A.19:5.2.2.2 Normalization‑based comparability (≼_normalization)
Preface node
heading:a-19-5-2-2-2-normalization-based-comparability-normalization:20443
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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/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 landing in 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/edition (per A.19.UNM). Evidence/calibration backing and waiver discipline are owned by C.16 (MM‑CHR). The key here is that no comparison is magic – if values differ in scale or context, the normalization route and its limitations must be explicit.
Mnemonic: “Never compare before you land both points in 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.