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.
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 a strong skill description that clearly articulates specific capabilities around structuring and deriving research formulas, includes natural trigger terms in both English and Chinese, and explicitly defines both what the skill does and when to use it. The description also helpfully draws a boundary against adjacent skills (finished theorem proofs), reducing conflict risk. Minor note: the bilingual trigger term is a nice touch for multilingual users.
| Dimension | Reasoning | Score |
|---|---|---|
Specificity | Lists multiple specific concrete actions: 'structures and derives research formulas', 'build a theory line', 'organize assumptions', 'turn scattered equations into a coherent derivation', 'rewrite theory notes into a paper-ready formula document'. These are concrete, actionable capabilities. | 3 / 3 |
Completeness | Clearly answers both 'what' (structures and derives research formulas, organizes assumptions, turns scattered equations into coherent derivations) and 'when' (explicit 'Use when' clause specifying conditions: derivation target not fully fixed, main object needs choosing, user needs a derivation package rather than a finished proof). | 3 / 3 |
Trigger Term Quality | Includes strong natural trigger terms: '推导公式' (Chinese for derive formulas), 'build a theory line', 'organize assumptions', 'scattered equations', 'coherent derivation', 'paper-ready formula document', 'derivation target', 'theorem proof'. Good coverage of terms a researcher would naturally use, including bilingual triggers. | 3 / 3 |
Distinctiveness Conflict Risk | Occupies a clear niche: research formula derivation and structuring, distinct from general math solving, theorem proving, or paper writing. The explicit boundary ('rather than a finished theorem proof') helps disambiguate from adjacent 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 strong, highly actionable skill for a specialized research task. Its greatest strengths are the clear 8-step workflow with explicit validation checkpoints, honest failure modes (blocker reports), and a concrete output template. The main weakness is moderate verbosity with some redundancy across steps, and the entire skill is inline rather than leveraging progressive disclosure for its substantial length.
Suggestions
Reduce redundancy by consolidating the identity/proposition/approximation/interpretation classification into a single reference point rather than repeating it in Steps 5, 7, and 8.
Consider extracting the detailed 'Required File Structure' template and 'Output Modes' into a referenced file (e.g., DERIVATION_TEMPLATE.md) to shorten the main skill body.
| Dimension | Reasoning | Score |
|---|---|---|
Conciseness | The skill is fairly long (~200+ lines) and some sections could be tightened—e.g., the detailed enumeration of derivation types (identity/proposition/approximation/interpretation) is repeated across Steps 5, 7, and 8. However, most content is domain-specific guidance that Claude wouldn't inherently know, so it's not padding with basic concepts. It's mostly efficient but has redundancy. | 2 / 3 |
Actionability | The skill provides highly concrete, step-by-step instructions with specific classification categories, a complete output file template in markdown, explicit decision criteria (e.g., how to choose the invariant object, how to classify steps), and clear output modes for different scenarios. The required file structure is copy-paste ready. | 3 / 3 |
Workflow Clarity | The 8-step workflow is clearly sequenced with explicit validation in Step 8, a feedback loop that downgrades status to a blocker report if coherence cannot be achieved, and clear checkpoints (e.g., 'Do not start symbolic manipulation before this is fixed'). The workflow handles error cases (incoherent derivations) with explicit fallback paths. | 3 / 3 |
Progressive Disclosure | The content is well-structured with clear sections and headers, but it's essentially a monolithic document with no references to external files for detailed guidance. The relationship to proof-writer is nicely signaled, but the lengthy inline content (derivation map details, writing rules, verification checklist) could benefit from being split into referenced sub-documents for a skill of this complexity. | 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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