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:23657

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    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 the normalization crosses context boundaries (i.e., CS₁ and CS₂ are in different bounded contexts), then by FPF policy this mapping MUST be treated as a formal Alignment Bridge (F.9) with an associated congruence‑loss (CL) level and MUST be declared via the relevant mechanism’s A.6.1 Transport (BridgeId + channel + ReferencePlane(src,tgt); no implicit crossings). In such cases, any conclusions drawn carry an assurance penalty per B.3 (Φ(CL)).

    Auditability. Each cited NormalizationMethodInstanceId used for comparison SHOULD be transparent via its referenced description or edition (per A.19.UNM). Evidence, calibration backing, and waiver discipline are governed by C.16 (MM‑CHR). The key here is that no comparison is magic - if values differ in scale or context, the normalization choice and its limitations must be explicit.

    Mnemonic: “Never compare before both values are mapped into the same well-typed space.” In other words, always map measurements to a common basis (same CharacteristicSpace and units) before attempting to say one state is ≥ or ≤ another. Directly comparing raw numbers from different scales or contexts is not allowed.

    Last Updated: 2026-06-17 — upstream FPF commit 646b0b9b (github.com/ailev/FPF)