1, GeometryType.POINT)
+        result = dof_removed(MateType.COINCIDENT, ref_a, ref_b)
+        assert result == MateType.COINCIDENT.default_dof
+
+
+# ---------------------------------------------------------------------------
+# Mate.validate
+# ---------------------------------------------------------------------------
+
+
+class TestMateValidation:
+    """Mate.validate() compatibility checks."""
+
+    def test_valid_concentric(self) -> None:
+        ref_a = _make_ref(0, GeometryType.AXIS)
+        ref_b = _make_ref(1, GeometryType.AXIS)
+        m = Mate(mate_id=0, mate_type=MateType.CONCENTRIC, ref_a=ref_a, ref_b=ref_b)
+        m.validate()  # should not raise
+
+    def test_invalid_concentric_face(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.AXIS)
+        m = Mate(mate_id=0, mate_type=MateType.CONCENTRIC, ref_a=ref_a, ref_b=ref_b)
+        with pytest.raises(ValueError, match="CONCENTRIC"):
+            m.validate()
+
+    def test_valid_coincident_face_face(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(1, GeometryType.FACE)
+        m = Mate(mate_id=0, mate_type=MateType.COINCIDENT, ref_a=ref_a, ref_b=ref_b)
+        m.validate()  # should not raise
+
+    def test_invalid_self_mate(self) -> None:
+        ref_a = _make_ref(0, GeometryType.FACE)
+        ref_b = _make_ref(0, GeometryType.FACE, geometry_id="Face002")
+        m = Mate(mate_id=0, mate_type=MateType.COINCIDENT, ref_a=ref_a, ref_b=ref_b)
+        with pytest.raises(ValueError, match="Self-mate"):
+            m.validate()
+
+    def test_invalid_parallel_point(self) -> None:
+        ref_a = _make_ref(0, GeometryType.POINT)
+        ref_b = _make_ref(1, GeometryType.AXIS)
+        m = Mate(mate_id=0, mate_type=MateType.PARALLEL, ref_a=ref_a, ref_b=ref_b)
+        with pytest.raises(ValueError, match="PARALLEL"):
+            m.validate()
+
+    def test_invalid_tangent_axis(self) -> None:
+        ref_a = _make_ref(0, GeometryType.AXIS)
+        ref_b = _make_ref(1, GeometryType.FACE)
+        m = Mate(mate_id=0, mate_type=MateType.TANGENT, ref_a=ref_a, ref_b=ref_b)
+        with pytest.raises(ValueError, match="TANGENT"):
+            m.validate()
+
+    def test_missing_direction_for_axis(self) -> None:
+        ref_a = GeometryRef(
+            body_id=0,
+            geometry_type=GeometryType.AXIS,
+            geometry_id="Axis001",
+            origin=np.zeros(3),
+            direction=None,  # missing!
+        )
+        ref_b = _make_ref(1, GeometryType.AXIS)
+        m = Mate(mate_id=0, mate_type=MateType.CONCENTRIC, ref_a=ref_a, ref_b=ref_b)
+        with pytest.raises(ValueError, match="direction"):
+            m.validate()