{"slug":"wanshuiyin-formula-derivation","name":"formula-derivation","description":"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.","long_description":"---\nname: formula-derivation\ndescription: 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.\nargument-hint: \"[problem-goal-current-formulas-or-notes]\"\nallowed-tools: Read, Write, Edit, Grep, Glob\n---\n\n# Formula Derivation: Research Theory Line Construction\n\nBuild an honest derivation package, not a fake polished theorem story.\n\n## Constants\n\n- DEFAULT_DERIVATION_DOC = `DERIVATION_PACKAGE.md` in project root\n- STATUS = `COHERENT AS STATED | COHERENT AFTER REFRAMING / EXTRA ASSUMPTION | NOT YET COHERENT`\n\n## Context: $ARGUMENTS\n\n## Goal\n\nProduce exactly one of:\n1. a coherent derivation package for the original target\n2. a reframed derivation package with corrected object / assumptions / scope\n3. a blocker report explaining why the current notes cannot yet support a coherent derivation\n\n## Inputs\n\nExtract and normalize:\n- the target phenomenon, formula, relation, or theory line\n- the intended role of the derivation:\n  - exact identity / algebra\n  - proposition / local theorem\n  - approximation\n  - mechanism interpretation\n- explicit assumptions\n- notation and definitions\n- any user-provided formula chain, sketch, messy notes, or current draft\n- nearby local theory files if the request points to them\n- desired output style if specified:\n  - internal alignment note\n  - paper-style theory draft\n  - blocker report\n\nIf the target, object, notation, or assumptions are ambiguous, state the exact interpretation you are using before deriving anything.\n\n## Workflow\n\n### Step 1: Gather Derivation Context\nDetermine the target derivation file with this priority:\n1. a file path explicitly specified by the user\n2. a derivation draft already referenced in local notes\n3. `DERIVATION_PACKAGE.md` in project root as the default target\n\nRead the relevant local context:\n- the chosen target derivation file, if it already exists\n- any local theory notes, formula drafts, appendix notes, or files explicitly mentioned by the user\n\nExtract:\n- target formula / theory goal\n- current formula chain\n- assumptions\n- notation\n- known blockers\n- desired output mode\n\n### Step 2: Freeze the Target\nState explicitly:\n- what is being explained, derived, or supported\n- whether the immediate goal is:\n  - identity / algebra\n  - proposition\n  - approximation\n  - interpretation\n- what the derivation is expected to output in the end\n\nDo not start symbolic manipulation before this is fixed.\n\n### Step 3: Choose the Invariant Object\nIdentify the single quantity or conceptual object that should organize the derivation.\n\nTypical possibilities include:\n- objective / utility / loss\n- total cost / energy / welfare\n- conserved quantity / state variable\n- expected metric / effective rate / effective cost\n\nIf the current notes start from a narrower quantity, decide explicitly whether it is:\n- the true top-level object\n- a proxy\n- a local slice\n- an approximation\n\nDo not let a convenient proxy silently replace the actual conceptual object.\n\n### Step 4: Normalize Assumptions and Notation\nRestate:\n- all assumptions\n- all symbols\n- regime boundaries or special cases\n- which quantities are fixed, adaptive, or state dependent\n\nIdentify:\n- hidden assumptions\n- undefined notation\n- scope ambiguities\n- whether the current formula chain already mixes exact steps with approximations\n\nPreserve the user's original notation unless a cleanup is necessary for coherence.\nIf you adopt a cleaner internal formulation, keep that as a derivation device rather than silently replacing the user's target.\n\n### Step 5: Classify the Derivation Steps\nFor every nontrivial step, determine whether it is:\n- **identity**: exact algebraic reformulation\n- **proposition**: a claim requiring conditions\n- **approximation**: model simplification or surrogate\n- **interpretation**: prose-level meaning of a formula\n\nNever merge these categories without signaling the transition.\nIf one part is only interpretive, do not present it as if it were mathematically proved.\n\n### Step 6: Build a Derivation Map\nChoose a derivation strategy, for example:\n- definition -> substitution -> simplification\n- primitive law -> intermediate variable -> target expression\n- global quantity -> perturbation -> decomposition\n- exact model -> approximation -> interpretable closed form\n- general dynamic object -> simplified slice -> local theorem -> return to general case\n\nThen write a derivation map:\n- target formula or theory line\n- required intermediate identities or lemmas\n- which assumptions each nontrivial step uses\n- where approximations enter\n- where special-case and general-case regimes diverge or collapse\n\nIf the derivation needs a decomposition, derive it from the chosen global quantity.