Conciseness

The body is directive and terse throughout — bullet lists, no explanation of concepts Claude already knows — with only minor redundancy: 'Key Rules' restates rules already given in Steps 2, 3, and 5, and 'Output Modes' partially restates 'Goal' and Step 6. It is above the anchor-3 midpoint (mostly efficient) but not every token earns its place as anchor 5 demands.

Actionability

For an instruction-only skill the guidance is fully concrete: named status constants, an explicit target-file priority list, a copy-paste-ready PROOF_PACKAGE.md template, formatting rules ('$...$ for inline math and $$...$$ for display equations'), and itemized verification checklists. No vague or abstract direction remains.

Workflow Clarity

Six clearly sequenced steps with a feasibility triage gate ('If the claim is not provable as stated, do NOT fabricate a proof') and a dedicated final-verification step containing an explicit error-recovery feedback loop ('If a key step still cannot be justified, downgrade the status and write a blockage report instead of forcing a proof'). This matches the anchor-5 pattern of clear sequence, explicit validation, and feedback loops.

Progressive Disclosure

The body is well-sectioned and easy to navigate with a single clearly-signaled cross-skill reference ([../lean-formalize/SKILL.md]) and no buried or nested references. However, at ~230 lines everything is inline; the required file-structure template and the mathematical rigor rules could plausibly live in a reference file, leaving minor organization gaps relative to anchor 5's 'content appropriately split'.

Specificity

The description lists multiple concrete actions — 'Writes rigorous mathematical proofs', 'prove a theorem, lemma, proposition, or corollary', 'fill in missing proof steps', 'formalize a proof sketch', 'determine whether a claimed proof can actually be completed' — giving comprehensive coverage of the skill's capabilities. It exceeds anchor 4, which requires minor gaps in coverage.

Completeness

Both 'what' and 'when' are explicitly answered: the first sentence states what the skill does, and 'Use when asked to prove a theorem, lemma, proposition, or corollary...' provides concrete trigger phrases. This matches the anchor-5 example structure exactly.

Trigger Term Quality

Good keyword coverage with natural phrases ('prove a theorem', 'fill in missing proof steps', 'formalize a proof sketch') and bilingual synonyms (补全证明, 写证明, 证明某个命题). It falls short of anchor 5 because common user phrasings like 'check my proof', 'verify this proof', or 'is this proof correct' are not explicitly covered — 'determine whether a claimed proof can actually be completed' only partially addresses verification requests.

Distinctiveness Conflict Risk

The niche (rigorous mathematical proof drafting for ML/AI theory, including feasibility triage of claimed proofs) is clearly distinct with trigger terms unlikely to fire for unrelated skills. Overlap risk with adjacent math/formalization skills is minimal.