Conciseness

The ~900-line body is noticeably repetitive: the deep-fix opt-in semantics ("omitted entirely when the flag is not set", "treat 'unavailable' identically to the field being absent") are spelled out four separate times (Phase 1 addendum, the Deep-Fix Mode section, Submission Artifact Emission, and Key Rules), and the restatement-check spec is likewise repeated three times; the Side-Condition Checklist table also restates conditions for standard theorems (DCT, MCT, Fubini, Jensen, Cauchy-Schwarz) Claude already knows. It is not a 1 because most of the content is skill-specific operational detail (ARIS reviewer routing, thread management) rather than general-concept padding.

Actionability

Guidance is fully executable: the exact verbatim reviewer prompt blocks, exact MCP call signatures with pinned values ("model: gpt-6-astra", config: {"model_reasoning_effort": "ultra"}), concrete compile commands ("pdflatex -interaction=nonstopmode <file>.tex ..."), copy-paste bash guard scripts for the wiki ledger, and exact JSON artifact schemas. It is not a 4 because both the common path and rare failure paths are covered with paste-ready specifics.

Workflow Clarity

Phases 0 through 5.5 are clearly sequenced with explicit validation checkpoints at every stage — the objective Acceptance Gate, per-fix compile checks, the fan-out coverage receipt with coverage_complete gating, blind re-review for FATAL/CRITICAL fixes, and the regression proof-audit — plus explicit feedback loops (repeat Phases 2-3 up to MAX_REVIEW_ROUNDS) and a defined failure path (Phase 3.9 Unrecoverable Protocol). It is not a 4 because validation is explicit and recoverable rather than implicit or partial.

Progressive Disclosure

Section structure and navigation are good and the sibling references are clearly signaled one level deep ("[shared-references/fan-out-pattern.md]", "shared-references/reviewer-routing.md", "[lean-formalize](../lean-formalize/SKILL.md)"), but no bundle files exist and roughly 400 lines of material — the deep-fix JSON schema spec, the Phase 3.6 restatement algorithm, the PROOF_AUDIT.json artifact schema, and the research-wiki bash guard script — are inlined in SKILL.md where they clearly belong in separate reference files. It is not a 4 because the bulk of detailed spec content is inlined rather than appropriately split; it is not a 2 because headers are clear, references are well-signaled, and navigation works.

Specificity

The description lists five concrete, distinct actions — "Reads a LaTeX proof, identifies gaps via cross-model review (external reviewer backend, ultra reasoning), fixes each gap with full derivations, re-reviews, and generates an audit report" — covering the entire pipeline end to end. It is not a 4 because the action coverage is comprehensive with no minor gaps, matching the 'lists multiple specific concrete actions; comprehensive coverage' anchor exactly.

Completeness

Both 'what' and 'when' are answered explicitly: the first two sentences state the full workflow (what), and "Use when user says '检查证明', 'verify proof', 'proof check', '审证明', 'check this proof'" is an explicit when-clause with concrete trigger phrases. It is not a 4 because the when-clause is fully explicit with literal trigger phrases, not merely present-but-imprecise.

Trigger Term Quality

Natural user phrasings are covered comprehensively with synonyms and variants: "verify proof", "proof check", "check this proof", plus bilingual triggers "检查证明" and "审证明", and the descriptive trigger "rigorous mathematical verification of a theory paper". It is not a 4 because it already includes multiple synonymous natural phrases rather than missing a few.

Distinctiveness Conflict Risk

It carves out a clear niche — rigorous mathematical proof verification/fixing of LaTeX proofs via cross-model review — with triggers unlikely to fire for unrelated skills (generic code review or text checking would not say 'verify proof' or '审证明'). It is not a 4 because the niche and its triggers are essentially unique, with no meaningful overlap with closely related skills.