FPF Reference

    MATHEMATICAL-MODELING - Use a mathematical lens when it changes the next action

    Preface node heading:mathematical-modeling-use-a-mathematical-lens-when-it-changes-the-next-action:582

    What this page is

    This is generated FPF reference text from the specification preface or supporting sections. It helps interpret FPF; it is not FPF Reference product documentation.

    Methodology

    Use it to understand how the specification wants to be read, then return to a route, pattern, or work packet for active work. Cite generated IDs only when the wording changes the task decision.

    Content

    • Situation and question. A project question may benefit from a mathematical object or lens, but the next action and lost structure are not yet clear. Ask: can one cheap lens result change the next admissible action?
    • Optional obstacle. A metaphor such as graph-like, field-like, or optimization-like is being treated as ontology or evidence.
    • Template A. C.29 Solution -> MathLensUse.LensCandidateNote. Select when no adequate mathematical object has yet been named.
    • Template B. C.29 Solution -> MathLensUse.OneLine. Select when candidate mathematical object, mapping, preserved structure, lost structure, payoff, next action, rival or fallback, and stop condition can be stated.
    • Boundaries. Stop at NoMathLensUseNeededNote, candidate note, or one-line result according to C.29. Return when EntityOfConcern, mapping, observation, preserved structure, or intended use changes. Wrong-turn recovery removes lens-as-world or lens-as-evidence overread. Stronger neighbors are C.29 MiniCard or FullCard, C.16 measurement, C.28 causal use, and C.30 architecture use.
    • Public coarsening. "Mathematical-modeling note" restores to the selected MathLensUse.* output.

    Last Updated: 2026-07-12 — upstream FPF commit 44dd8818 (github.com/ailev/FPF)