\nDo not make a split appear magically from one local variable itself.\n\n### Step 7: Write the Derivation Document\nWrite to the chosen target derivation file.\n\nIf the target derivation file already exists:\n- read it first\n- update the relevant section\n- do not blindly duplicate prior content\n\nIf the user does not specify a target, default to `DERIVATION_PACKAGE.md` in project root.\n\nDo NOT write directly into paper sections or appendix `.tex` files unless the user explicitly asks for that target.\n\nThe derivation package must include:\n- target\n- status\n- invariant object\n- assumptions\n- notation\n- derivation strategy\n- derivation map\n- main derivation steps\n- remarks / interpretations\n- boundaries and non-claims\n\nWriting rules:\n- do not hide gaps with words like \"clearly\", \"obviously\", or \"similarly\"\n- define every symbol before use\n- mark approximations explicitly\n- separate derivation body from remarks\n- if the true object is dynamic or state dependent but a simpler slice is analyzed, say so explicitly\n- if a formula line is only heuristic, label it honestly\n\n### Step 8: Final Verification\nBefore finishing the target derivation file, verify:\n- the target is explicit\n- the invariant object is stable across the derivation\n- every assumption used is stated\n- each formula step is correctly labeled as identity / proposition / approximation / interpretation\n- the derivation does not silently switch objects\n- special cases and general cases still belong to one theory line\n- boundaries and non-claims are stated\n\nIf the derivation still lacks a coherent object, stable assumptions, or an honest path from premises to result, downgrade the status and write a blocker report instead of forcing a clean story.\n\n## Required File Structure\n\nWrite the target derivation file using this structure:\n\n```md\n# Derivation Package\n\n## Target\n[what is being derived or explained]\n\n## Status\nCOHERENT AS STATED / COHERENT AFTER REFRAMING / NOT YET COHERENT\n\n## Invariant Object\n[top-level quantity organizing the derivation]\n\n## Assumptions\n- ...\n\n## Notation\n- ...\n\n## Derivation Strategy\n[chosen route and why]\n\n## Derivation Map\n1. Target depends on ...\n2. Intermediate step A uses ...\n3. Approximation enters at ...\n\n## Main Derivation\nStep 1. ...\nStep 2. ...\n...\n\n## Remarks and Interpretation\n- ...\n\n## Boundaries and Non-Claims\n- ...\n\n## Open Risks\n- ...\n```\n\n## Output Modes\n\n### If the derivation is coherent as stated\nWrite the full structure above with a clean derivation package.\n\n### If the notes are close but not coherent yet\nWrite:\n- the exact mismatch\n- the corrected invariant object, assumption, or scope\n- the reframed derivation package\n\n### If the derivation cannot be made coherent honestly\nWrite:\n- `Status: NOT YET COHERENT`\n- the exact blocker:\n  - missing object\n  - unstable assumptions\n  - notation conflict\n  - unsupported approximation\n  - theorem-level claim without enough conditions\n- what extra assumption, reframe, or intermediate derivation would be needed\n\n## Relationship to `proof-writer`\n\nUse `formula-derivation` when the user says things like:\n- “我不知道怎么起这条推导主线”\n- “这个公式到底该从哪个量出发”\n- “帮我把理论搭顺”\n- “把说明文档变成可写进论文的公式文档”\n- “这几段公式之间逻辑不通”\n\nUse `proof-writer` only after:\n- the exact claim is fixed\n- the assumptions are stable\n- the notation is settled\n- and the task is now to prove or refute that claim rigorously\n\n## Chat Response\n\nAfter writing the target derivation file, respond briefly with:\n- status\n- whether the target survived unchanged or had to be reframed\n- what file was updated\n\n## Key Rules\n\n- Never fabricate a coherent derivation if the object, assumptions, or scope do not support one.\n- Prefer reframing the derivation over overclaiming.\n- Separate assumptions, identities, propositions, approximations, and interpretations.\n- Keep one invariant object across special and general cases whenever possible.\n- Treat simplified constant-parameter cases as analysis slices, not as the conceptual main object.\n- If uncertainty remains, mark it explicitly in `Open Risks`; do not hide it in polished prose.\n- Coherence matters more than elegance.