# GAP paper-to-code map

| Paper operation | Implementation | Validated output |
|---|---|---|
| Surface rename | `surface.py` | `SurfaceVariant` with a collision-free one-to-one identifier map |
| 1. Reference solution to proof DAG | `KernelPipeline.construct_dag` | Acyclic `ProofDAG` connected to the terminal claim |
| 2. Content-free method plan | `KernelPipeline.summarize_methods` | `MethodPlan` with the DAG's node IDs and topological order |
| 3. Guarded leaf replacement | `KernelPipeline.generate_replacement` | `ReplacementSpec` with explicit guards and evidence |
| 4. Diffusion through the DAG | `KernelPipeline.diffuse_dag` | `DiffusedProof` preserving node order, dependencies, and method labels |
| 5. Problem rendering | `KernelPipeline.render_question` | Self-contained `KernelCandidate` aligned with the regenerated proof |
| Five-judge verification | `KernelPipeline.verify_candidate` | Five `JudgeVerdict` objects per round |
| Consecutive-pass protocol | `KernelPipeline.verify_candidate` | `K=2`; rejection resets the streak |
| Repair loop | `KernelPipeline._repair` | Corrected candidate with a distinct content hash; maximum `T=15` rounds |
| Audit sampling flag | `KernelPipeline._audit_selected` | Deterministic 10% post-hoc audit selection |

## Per-item artifacts

```text
items/<item-id>/
  input.json
  config.json
  calls/<request-id>.json
  stages/<stage>.json
  iterations/<round>.json
  final.json
```

Each JSON artifact includes a SHA-256 digest of its canonical payload. Judge
calls remain separate rather than being collapsed into a vote count.

## Claim boundary

The verifier is a filtering protocol, not a formal proof of mathematical
correctness. Accepted variants should additionally be inspected in the
post-hoc human audit described in the accompanying paper.