formula-derivation

# Formula Derivation Use this skill when the task is not merely to prove a finished theorem, but to **build the derivation itself**: - define the right object, - decide what should be assumed, - determine what is identity vs proposition vs approximation, - connect simple and general regimes without splitting into two unrelated stories, - and turn messy notes into a derivation line that can later be written into a paper. Do **not** use this skill as a replacement for strict proof writing once the exact claim is already fixed and the user wants a theorem-proof package. In that case, hand off to `proof-writer`. ## Core Principle The derivation must be built around **one invariant object**. Do not start from scattered formulas. Start from the object that survives across regimes, then derive proxies, decompositions, and interpretations from it. ## What to Produce Prefer one of these outputs: 1. a **mainline derivation note** for internal alignment; 2. a **paper-style theory draft** with tighter narrative; 3. a **blocker report** if the current notes cannot support a coherent derivation. ## Workflow ### 1. Freeze the Target State explicitly: - what phenomenon is being explained; - what claim is being supported; - whether the goal is: - identity / algebra, - local comparative statics, - approximation, - or mechanism interpretation. Do not start symbolic manipulation before this is fixed. ### 2. Choose the Invariant Object Find the single quantity that should r...