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.
89
88%
Does it follow best practices?
Impact
Pending
No eval scenarios have been run
Passed
No known issues
Quality
Discovery
100%Based on the skill's description, can an agent find and select it at the right time? Clear, specific descriptions lead to better discovery.
This is an excellent skill description that clearly defines its scope (mathematical proofs for ML/AI theory), lists multiple concrete actions, provides explicit trigger guidance via a 'Use when...' clause, and includes multilingual trigger terms. It is highly distinctive and would be easy for Claude to correctly select from a large pool of skills.
| Dimension | Reasoning | Score |
|---|---|---|
Specificity | Lists multiple specific concrete actions: 'prove a theorem, lemma, proposition, or corollary', 'fill in missing proof steps', 'formalize a proof sketch', and 'determine whether a claimed proof can actually be completed under the stated assumptions'. These are distinct, well-defined tasks. | 3 / 3 |
Completeness | Clearly answers both 'what' (writes rigorous mathematical proofs for ML/AI theory) and 'when' with an explicit 'Use when...' clause listing multiple specific trigger scenarios. | 3 / 3 |
Trigger Term Quality | Excellent coverage of natural trigger terms including 'prove a theorem', 'lemma', 'proposition', 'corollary', 'proof steps', 'proof sketch', and even Chinese-language equivalents ('补全证明', '写证明', '证明某个命题'). These are terms users would naturally use when requesting proof assistance. | 3 / 3 |
Distinctiveness Conflict Risk | Highly distinctive — scoped specifically to mathematical proofs in the ML/AI theory domain, with very specific trigger terms like 'theorem', 'lemma', 'corollary', 'proof sketch', and 'formalize'. Unlikely to conflict with general math help or coding skills. | 3 / 3 |
Total | 12 / 12 Passed |
Implementation
77%Reviews the quality of instructions and guidance provided to agents. Good implementation is clear, handles edge cases, and produces reliable results.
This is a well-crafted skill for a complex intellectual task. Its greatest strengths are the clear multi-step workflow with validation checkpoints, the explicit three-way status classification that prevents proof fabrication, and the concrete output template. The main weaknesses are moderate redundancy across sections and a monolithic structure that could benefit from splitting detailed reference material into separate files.
Suggestions
Remove redundant content between the 'Inputs' section and Step 1 'Gather Proof Context' — they extract nearly identical information.
Consider moving the 'Required File Structure' template and 'Output Modes' into a separate reference file (e.g., PROOF_TEMPLATE.md) to reduce the main skill's length.
| Dimension | Reasoning | Score |
|---|---|---|
Conciseness | The skill is reasonably efficient for a complex multi-step workflow, but contains some redundancy (e.g., the inputs to extract are listed in both Step 1 and the Inputs section, and some instructions like 'never fabricate a proof step' appear multiple times). Some bullet points in Step 3 and Step 5 restate what Claude already knows about mathematical rigor. | 2 / 3 |
Actionability | The skill provides highly concrete, specific guidance: exact file structure template, explicit status categories, precise banned phrases ('clearly', 'obviously'), specific workflow steps, and concrete output formats for each of the three possible outcomes. For an instruction-only skill about proof writing, this is maximally actionable. | 3 / 3 |
Workflow Clarity | The 6-step workflow is clearly sequenced with explicit validation (Step 3 feasibility triage before writing, Step 6 final verification checklist). There are clear feedback loops: if a step can't be justified, downgrade status and write a blockage report. The three output modes provide clear branching logic for different outcomes. | 3 / 3 |
Progressive Disclosure | The content is well-organized with clear sections and headers, but it's a long monolithic document (~200+ lines of detailed instructions) with no references to external files. The file structure template, output modes, and detailed rigor requirements could be split into separate reference files to keep the main skill leaner. | 2 / 3 |
Total | 10 / 12 Passed |
Validation
81%Checks the skill against the spec for correct structure and formatting. All validation checks must pass before discovery and implementation can be scored.
Validation — 9 / 11 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 | 9 / 11 Passed | |
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