\n","tagline":"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","category":"research","tags":["agent-skill"],"author":"wanshuiyin","verified":false,"attribution":{"status":"registry_indexed","statusLabel":"Registry indexed","shortLabel":"REGISTRY INDEXED","sourceLabel":"incremental repository rescan","sourceDetail":"wanshuiyin/Auto-claude-code-research-in-sleep","creatorName":"wanshuiyin","creatorUrl":"https://github.com/wanshuiyin","sourceUrl":"https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation","indexedBy":"OpenAgentSkill community index","claimUrl":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation#claim-this-skill","claimCta":"Claim this skill","trustNote":"This listing was indexed from public sources and is not marked official until a maintainer claim is approved.","publicNote":"Attribution links to the public repository or creator profile. 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Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"cursor\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. 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Reviewed with permission notes; Review before production","verification_result":"Report the smallest successful task, files touched, warnings, and any missing setup."}},"outcome_feedback":{"endpoint":"https://www.openagentskill.com/api/agent/outcome","method":"POST","requires_resolve_event_id":true,"event_id_source":"Use install_receipt.outcome_feedback.event_id or feedback.event_id returned by /api/agent/resolve for the current task.","expected_outcomes":["success","failed","not_relevant","blocked_by_risk","setup_required"],"payload_template":{"event_id":"<install_receipt.outcome_feedback.event_id or feedback.event_id from /api/agent/resolve>","skill_slug":"wanshuiyin-formula-derivation","task":"Use formula-derivation in an agent workflow","agent":"codex","outcome":"success","install_used":true,"risk_blocked":false,"setup_required":false,"task_success":true,"output_quality":4,"error_type":null,"human_review_required":false,"workspace":"sandbox","time_to_useful_ms":120000,"notes":"Report the smallest successful task, setup friction, files touched, and risk notes."}},"endpoints":{"web":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation","api":"https://www.openagentskill.com/api/agent/skills/wanshuiyin-formula-derivation","audit":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation/audit","eval":"https://www.openagentskill.com/api/agent/evals?slug=wanshuiyin-formula-derivation&task=Use%20formula-derivation%20in%20an%20agent%20workflow&max_risk=medium","resolve":"https://www.openagentskill.com/api/agent/resolve?task=Use%20formula-derivation%20in%20an%20agent%20workflow&agent=codex&max_risk=medium","receipt":"https://www.openagentskill.com/api/agent/receipt?task=Use%20formula-derivation%20in%20an%20agent%20workflow&agent=codex&max_risk=medium&format=text","install":"https://www.openagentskill.com/api/skills/wanshuiyin-formula-derivation/install","manifest":"https://www.openagentskill.com/api/registry/manifest/wanshuiyin-formula-derivation"}},"machine_metadata":{"version":"openagentskill-agent-metadata-v2","skill":{"slug":"wanshuiyin-formula-derivation","name":"formula-derivation","description":"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.","category":"research","url":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation","repository":"https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation","github_repo":"wanshuiyin/Auto-claude-code-research-in-sleep"},"suited_tasks":["Research agents workflows","Claude Code teams","teams that value GitHub adoption signals","Search sources","Extract claims","Synthesize findings","Navigate local resources","Run repeatable desktop actions"],"suited_agents":["Codex","Claude Code","Cursor","OpenAgentSkill CLI","CLI"],"install":{"command":"npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation","ready":true,"targets":[{"id":"openagentskill-cli","label":"CLI","kind":"command","value":"npx --yes https://github.com/Leon-Drq/openagentskill/releases/download/cli-v0.3.0/openagentskill-0.3.0.tgz add wanshuiyin-formula-derivation"},{"id":"codex","label":"Codex","kind":"agent-prompt","value":"Install the \"formula-derivation\" agent skill from https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation. Read its SKILL.md or equivalent instructions first, install only the files needed for this workspace, and summarize any required setup before using it. Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"codex\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. Report success only after the skill is installed and a minimal verification passes."