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

90%

Does it follow best practices?

Run evals on this skill

Adds up to 20 points to the overall score

View guide

Securityby

Passed

No findings from the security scan

Quality

Content

81%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.

The body is a strong, well-structured instruction-only workflow with explicit validation and feedback loops. Its main weakness is mild redundancy across the Workflow, Mathematical rigor, and Key Rules sections, and a long single file that could benefit from reference splitting.

Suggestions

Consolidate the repeated directives (never fabricate a step, preserve the original statement, prefer weakening over overclaiming) into a single Key Rules section and reference it from the Workflow rather than restating in Step 3, Step 5, and Step 6.

Move the three Output Modes branches into a separate reference file (e.g. OUTPUT_MODES.md) and keep a one-line pointer in the main body to shorten the file and improve progressive disclosure.

De-duplicate the PROOF_PACKAGE.md code fence against the Required File Structure section so the canonical template lives in one place.

Dimension	Reasoning	Score
Conciseness	Lean and competence-assuming throughout — no padding explaining what a proof or lemma is — but several directives (e.g. the never-fabricate and preserve-original-statement rules) are restated across Workflow, Mathematical rigor requirements, and Key Rules, which could be consolidated.	4 / 5
Actionability	Concrete and specific — exact file-structure template, an explicit status enum, a named list of forbidden hand-waving phrases, and a feasibility triage checklist — appropriate for an instruction-only skill, though the inline PROOF_PACKAGE template is a near-copy of the Required File Structure section and could be referenced once.	4 / 5
Workflow Clarity	A clear six-step sequence with explicit validation checkpoints (Step 3 Feasibility Triage, Step 6 Final Verification) and a defined feedback loop (downgrade status and write a blockage report instead of forcing a proof), satisfying the destructive-operation validation requirement.	5 / 5
Progressive Disclosure	Well organized with clear section headers and a self-contained single-file structure, but at ~215 lines with no bundle files or external references some content (e.g. output-mode detail) could be split out, leaving it just short of the top anchor.	4 / 5
	Total	17 / 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.

The description is excellent: it states concrete capabilities, provides explicit and natural trigger phrases in multiple languages, and clearly answers both what and when. No significant weaknesses to address.

Dimension	Reasoning	Score
Specificity	Multiple concrete actions are named explicitly — 'Writes rigorous mathematical proofs', 'fill in missing proof steps', 'formalize a proof sketch', and 'determine whether a claimed proof can actually be completed' — matching the comprehensive-coverage anchor.	5 / 5
Completeness	It explicitly answers both what ('Writes rigorous mathematical proofs for ML/AI theory') and when ('Use when asked to prove...') with concrete trigger phrases, matching the top anchor.	5 / 5
Trigger Term Quality	Natural user phrasing is well covered ('prove a theorem, lemma, proposition, or corollary', 'fill in missing proof steps', 'formalize a proof sketch') plus multilingual synonyms (补全证明, 写证明, 证明某个命题), matching the comprehensive-coverage anchor.	5 / 5
Distinctiveness Conflict Risk	It carves a clear niche (rigorous ML/AI proof writing) with distinct, specific triggers and minimal overlap with other skill domains.	5 / 5
	Total	20 / 20 Passed

Validation

87%

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 — 14 / 16 Passed

Validation for skill structure

Criteria	Description	Result
allowed_tools_field	'allowed-tools' contains unusual tool name(s)	Warning
frontmatter_unknown_keys	Unknown frontmatter key(s) found; consider removing or moving to metadata	Warning

	Total	14 / 16 Passed

Repository: wanshuiyin/Auto-claude-code-research-in-sleep
Path: skills/proof-writer/SKILL.md
Commit: f4f20f9

Reviewed: 1 day ago

Table of Contents

Discovery Implementation Validation

Is this your skill?

If you maintain this skill, you can claim it as your own. Once claimed, you can manage eval scenarios, bundle related skills, attach documentation or rules, and ensure cross-agent compatibility.