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:617

    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.
    • Result test. The selected C.29 branch can promise only NoMathLensUseNeededNote, MathLensUse.LensCandidateNote, or MathLensUse.OneLine, identified by its mathematical object, mapping, preserved and lost structure, payoff, rival, next action, and stop condition. Name the exact evaluation, decision, U.WorkPlan, transformation question, or other governed use-object it would answer and the relation, binding, or supported claim that makes it this modeling use's result. MiniCard, FullCard, measurement, or causal work is a continuation only when current; otherwise stop with the missing mapping, correspondence, payoff, governor, or information.
    • Public coarsening. "Mathematical-modeling note" restores to the selected MathLensUse.* output.

    Last Updated: 2026-07-29 — upstream FPF commit 2ada4136 (github.com/ailev/FPF)