Conciseness

No time is wasted explaining concepts Claude already knows, but the same extraction list (claim, assumptions, notation, sketch) is repeated nearly verbatim in "Inputs", "Step 1: Gather Proof Context" ("Extract: exact claim, assumptions, notation, proof sketch"), and again in "Step 2: Normalize the Claim" ("Restate: the exact claim being proved, all assumptions, all symbols"). The PROOF_PACKAGE.md default is also stated three times (Constants, Step 1, Step 5); a tightening pass could cut ~25-30% of lines, which is more than the "minor instances" of the anchor-4 example.

Actionability

For an instruction-only skill the guidance is fully concrete: a copy-paste-ready required file structure template, an enumerated STATUS constant, named proof strategies, explicit math formatting rules ("use $...$ for inline math and $$...$$ for display equations", "never use 'clearly', 'obviously'..."), and three fully-specified output modes. Not score 4 because no key execution detail is missing for the common cases.

Workflow Clarity

The six steps are clearly sequenced (gather → normalize → triage → dependency map → write → verify) with an explicit validation checklist in Step 6 ("verify: the theorem statement exactly matches what was actually shown... every inequality direction is correct") and a feedback loop: "If a key step still cannot be justified, downgrade the status and write a blockage report instead of forcing a proof". Step 3's feasibility triage adds an early checkpoint, matching the anchor-5 pattern of sequence + explicit validation + error-recovery loop.

Progressive Disclosure

The body is well-sectioned and its one external pointer (the Lean route invoking ../lean-formalize/SKILL.md) is clearly signaled with explicit triggering conditions and an anti-recursion rule. Not score 5 because at ~230 lines with no bundle files, sizable self-contained blocks (the file-structure template, rigor requirements, output modes) stay inline where a reference file would keep SKILL.md a leaner overview; not score 3 because structure and navigation are genuinely good with nothing buried.

Specificity

"Writes rigorous mathematical proofs for ML/AI theory" names the domain, and the description lists four 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". This is comprehensive coverage of the skill's capability space, matching the anchor-5 pattern of multiple specific concrete actions.

Completeness

Both questions are answered explicitly: the "what" is "Writes rigorous mathematical proofs for ML/AI theory" and the "when" opens with "Use when asked to prove a theorem, lemma, proposition, or corollary, ... or determine whether a claimed proof can actually be completed". This mirrors the anchor-5 example structure of a clear capability statement followed by concrete trigger phrases.

Trigger Term Quality

Natural user phrasings are thoroughly covered — "prove a theorem", "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) and the proof-viability question. Not score 4 because no common variation a user would naturally say for this task is missing.

Distinctiveness Conflict Risk

Mathematical proof-writing for ML/AI theory is a clear niche, and triggers (prove theorem/lemma/proposition/corollary, fill proof steps, formalize a sketch) are unlikely to fire for unrelated skills. Even the nearest neighbor (a Lean formalization skill) is distinguished by the "writes proofs / assesses provability" framing rather than code-level formalization.