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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.

76

Quality

94%

Does it follow best practices?

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SKILL.md
Quality
Evals
Security

Quality

Content

92%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 well-structured, actionable proof-writing skill with a clear multi-step workflow, explicit validation checkpoints, feedback loops against fabrication, and a concrete output template. The only mild weakness is some redundant reinforcement of anti-fabrication rules across multiple sections.

Suggestions

Consolidate the repeated anti-fabrication guidance ('Do NOT fabricate', 'Never fabricate a missing proof step') into a single Key Rules section and reference it from Steps 3, 5, and 6 to reduce redundancy.

The mathematical rigor requirements list in Step 5 partially overlaps with the Final Verification checklist in Step 6; consider merging the shared items to tighten the token budget.

If the skill grows, move the required file-structure template and output-mode examples into a references/ file and link from SKILL.md to preserve progressive disclosure.

DimensionReasoningScore

Conciseness

The body is largely efficient and avoids explaining concepts Claude already knows, but sections like the rigor requirements list and repeated 'Do NOT fabricate' reminders across Steps 3, 5, 6 and Key Rules add some redundancy that could be trimmed.

4 / 5

Actionability

Provides fully concrete, copy-paste-ready guidance: a complete target file-structure template, explicit constants (DEFAULT_PROOF_DOC, STATUS values), a numbered workflow, and exact markdown math formatting rules covering the common cases.

5 / 5

Workflow Clarity

A clear 6-step sequence with an explicit feasibility triage checkpoint, a dedicated Final Verification step with a checklist, and an explicit feedback loop ('If a key step still cannot be justified, downgrade the status and write a blockage report') for the destructive/overclaiming risk.

5 / 5

Progressive Disclosure

For a self-contained skill under ~220 lines with no bundle files, the content is well-organized into clearly signaled sections (Constants, Workflow, Required File Structure, Output Modes, Key Rules), satisfying the simple-skill exception for well-organized structure.

5 / 5

Total

19

/

20

Passed

Description

96%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.

A strong, specific description that clearly states what the skill does and when to use it, with rich trigger-term coverage including multilingual synonyms. Only minor overlap risk with adjacent math/formalization skills keeps distinctiveness from a 5.

DimensionReasoningScore

Specificity

Lists multiple specific concrete actions (prove a theorem/lemma/proposition/corollary, fill in missing proof steps, formalize a proof sketch, determine whether a claimed proof can be completed under stated assumptions), giving comprehensive coverage of the proof-writing task.

5 / 5

Completeness

Explicitly answers 'what' (writes rigorous mathematical proofs for ML/AI theory) and 'when' with concrete trigger phrases ('Use when asked to prove...'), satisfying the top anchor.

5 / 5

Trigger Term Quality

Covers natural terms across two languages including synonyms and type variants (theorem, lemma, proposition, corollary, proof sketch) plus Chinese equivalents (补全证明, 写证明, 证明某个命题), closely matching the comprehensive-synonym anchor.

5 / 5

Distinctiveness Conflict Risk

The ML/AI theory proof niche is fairly distinct with specific triggers, but 'fill in missing proof steps' and 'formalize a proof sketch' could overlap marginally with general math-writing or formalization skills, so it sits just below the minimal-conflict anchor.

4 / 5

Total

19

/

20

Passed

Validation

100%

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

Validation16 / 16 Passed

Validation for skill structure

No warnings or errors.

Repository
wanshuiyin/Auto-claude-code-research-in-sleep
Reviewed

Table of Contents

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