formula-derivation

Start by freezing the target claim, then choose one invariant object that remains meaningful across regimes. List assumptions and notation first, classify each step as identity, proposition, approximation, or interpretation, and derive decompositions from the global quantity rather than local variables.

Organize notes around a single invariant object, move explanatory prose into remark or discussion paragraphs, and keep only equations and immediate consequences in the main derivation. End with explicit statements of what is proven, what remains approximate, and what should not be claimed.

Use formula derivation when the claim is not yet fixed and you need to build the derivation line, choose assumptions, and connect simple and general regimes. Once the exact claim and assumptions are stable, switch to rigorous theorem-proof work instead.

Keep the same invariant object across all regimes so the cases form one story. Present the simplified case as a tractable slice, such as a frozen-parameter approximation or constant-coefficient case, where certain terms vanish, then extend to the general case with added structure.

Derivation structuring clarifies assumptions, boundaries, and missing steps but does not deliver a rigorous proof of a fixed claim. It guards against overstating local propositions as universal theorems, but final theorem-proof packages require separate rigorous verification.