FPF Reference

    A.19:5.2.2.2 Normalization‑based comparability (≼_normalization)

    Preface node heading:a-19-5-2-2-2-normalization-based-comparability-normalization:29996

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    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

    When two state vectors do not meet the strict conditions for coordinatewise comparison (e.g. they come from different spaces, or the “same” Characteristics are measured on different scales or units), the only sanctioned way to compare them is: normalize, then compare.

    Concretely: if we have state x in CS₁ and state y in CS₂, a normalization‑based comparison is permitted only if the model can cite a set of NormalizationMethodInstanceId(s) under a chosen UNM (per A.19.UNM) that lands the relevant coordinates of x into CS₂ (or lands both into a declared common target space). The result is understood as NCVs (or an ≡_UNM quotient class) per A.19.UNM.

    Comparability rule (normalize-then-compare). We say x ≼normalization y only if, after applying the cited normalization instances to produce a representation of x in CS₂ (or a common target), the mapped state can be compared coordinatewise under ≼_coord. In other words, we never compare raw x and y; we compare after mapping into a common, well-typed space.

    If a normalization use also spans different reference schemes or planes, keep the decisions separate. The A.19.UNM instance supplies the coordinate mapping. Cite an F.9 Bridge only when the use relates two exact F.17 local senses and its direct predicate obtains; state the bounded-use claim and reliance separately, with CL only as optional evidence shorthand. A ReferencePlane crossing cites its applicable plane relation. CPM supplies the comparison scope and evaluation window, and B.3 enters only for an actual assurance use. None of these relations or consequences follows from the scheme or plane difference alone.

    Inspectability. Each normalization instance used for comparison is recoverable through its A.19.UNM declaration. C.16 governs measurement and calibration backing. When values differ in scale, reference scheme, or plane, keep the normalization, any independently obtaining semantic Bridge with its separate use claim, any applicable plane relation, and their limitations explicit.

    Mnemonic: Never compare before both values are carried into the same well-typed space; never claim the same predicate, scope, plane, or window merely from matching labels.

    Last Updated: 2026-09-03 — upstream FPF commit b999972c (github.com/ailev/FPF)