},{"id":"claude-code","label":"Claude Code","kind":"agent-prompt","value":"Add \"formula-derivation\" as a Claude Code skill from https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation. Inspect the skill instructions, place the reusable skill files in the appropriate local skills location for this project, and report the activation steps. Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"claude-code\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. Report success only after the skill is installed and a minimal verification passes."},{"id":"cursor","label":"Cursor","kind":"agent-prompt","value":"Turn \"formula-derivation\" from https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation into a reusable Cursor project rule or agent instruction. Preserve the core workflow, adapt paths to this repo, and keep the rule scoped to tasks where it is relevant. Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"cursor\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. Report success only after the skill is installed and a minimal verification passes."}],"handoff_url":"https://www.openagentskill.com/api/skills/wanshuiyin-formula-derivation/install","manifest_url":"https://www.openagentskill.com/api/registry/manifest/wanshuiyin-formula-derivation"},"trust":{"score":81,"label":"Strong shortlist","version":"trust-score-v4","install_policy":"human_review_before_install","evidence":{"stars":"16K GitHub stars","repoActivity":"16K stars, 1.4K forks","lastPushed":"1d since push","license":"MIT","repository":"https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation","install":"npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation","installSafety":"standard package or runtime install path","permissionSurface":"filesystem or document access","documentation":"Strong README/SKILL.md context","agentOutcomes":"No agent outcome data yet"},"outcome_evidence":{"total":0,"successes":0,"failures":0,"not_relevant":0,"success_rate":null,"recent_success_rate":null,"recent_failure_rate":null,"install_attempts":0,"install_success_rate":null,"risk_blocked":0,"setup_required":0,"avg_output_quality":null,"production_outcomes":0,"last_outcome_at":null,"label":"No agent outcome data yet"},"auto_install":{"allowed":false,"sandbox_required":true,"reason":"Human review or sandbox validation is required before automatic installation."},"best_for":["research","agent-skill"],"known_risks":["The provided SKILL.md excerpt appears to be cut off near the end of Step 6; if the actual file is incomplete, the workflow would lack a final output template and closure.","Quality score needs review"]},"agent_proven":{"version":"agent-proven-v1","score":0,"tier":"unproven","label":"Needs first agent run","summary":"No agent outcome reports yet. Use Resolve, run one narrow sandbox task, then report the result.","metrics":{"totalOutcomes":0,"successfulOutcomes":0,"failedOutcomes":0,"installAttempts":0,"installSuccessRate":null,"successRate":null,"recentSuccessRate":null,"recentFailureRate":null,"riskBlocked":0,"setupRequired":0,"notRelevant":0,"avgOutputQuality":null,"avgTimeToUsefulMs":null,"productionOutcomes":0,"humanReviewRequired":0,"uniqueAgents":0,"lastOutcomeAt":null},"signals":[],"penalties":["No real agent outcome evidence yet"]},"audit":{"score":87,"risk_level":"safe_to_try","risk_label":"Safe to try","warnings":["The provided SKILL.md excerpt appears to be cut off near the end of Step 6; if the actual file is incomplete, the workflow would lack a final output template and closure.","The documented excerpt does not show an explicit setup or limitations section, though the skill appears to need no setup.","Quality score needs review"]},"safety_gate":{"tier":"reviewed","label":"Reviewed with permission notes","auto_install_policy":"review","auto_install_allowed":false,"human_review_required":true,"blocked":false,"recommended_action":"Require human approval before installing into a real workspace."},"quality":{"score":89,"label":"Excellent"},"supply":{"track":"Research and knowledge work","scenario":"Research agents","maintenance":"1d since push","risk":"Safe to try"},"alternative_skills":[],"do_not_use_when":["teams that need a vendor-supported SLA","production agents without a repository review","The provided SKILL.md excerpt appears to be cut off near the end of Step 6; if the actual file is incomplete, the workflow would lack a final output template and closure.","No OpenAgentSkill engagement data yet","The documented excerpt does not show an explicit setup or limitations section, though the skill appears to need no setup.","Quality score needs review","Production credentials, payments, or irreversible