A.19.UNM:4.0 - Vocabulary (normative)

NormalizationMethodId. A stable token naming a normalization method kind, used in CN_Spec.normalization.methods.

NormalizationMethod. The method kind (class) that defines:

1. its input/output domains, the directed transformation and the invariants it preserves (NormalizationInvariant[*]), with any distinctions it loses,
2. its closure rules (composition, and inverses where defined), and
3. its validity rules (admitted bearer, scope, qualification window, reference or comparison basis, and intended-use constraints).

NormalizationMethodDescription. An editioned epistemic description of a normalization method (bounds, validity region/window, scope constraints, and evidence links governed by C.16). NormalizationMethodDescriptionRef. A ref to an editioned NormalizationMethodDescription, used in CN_Spec.normalization.method_descriptions.

NormalizationMethodInstanceId. A stable token naming a normalization method configured for specific coordinates in a base U.CharacteristicSpace, with a named validity window and (when required) evidence pins. One such configuration can be used by several distinct apply occurrences; this identifier does not identify a calculation invocation. Used in CN_Spec.normalization.instances.

NormalizationMethodInstance. That configured method, referenced by NormalizationMethodInstanceId. Its coordinate qualification and validity window are separate from the extent of a calculation that uses it.

CV (CoordinateValue). A raw coordinate value for a named measurable slot in a chart: conceptually ⟨slot_id, raw_value⟩ (plus any chart/slice scoping needed by the chart). UNM re‑parameterizes CV → NCV under declared invariants and validity constraints.

NCV (NormalizedCharacteristicValue). A normalized value for a coordinate (UNM does not “normalize characteristics”; it normalizes coordinate values under declared invariants).

Directed transformation. The selected method states its actual input domain D, target N and transformation rule. For a partial normalizer, D is the subset where a result is defined. An edge from x to its output does not supply a reverse edge. A relation-valued or uncertain output needs its declared result semantics; the function theorem below cannot be applied without a function and equality on its output values.

≡_UNM (equality of normalization outputs). For one fixed function n:D→N, define x ≡_UNM y iff n(x)=n(y). Equality in N gives reflexivity, symmetry and transitivity on D. Thus the fibers form the set quotient D/≡_UNM. Inputs outside D have neither an n-value nor membership in this partition. This relation is distinct from the directed transformation graph.

Operational quotient. To inherit a total operation on classes, equivalent argument tuples must produce equivalent outputs. For a partial operation, its availability must also agree across equivalent tuples. Use the relevant equivalence on each input and output sort. A receiving query q is recoverable only when x ≡_UNM y implies q(x)=q(y). Only after these tests may the equivalence be called a congruence for the named operations. A set quotient alone supplies no such result.

Reversible chart change. A declared inverse recovers the input on the transformation’s stated image. A strictly monotone encoding on a totally ordered domain is injective and invertible on that image, even if the declared target contains other values. A merely monotone LUT may merge inputs. Repeated normalization or idempotence requires its own composable domain and law; it does not follow from the fibers.

NormalizationInvariant. A named invariant (e.g., unit alignment, polarity, reference plane) declared in CN_Spec.normalization.invariants and/or the selected NormalizationMethodDescription. Preserving the declared NormalizationInvariant[*] is the core admissibility claim for a normalization method instance.

NormalizationFixSpec. A declared policy selecting a representative of an already established ≡_UNM class when the receiving use needs one. It does not recover which member was the actual input or restore a lost query answer. Bound via CN_Spec.normalization.fix; omit it when no class representative is needed. UNM_id. An optional identifier in CN_Spec.normalization.UNM_id? selecting the UNM mechanism instance used by this CN‑frame. This is routing/governance; it is distinct from NormalizationMethodInstanceId (configured normalization method). ValidityWindow. A named validity window attached to a NormalizationMethodInstanceId, bounding where/when the instance is admissible (no implicit “latest”).

Relation and reuse boundary. A normalized value remains tied to the exact normalization-method instance and edition, characteristic-space and CN-Spec editions, bearer, scope and window, reference or comparison basis, evidence, and intended comparison. Reusing it does not by itself establish a transfer relation. Cite an F.9 Bridge or a plane relation only when that relation actually obtains, and state the receiving use separately. Lexical discipline. Name a UNM operation as normalization, re-parameterization or a coordinate mapping under its declared invariants. Use a specialized FPF Map designation only when its defining conditions apply; an ordinary mathematical mapping does not thereby assert that specialized kind or an F.9 Bridge. Legacy κ‑notation for normalization is retired; do not re‑introduce it.