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# GAP minimal reproduction package
This repository provides a one-item end-to-end reference implementation of
GAP: four surface-renaming families and one verified kernel variant. The
default kernel path executes the manuscript's five conceptual operations as
five typed, separately saved model calls.
## One-click reproduction
Open `GAP_End_to_End.ipynb` and choose **Run All**. The notebook:
1. installs the package;
2. loads one canonical Putnam problem;
3. generates the four surface variants;
4. constructs a concrete proof DAG whose nodes are intermediate claims;
5. abstracts one content-free method label per DAG node;
6. records guarded old/new replacements and propagates them node by node;
7. renders the diffused terminal claim into a new question and solution;
8. runs five judges until the unchanged full-provenance bundle receives two consecutive
unanimous rounds;
9. exports and validates one machine-readable GAP record.
The default model is `o3`. Set `OPENAI_API_KEY`, place
`OPENAI_API_KEY=...` in the gitignored `.env` file, or enter it in the
notebook's hidden prompt. The key is never written to run artifacts.
For a no-API software check:
```bash
GAP_OFFLINE_SMOKE=1 jupyter notebook GAP_End_to_End.ipynb
```
Offline smoke mode uses fixed responses. It validates pipeline wiring,
verification control flow, and release assembly; it does not assess generated
mathematics.
## Prompt fidelity
The historical two-call Prompt-A/Prompt-B, surface-renaming prompts, and
review/repair prompts recovered from `PutnamVariants@c3bed737` remain byte
pinned in `src/gap_pipeline/prompts.py`, `PROMPT_SHA256SUMS`, and
`tests/test_prompts.py`. They document the actual original generator.
The executable manuscript-aligned prompts are in
`src/gap_pipeline/kernel_prompts.py`. They refine the historical intent into
five explicit contracts because the recovered original generator only made
two calls and did not emit a concrete DAG, applied replacement map, or
node-by-node diffusion trace. This distinction is deliberate and auditable,
not hidden as prompt identity.
The OpenAI adapter does not send `temperature`; this is compatible with `o3`,
whose supported value is its default. See `STAGE_MAP.md` for the exact
paper-to-code and historical-source maps.
`ProofDAG` supports branching dependencies and validates topological order,
known dependencies, acyclicity, and terminal connectivity. Replacement plans
record the exact old/new value, source node, guard condition, and guard
justification. Diffusion must preserve every node ID, dependency, and method
label. Judges must cover every proof-node ID and replacement-slot ID before
their verdict counts.
## Install and test
```bash
python -m pip install -e '.[api,test]'
pytest
```
Without installation:
```bash
PYTHONPATH=src pytest
PYTHONPATH=src python -m gap_pipeline.cli --help
```
PowerShell equivalents:
```powershell
$env:PYTHONPATH = "src"
python -m pytest
python -m gap_pipeline.cli --help
```
## Live one-item commands
Generate the kernel variant:
```bash
export OPENAI_API_KEY=...
PYTHONPATH=src python -m gap_pipeline.cli generate-kernel \
--dataset examples/sample_data \
--item-id 1998-B-1 \
--run-dir runs/kernel \
--proposer-model o3 \
--judge-model o3
```
In PowerShell, use `$env:OPENAI_API_KEY = "..."` and backticks for line
continuation, or use the gitignored `.env` file through the notebook.
Generate all surface variants:
```bash
PYTHONPATH=src python -m gap_pipeline.cli generate-surfaces \
--dataset examples/sample_data \
--item-id 1998-B-1 \
--run-dir runs/surface \
--proposer-model o3
```
Assemble the final record:
```bash
PYTHONPATH=src python -m gap_pipeline.cli export-release \
--source-dataset examples/sample_data \
--surface-run-dir runs/surface \
--kernel-run-dir runs/kernel \
--output-root release \
--item-id 1998-B-1
```
## Verification protocol
Kernel verification uses `J=5` judges, requires `K=2` consecutive unanimous
rounds for the same complete provenance bundle, and allows at most `T=15`
rounds. A rejected round resets the streak and reruns stages 3--5 from a new
guarded replacement plan using the judge feedback. Every call, stage output,
iteration, and final record is saved under the chosen run directory.
## Scope
This package demonstrates and tests the one-item software path. It does not
reconstruct unavailable proposal/rejection logs from the original 1,051-item
generation run, and a successful LLM verification loop is not a substitute for
the separate blinded mathematical audit described in the rebuttal plan.
|
