prove-soplisted

# Prove SOP Treat this skill as a router. Read [references/proof-loop.md](references/proof-loop.md) before starting a new proof or resuming an incomplete proof loop. ## Route the request 1. Identify the proposition, assumptions, requested rigor, and desired output. 2. Look up related proof failures with `mcp__memory__match_signatures(..., domain="proof")` before drafting. 3. Register the proposition if it is not already in the shared graph. 4. Follow the proof loop reference through skeleton selection, draft diagnosis, correction, and review. 5. Add an empirical companion only when a constant or premise needs data. 6. Use Lean only as optional reinsurance for a small, closed, formalization-ready claim; a missing Lean tool or failed attempt does not invalidate a sound natural-language proof. ## Required boundaries - Compare only candidates of the same graph kind. - Treat BT intervals as uncalibrated approximate posterior summaries. Never call their separation a significance test or use it as the sole stopping rule. - `diagnose_snippet` is read-only; persist each judgment explicitly with `register_diagnosis`. - Corrected drafts need a new segmentation and diagnostic manifest. Preserve old manifests as audit history. - Check wall-clock budget before a Lean attempt expected to take at least five minutes, and record actual use afterward. - If the optional `prover` or `budgeter` agent is unavailable, perform the same checks inline and report that the spec