account changes without explicit human review","Sensitive private data before reviewing repository code, license, and permission surface"],"agent_contract":{"task_input":"Use formula-derivation in an agent workflow","recommended_action":"Require human approval before installing into a real workspace.","install_policy":"review","minimum_review_before_use":["Trust: 81/100 Strong shortlist","Audit: 87/100 Safe to try","Safety: 67/100 Review before install","Review repository, license, install command, and permission surface before production use."],"expected_agent_output":{"selected_skill":"wanshuiyin-formula-derivation (formula-derivation)","install_command":"npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation","risk_summary":"Safe to try; Reviewed with permission notes; Review before production","verification_result":"Report the smallest successful task, files touched, warnings, and any missing setup."}},"outcome_feedback":{"endpoint":"https://www.openagentskill.com/api/agent/outcome","method":"POST","requires_resolve_event_id":true,"event_id_source":"Use install_receipt.outcome_feedback.event_id or feedback.event_id returned by /api/agent/resolve for the current task.","expected_outcomes":["success","failed","not_relevant","blocked_by_risk","setup_required"],"payload_template":{"event_id":"<install_receipt.outcome_feedback.event_id or feedback.event_id from /api/agent/resolve>","skill_slug":"wanshuiyin-formula-derivation","task":"Use formula-derivation in an agent workflow","agent":"codex","outcome":"success","install_used":true,"risk_blocked":false,"setup_required":false,"task_success":true,"output_quality":4,"error_type":null,"human_review_required":false,"workspace":"sandbox","time_to_useful_ms":120000,"notes":"Report the smallest successful task, setup friction, files touched, and risk notes."}},"endpoints":{"web":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation","api":"https://www.openagentskill.com/api/agent/skills/wanshuiyin-formula-derivation","audit":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation/audit","eval":"https://www.openagentskill.com/api/agent/evals?slug=wanshuiyin-formula-derivation&task=Use%20formula-derivation%20in%20an%20agent%20workflow&max_risk=medium","resolve":"https://www.openagentskill.com/api/agent/resolve?task=Use%20formula-derivation%20in%20an%20agent%20workflow&agent=codex&max_risk=medium","receipt":"https://www.openagentskill.com/api/agent/receipt?task=Use%20formula-derivation%20in%20an%20agent%20workflow&agent=codex&max_risk=medium&format=text","install":"https://www.openagentskill.com/api/skills/wanshuiyin-formula-derivation/install","manifest":"https://www.openagentskill.com/api/registry/manifest/wanshuiyin-formula-derivation"}},"supply_profile":{"track":{"slug":"research","label":"Research and knowledge work","shortLabel":"Research","description":"Deep research, source comparison, literature review, RAG, knowledge search, and reports."},"scenario":{"label":"Research agents","description":"I need my agent to research a topic, compare sources, and produce a concise report.","useCases":[{"slug":"research-agents","title":"Research agents"},{"slug":"local-desktop","title":"Local desktop"},{"slug":"workflow-automation","title":"Workflow automation"}]},"applicableAgents":["Claude Code","CLI","Codex","Cursor"],"install":{"ready":true,"command":"npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation","primaryTarget":"CLI","targetCount":4},"githubQuality":{"stars":15840,"starsLabel":"16K","forks":1372,"license":"MIT","qualityScore":89,"trustScore":81,"auditScore":87},"maintenance":{"status":"fresh","label":"1d since push","daysSincePush":1,"lastPushedAt":"2026-09-06T17:32:49+00:00"},"risk":{"level":"safe_to_try","label":"Safe to try","requiresReview":true,"notes":["The provided SKILL.md excerpt appears to be cut off near the end of Step 6; if the actual file is incomplete, the workflow would lack a final output template and closure.","The documented excerpt does not show an explicit setup or limitations section, though the skill appears to need no setup.","Quality score needs review"]},"coverageTags":["Research","Research agents","agent-skill"]},"audit":{"audit_score":87,"risk_level":"safe_to_try","risk_label":"Safe to try","quality_score":89,"trust_score":81,"maintenance_score":100,"security_score":83,"install_score":92,"warnings":["The provided SKILL.md excerpt appears to be cut off near the end of Step 6; if the actual file is incomplete, the workflow would lack a final output template and closure.","The documented excerpt does not show an explicit setup or limitations section, though the skill