| name | prove-sop |
| description | Build and audit a statistical or mathematical proof from proposition capture through skeleton selection, diagnosis, correction, optional empirical checking, and optional Lean reinsurance. Use when the user asks to prove or rigorously derive a proposition, a graph proposition lacks a verified proof, or a reviewer requires a theorem-side gate. |
Prove SOP
Treat this skill as a router. Read references/proof-loop.md
before starting a new proof or resuming an incomplete proof loop.
Route the request
- Identify the proposition, assumptions, requested rigor, and desired output.
- Look up related proof failures with
mcp__memory__match_signatures(..., domain="proof") before drafting.
- Register the proposition if it is not already in the shared graph.
- Follow the proof loop reference through skeleton selection, draft diagnosis,
correction, and review.
- Add an empirical companion only when a constant or premise needs data.
- 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 specialized agent surface was absent.
Completion
Finish only when the proposition and final draft are identifiable, the latest
diagnostic manifest is empty or every remaining limitation is explicit, the
manuscript states Lean verification status honestly, and any empirical companion
has passed its own preregistration and provenance gates.
