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