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formula-derivation

Structures and derives research formulas when the user wants to 推导公式, build a theory line, organize assumptions, turn scattered equations into a coherent derivation, or rewrite theory notes into a paper-ready formula document. Use when the derivation target is not yet fully fixed, the main object still needs to be chosen, or the user needs a coherent derivation package rather than a finished theorem proof.

Quality

82%

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SKILL.md
Quality
Evals
Security

Quality

Content

73%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 presents a coherent, honest 8-step workflow with strong validation and failure handling, and gives concrete templates and rules that make it easy to execute. Its main weakness is redundancy — the same writing rules and package contents are restated across steps, the template, and Key Rules — plus a missing worked example and an unverifiable cross-skill reference.

Suggestions

Consolidate the repeated honesty rules: merge Step 7's writing rules, Step 8's verification checklist, and the Key Rules section into one authoritative list to remove 2-3x repetition of the same guidance.

Replace the separate package-content list in Step 7 with a pointer to the Required File Structure template, or move the 40-line template into a references/ file (e.g. references/derivation-template.md) that Step 7 links to.

Add one short worked mini-example in Step 5 or Step 7 showing a formula step labeled as identity/proposition/approximation/interpretation, so the classification scheme is demonstrated rather than only defined.

Verify the ../lean-formalize/SKILL.md link resolves in the deployed bundle, or describe the sibling skill by name only to avoid a dangling relative path.

DimensionReasoningScore

Conciseness

No filler or explanations of concepts Claude already knows, but there is noticeable redundancy: rules like "do not hide gaps", "mark approximations explicitly", and object-stability warnings each appear two to three times across Step 5, Step 7 writing rules, Step 8, Output Modes, and Key Rules, and the Required File Structure template repeats Step 7's package-content list. The body could be tightened meaningfully.

3 / 5

Actionability

Concrete, executable guidance throughout: a default file constant, a status enum, a file-selection priority order, an exact copy-paste document template, and explicit step-classification categories. Minor gap: no worked mini-example showing a labeled derivation step (identity/proposition/approximation/interpretation) or a sample blocker report.

4 / 5

Workflow Clarity

Eight clearly sequenced steps with an explicit verification checklist (Step 8) and a failure feedback loop ("downgrade the status and write a blocker report instead of forcing a clean story"), a gating rule in Step 2, and three branched output modes for error recovery.

5 / 5

Progressive Disclosure

A single well-sectioned file with no bundle files, but at ~286 lines the 40-line document template is inlined where a reference file could carry it, and the one external link ([../lean-formalize/SKILL.md]) points outside the bundle and cannot be verified to exist in this review context, a minor navigation gap.

4 / 5

Total

16

/

20

Passed

Description

87%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.

A strong description that explicitly covers what the skill does and when to use it, with natural bilingual trigger phrases and an explicit boundary against theorem-proving skills. Its only weaknesses are minor: some concrete deliverables are only implied and a few natural English trigger variations are missing.

DimensionReasoningScore

Specificity

Lists several concrete actions ("build a theory line", "organize assumptions", "turn scattered equations into a coherent derivation", "rewrite theory notes into a paper-ready formula document") but the skill's concrete deliverables (status-labeled derivation package, blocker reports) are only implied via "coherent derivation package", so coverage has minor gaps rather than being comprehensive.

4 / 5

Completeness

Explicitly answers both what ("Structures and derives research formulas... turn scattered equations into a coherent derivation") and when ("Use when the derivation target is not yet fully fixed, the main object still needs to be chosen, or the user needs a coherent derivation package rather than a finished theorem proof") with concrete trigger conditions and a clear contrast against proof tasks.

5 / 5

Trigger Term Quality

Good keyword coverage including natural bilingual phrases ("推导公式", "build a theory line", "rewrite theory notes") that users would actually say, but common English variations like "derive this formula/equation" are not echoed as explicit trigger phrasings.

4 / 5

Distinctiveness Conflict Risk

Clear niche of pre-proof derivation construction; the "rather than a finished theorem proof" clause explicitly fences it off from the closest sibling skills, and triggers like "推导公式" and "theory line" are distinct.

5 / 5

Total

18

/

20

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 — 13 / 16 Passed

Validation for skill structure

CriteriaDescriptionResult

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

relative_links

Relative link issues: 1 suspicious

Warning

Total

13

/

16

Passed

Repository

wanshuiyin/Auto-claude-code-research-in-sleep

Path

skills/formula-derivation/SKILL.md

Reviewed

Table of Contents

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