proof-writer

Writes rigorous mathematical proofs for ML/AI theory. Use when asked to prove a theorem, lemma, proposition, or corollary, fill in missing proof steps, formalize a proof sketch, 补全证明, 写证明, 证明某个命题, or determine whether a claimed proof can actually be completed under the stated assumptions.

Quality

94%

Does it follow best practices?

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Securityby

Passed

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Quality

Content

88%Weight 40%Scale 1-5

Reviews the quality of instructions and guidance provided to agents. Good implementation is clear, handles edge cases, and produces reliable results.

A strong, highly actionable instruction-only skill with a clear six-step workflow, an explicit final verification checklist, and honest fallback modes that prevent fabricated proofs. Main weaknesses are systematic rule repetition across sections and no use of bundle reference files for a longish single file.

Suggestions

Consolidate the repeated integrity rules ('never fabricate', 'preserve the original statement', 'prefer weakening') into the Key Rules section only, removing the restatements in Steps 2, 3, and 5 to save tokens.

Move the full Required File Structure template and the mathematical rigor requirements checklist into a references/PROOF_TEMPLATE.md file, keeping a brief summary inline in SKILL.md.

Trim the enumerated proof-strategy list ('direct, contradiction, induction...') to a single line, since Claude already knows the standard strategies and only needs permission to choose one.

Dimension	Reasoning	Score
Conciseness	Imperative and dense throughout with no explanation of concepts Claude already knows; the proof-strategy menu and systematic cross-section repetition of rules ('Never fabricate' and 'preserve the user's original statement' each appear three times) are minor trimmable excess rather than padding.	4 / 5
Actionability	Fully concrete guidance for an instruction-only skill: explicit status enum, a copy-paste-ready PROOF_PACKAGE.md template, enumerated per-mode output behavior for all three cases, and an explicit banned-phrase list ('clearly', 'obviously', 'by standard arguments').	5 / 5
Workflow Clarity	Six clearly sequenced steps culminating in Step 6, an explicit verification checklist with a feedback loop ('If a key step still cannot be justified, downgrade the status and write a blockage report instead of forcing a proof').	5 / 5
Progressive Disclosure	Well-organized single-file skill with clear section headers and no bundle files, but at ~217 lines all content is inline; the required file template and rigor requirements could plausibly live in a references/ file, so content is not cleanly 'appropriately split'.	4 / 5
	Total	18 / 20 Passed

Description

100%Weight 40%Scale 1-5

Based on the skill's description, can an agent find and select it at the right time? Clear, specific descriptions lead to better discovery.

An exemplary description: third person, concrete action verbs, an explicit 'Use when' clause enumerating natural trigger terms in both English and Chinese, and a clearly delineated niche. No weaknesses identified against any anchor.

Dimension	Reasoning	Score
Specificity	Lists four distinct concrete actions — 'Writes rigorous mathematical proofs', 'fill in missing proof steps', 'formalize a proof sketch', 'determine whether a claimed proof can actually be completed' — comprehensively covering the proof-writing task with no gaps.	5 / 5
Completeness	Explicitly answers both 'what' ('Writes rigorous mathematical proofs for ML/AI theory') and 'when' ('Use when asked to prove a theorem...') with concrete enumerated trigger phrases.	5 / 5
Trigger Term Quality	Covers the natural trigger phrases users would say ('prove a theorem, lemma, proposition, or corollary', 'fill in missing proof steps', 'formalize a proof sketch') and adds Chinese synonyms (补全证明, 写证明, 证明某个命题) for comprehensive coverage.	5 / 5
Distinctiveness Conflict Risk	A clear niche (mathematical proof writing for ML/AI theory) with distinct triggers (theorem, lemma, proposition, corollary, proof sketch) that are unlikely to fire for unrelated skills.	5 / 5
	Total	20 / 20 Passed

Validation

100%

Warnings & errors only

Checks the skill against the spec for correct structure and formatting. All validation checks must pass before discovery and implementation can be scored.

Validation — 16 / 16 Passed

Validation for skill structure

No warnings or errors.

Repository: wanshuiyin/Auto-claude-code-research-in-sleep
Path: skills/skills-codex/proof-writer/SKILL.md
Commit: 2132036

Reviewed: 4 days ago

Table of Contents

Discovery Implementation Validation

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