appears to need no setup.","Quality score needs review"]},"quality_signals":{"model":"v2","star_score":29.4,"usage_score":0,"review_score":5.1,"metadata_score":3,"freshness_score":15},"platforms":["Claude Code"],"use_cases":[{"slug":"research-agents","title":"Research agents","url":"https://www.openagentskill.com/use-cases/research-agents"},{"slug":"local-desktop","title":"Local desktop","url":"https://www.openagentskill.com/use-cases/local-desktop"},{"slug":"workflow-automation","title":"Workflow automation","url":"https://www.openagentskill.com/use-cases/workflow-automation"},{"slug":"document-processing","title":"Document processing","url":"https://www.openagentskill.com/use-cases/document-processing"}],"stacks":[{"slug":"research-report-agent","title":"Research report agent","url":"https://www.openagentskill.com/collections/research-report-agent"},{"slug":"content-growth-agent","title":"Content growth agent","url":"https://www.openagentskill.com/collections/content-growth-agent"},{"slug":"rag-knowledge-base","title":"RAG knowledge base","url":"https://www.openagentskill.com/collections/rag-knowledge-base"}],"install":"npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation","install_targets":[{"id":"openagentskill-cli","label":"CLI","title":"OpenAgentSkill CLI","kind":"command","value":"npx --yes https://github.com/Leon-Drq/openagentskill/releases/download/cli-v0.3.0/openagentskill-0.3.0.tgz add wanshuiyin-formula-derivation","description":"Resolve policy, run the source installer safely, and report a verified install receipt.","copyLabel":"Copy command"},{"id":"codex","label":"Codex","title":"Codex install prompt","kind":"agent-prompt","value":"Install the \"formula-derivation\" agent skill from https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation. Read its SKILL.md or equivalent instructions first, install only the files needed for this workspace, and summarize any required setup before using it. Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"codex\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. Report success only after the skill is installed and a minimal verification passes.","description":"Give Codex a repo-aware install prompt when the skill is not available through a local CLI.","copyLabel":"Copy prompt"},{"id":"claude-code","label":"Claude Code","title":"Claude Code skill prompt","kind":"agent-prompt","value":"Add \"formula-derivation\" as a Claude Code skill from https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation. Inspect the skill instructions, place the reusable skill files in the appropriate local skills location for this project, and report the activation steps. Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"claude-code\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. Report success only after the skill is installed and a minimal verification passes.","description":"Use this prompt to ask Claude Code to add the skill and explain the local activation steps.","copyLabel":"Copy prompt"},{"id":"cursor","label":"Cursor","title":"Cursor rule prompt","kind":"agent-prompt","value":"Turn \"formula-derivation\" from https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation into a reusable Cursor project rule or agent instruction. Preserve the core workflow, adapt paths to this repo, and keep the rule scoped to tasks where it is relevant. Skill purpose: 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. After the install attempt, report the result to https://www.openagentskill.com/api/agent/outcome with POST JSON {\"event_id\":\"install_<unique-id>\",\"skill_slug\":\"wanshuiyin-formula-derivation\",\"task\":\"Install formula-derivation\",\"agent\":\"cursor\",\"outcome\":\"success\",\"install_used\":true}. Replace event_id with a unique value and outcome with success or failed. Report success only after the skill is installed and a minimal verification passes.","description":"Use this when installing as Cursor project rules or reusable agent instructions.","copyLabel":"Copy prompt"}],"repository":"https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation","github_repo":"wanshuiyin/Auto-claude-code-research-in-sleep","version":"1.0.0","license":"MIT","urls":{"web":"https://www.openagentskill.com/skills/wanshuiyin-formula-derivation","repository":"https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/main/skills/formula-derivation","api":"/api/agent/skills/wanshuiyin-formula-derivation","install_api":"/api/skills/wanshuiyin-formula-derivation/install"},"meta":{"created_at":"2026-09-07T18:05:45.516304+00:00","updated_at":"2026-09-07T18:05:45.723436+00:00","agent_friendly":true}}