prove-sop

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

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 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.