{"slug":"morankor-proof-readability","name":"proof-readability","description":"Polish verified mathematical proofs without changing their mathematical content. Use after a proof has been accepted by the user, a reviewer, Lean, or a co-math review cycle; or when asked to improve proof exposition, readability, signposting, notation, references, or grammar while preserving the original argument.","long_description":"---\nname: proof-readability\ndescription: Polish verified mathematical proofs without changing their mathematical content. Use after a proof has been accepted by the user, a reviewer, Lean, or a co-math review cycle; or when asked to improve proof exposition, readability, signposting, notation, references, or grammar while preserving the original argument.\n---\n\n# Proof Readability\n\nEdit only proofs whose correctness has already been accepted. This is an exposition pass, not a proving pass.\n\nPrime invariant: never change the mathematics. Do not strengthen, weaken, replace, or silently repair an argument. If you find a real gap, stop editing that proof and report the gap precisely.\n\n## Preconditions\n\nBefore editing, confirm one of:\n\n- the user says the proof is already verified,\n- a co-math workstream has an approval file,\n- a Lean build or other formal check accepted the statement,\n- the task is explicitly limited to readability comments rather than direct edits.\n\nIf correctness is not established, offer a `math-proof` or `codex-math` verification pass first.\n\n## Six-Layer Pass\n\nWork in this order:\n\n1. **Architecture**: restate deferred results, add proof sketches where appropriate, make theorem/lemma roles clear, close composite proofs explicitly.\n2. **Signposting**: add proof openers, named steps, exhaustive case labels, assumption open/close markers, and goal statements before algebra.\n3. **Line-level justification**: add reasons for inequalities, signs, substitutions, citations, and relation chains.\n4. **Notation hygiene**: define symbols before use, recall object types, stabilize names, check argument order, and avoid notation dumps.\n5. **Intuition**: add short \"in words\" or intuition paragraphs outside the formal proof. Keep every intuition sentence literally defensible.\n6. **Sentence and formula grammar**: make formulas part of grammatical sentences, avoid starting sentences with symbols, replace logical shorthand in prose, and run read-aloud checks.\n\n## Safe Edits\n\n- Add signposts and roadmap sentences.\n- Expand an algebraic step already implicit in the proof.\n- Move definitions earlier when the definition itself is unchanged.\n- Fix references, labels, theorem names, punctuation, and prose grammar.\n- Add intuition after the proof or outside the formal argument.\n\n## Contested Edits\n\nPropose these in a report; do not apply them without explicit approval:\n\n- replacing a contradiction proof with a direct proof,\n- merging or splitting lemmas,\n- changing standing assumptions,\n- changing theorem statements, quantifiers, bounds, or conclusions,\n- reordering an equality or inequality chain when the new order itself needs proof.\n\n## Banned Phrases\n\nRemove or replace:\n\n- clearly,\n- obviously,\n- it is easy to see,\n- straightforward,\n- similar argument omitted,\n- by inspection,\n- this dominates that,\n- follows naturally.\n\nReplace each with the actual reason, a precise reference, or a flagged gap.\n\n## Report\n\nWhen done, summarize:\n\n- edits by layer,\n- any suspected gaps that were not edited,\n- any derived intermediate lines that need correctness spot-checking,\n- contested edits proposed but not applied,\n- remaining unresolved references or undefined symbols.\n","tagline":"Polish verified mathematical proofs without changing their mathematical content. Use after a proof has been accepted by the user, a reviewer, Lean, or a co-math review cycle; or when asked to improve proof exposition, readability, signposting, notation, references, or grammar whi","category":"coding-agents","commerce":{"type":"unknown","billing":"unknown","amount":null,"currency":null,"sourceUrl":null,"checkedAt":null,"runtime":"unknown","purchaseUrl":null,"checkout":"external","purchaseRequiresUserConsent":true},"tags":["agent-skill"],"author":"morankor","verified":false,"attribution":{"status":"registry_indexed","statusLabel":"Registry indexed","shortLabel":"REGISTRY INDEXED","sourceLabel":"github candidate review","sourceDetail":"morankor/theorist-toolbox","creatorName":"morankor","creatorUrl":"https://github.com/morankor","sourceUrl":"https://github.com/morankor/theorist-toolbox/tree/master/codex/.agents/skills/proof-readability","indexedBy":"OpenAgentSkill community index","claimUrl":"https://www.openagentskill.com/skills/morankor-proof-readability#claim-this-skill","claimCta":"Claim this skill","trustNote":"This listing was indexed from public sources and is not marked official until a maintainer claim is approved.","publicNote":"Attribution links to the public repository or creator profile. 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