formula-derivation

What the source does

• FilesystemNone observedNo reads or writes in the source
• NetworkNone observedNo outbound calls in the source
• ShellNone observedNo commands run in the source
• DependenciesPinnedNothing floats
• SecretsNone foundNo keys in source

Five audit layers

Gates applied: no behavioural pass.

Audit 0.4.1 · source sha 36162475b5aa · 29 Oct 2026Report an issue or request a re-scan

• Publisherwanshuiyin GitHub userOwner of the repository this skill is read from
• Source folderwanshuiyin/auto-claude-code-research-in-sleep/skills/formula-derivationThe exact folder we audited
• LicenceMITAs the repository states it
• Commit pinned for this verdict36162475b5aaA new audit runs when the source changes
• Repository statusNot archivedPushed today
• Sandboxed runNot runSkills are read, not executed; layer L4 is skipped

Its 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…

---
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.
argument-hint: "[problem-goal-current-formulas-or-notes]"
allowed-tools: Read, Write, Edit, Grep, Glob, Skill(lean-formalize)
---

# Formula Derivation: Research Theory Line Construction

Build an honest derivation package, not a fake polished theorem story.

## Constants

- DEFAULT_DERIVATION_DOC = `DERIVATION_PACKAGE.md` in project root
- STATUS = `COHERENT AS STATED | COHERENT AFTER REFRAMING / EXTRA ASSUMPTION | NOT YET COHERENT`

## Context: $ARGUMENTS

## Goal

Produce exactly one of:
1. a coherent derivation package for the original target
2. a reframed derivation package with corrected object / assumptions / scope
3. a blocker report explaining why the current notes cannot yet support a coherent derivation

## Inputs

Extract and normalize:
- the target phenomenon, formula, relation, or theory line
- the intended role of the derivation:
  - exact identity / algebra
  - proposition / local theorem
  - approximation
  - mechanism interpretation
- explicit assumptions
- notation and definitions
- any user-provided formula chain, sketch, messy notes, or current draft
- nearby local theory files if the request points to them
- desired output style if specified:
  - internal alignment note
  - paper-style theory draft
  - blocker report

If the target, object, notation, or assumptions are ambiguous, state the exact interpretation you are using before deriving anything.

## Workflow

### Step 1: Gather Derivation Context
Determine the target derivation file with this priority:
1. a file path explicitly specified by the user
2. a derivation draft already referenced in local notes
3. `DERIVATION_PACKAGE.md` in project root as the default target

Read the relevant local context:
- the chosen target derivation file, if it already exists
- any local theory notes, formula drafts, appendix notes, or files explicitly mentioned by the user

Extract:
- target formula / theory goal
- current formula chain
- assumptions
- notation
- known blockers
- desired output mode

### Step 2: Freeze the Target
State explicitly:
- what is being explained, derived, or supported
- whether the immediate goal is:
  - identity / algebra
  - proposition
  - approximation
  - interpretation
- what the derivation is expected to output in the end

Do not start symbolic manipulation before this is fixed.

### Step 3: Choose the Invariant Object
Identify the single quantity or conceptual object that should organize the derivation.

Typical possibilities include:
- objective / utility / loss
- total cost / energy / welfare
- conserved quantity / state variable
- expected metric / effective rate / effective cost

If the current notes start from a narrower quantity, decide explicitly whether it is:
- the true top-level object
- a proxy
- a local slice
- an approximation

Do not let a convenient proxy silently replace the actual conceptual object.

### Step 4: Normalize Assumptions and Notation
Restate:
- all assumptions
- all symbols
- regime boundaries or special cases
- which quantities are fixed, adaptive, or state dependent

Identify:
- hidden assumptions
- undefined notation
- scope ambiguities
- whether the current formula chain already mixes exact steps with approximations

Preserve the user's original notation unless a cleanup is necessary for coherence.
If you adopt a cleaner internal formulation, keep that as a derivation device rather than silently replacing the user's target.

### Step 5: Classify the Derivation Steps
For every nontrivial step, determine whether it is:
- **identity**: exact algebraic reformulation
- **proposition**: a claim requiring conditions
- **approximation**: model simplification or surrogate
- **interpretation**: prose-level meaning of a formula

Never merge these categories without signaling the transition.
If one part is only interpretive, do not present it as if it were mathematically proved.

### Step 6: Build a Derivation Map
Choose a derivation strategy, for example:
- definition -> substitution -> simplification
- primitive law -> intermediate variable -> target expression
- global quantity -> perturbation -> decomposition
- exact model -> approximation -> interpretable closed form
- general dynamic object -> simplified slice -> local theorem -> return to general case

Then write a derivation map:
- target formula or theory line
- required intermediate identities or lemmas
- which assumptions each nontrivial step uses
- where approximations enter
- where special-case and general-case regimes diverge or collapse

If the derivation needs a decomposition, derive it from the chosen global quantity.
Do not make a split appear magically from one local variable itself.

### Step 7: Write the Derivation Document
Write to the chosen target derivation file.

If the target derivation file already exists:
- read it first
- update the relevant section
- do not blindly duplicate prior content

If the user does not specify a target, default to `DERIVATION_PACKAGE.md` in project root.

Do NOT write directly into paper sections or appendix `.tex` files unless the user explicitly asks for that target.

The derivation package must include:
- target
- status
- invariant object
- assumptions
- notation
- derivation strategy
- derivation map
- main derivation steps
- remarks / interpretations
- boundaries and non-claims

Writing rules:
- do not hide gaps with words like "clearly", "obviously", or "similarly"
- define every symbol before use
- mark approximations explicitly
- separate derivation body from remarks
- if the true object is dynamic or state depende

Excerpt, first 6,000 characters of SKILL.md, verbatim from the audited commit. It is text from someone else’s repository, quoted so you can judge it before your agent reads it.

git clone https://github.com/wanshuiyin/auto-claude-code-research-in-sleep
git -C auto-claude-code-research-in-sleep checkout 36162475b5aa

Works in

1. 2026-10-29
   ✓SAFE B 89 / 100

   first audit · source 36162475b5aa

Questions about formula-derivation

• github.com/wanshuiyin/auto-claude-code-research-in-sleep/tree/ma — the audited source at commit 36162475b5aa and every finding aboveObserved · 29 Oct 2026

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