CA-002 · Rollout index
One archived session at a time: experiments, returned thinking summaries, frozen rule, and checked proof.
Exact prompts sent to this model
Initial task instructions
Verbatim instructions from the first archived model request, including this run’s response and evolution limits.
Initial user message
Discovery tool definitions supplied with the prompt
Proof-phase instructions and reference reveal (spoilers)
Sent only after the model submitted its frozen rule; not available during discovery.
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Model’s view
Interior hidden
Full recorded board
Interior revealed only for this replay
Exact action arguments
Exact submitted Lean hypothesis
Model’s submission explanation
Golden rule
Revealed to the model only after its hypothesis was frozen.
Returned thinking summary
Verbatim provider-returned summary. These are the model’s provisional claims, not conclusions endorsed by this viewer. If none was returned, no reasoning is reconstructed.
The proof, in English
Viewer annotations; the original Lean source above is unchanged.
| Lean step | Meaning |
|---|
A concrete disagreement
Four neighbors have state 1, four have state 2, and the center is 0.
Candidate: 6. It selects the larger tied mode, 2: (5 × 0 + 3 × 2) % 9 = 6.
Golden rule: 0. It sums both tied modes, 1 + 2: (3 × (1 + 2) + 5 × 0) % 9 = 0.
This is the local neighborhood supplied in the final proof, not an additional board experiment.
Exact archived checker output
Session provenance and verification
Archive and member hashes verified. Every recorded board action was replayed against the golden rule and matched the archived board. This viewer does not rerun models or proof checkers. Accepted proofs refer to the archived Lean and independent checker results.