A.19.UNM:5 - Archetypal Grounding (Tell–Show–Show)

Tell. UNM is the conceptual “front gate” that turns “raw coordinate values” into “values comparable under declared invariants”, by:

1. choosing an admissible normalization method instance (with evidence and validity window),
2. applying it to produce NCVs,
3. returning only the inverse, equivalence, class-level operation or query result whose additional conditions hold for the receiving use.

Show (System). A team compares alternatives using normalization-based comparability:

• CN-Spec declares:
  • comparability.mode = normalization-based
  • normalization.invariants = {unit-alignment, polarity}
  • a method instance M_unitScale with validity window VW_2026Q1 and evidence pins.
• UNM applies M_unitScale to each coordinate value, producing NCVs.
• CPM compares the NCV-profiles (not raw profiles).
• If evidence pins are missing for a slice, UNM returns GuardDecision = abstain, preventing “fake comparability”.

Show (Episteme) — a many-to-one LUT. Let D be {0,1,2} and n(0)=0, n(1)=n(2)=1. Applying n to 2 returns the transformed value 1. Equality of outputs partitions D into {0} and {1,2}: it is reflexive, symmetric and transitive. The directed edge 2→1 supplies no edge 1→2.

The query x>0 is constant on each class and can be answered from the class. The query x>1 is false at 1 and true at 2, so no function of their common class can recover it. Retain x, split that class with the needed distinction, or return the unresolved answer set {false,true} when that set answers the receiving question. Selecting 1 as a representative would answer a question about the representative, not the lost original input.

Now let a partial operation f be defined at 0 and 1 but not at 2, with f(1)=0. Because 1 ≡_UNM 2 while availability differs, f cannot descend to a representative-independent operation on these classes. Matching only the outputs that happen to exist would miss the failure. Preserve the distinguishing input or refine the class before applying f.

Show — reversible conversion and partial normalization. For exact temperature values in the declared physical domain, Celsius-to-kelvin conversion n(c)=c+273.15 has inverse c=k-273.15 on its image. For example, 20 °C maps to 293.15 K and back to 20 °C. Measurement uncertainty remains governed by its measurement result; the exact coordinate law does not remove it. More generally, a strictly monotone encoding has an inverse on its image, not automatically everywhere in the named target.

Restrict the LUT above to D={0,1}. Input 2 is then undefined, has no NCV and belongs to no kernel class of that partial normalizer. A policy’s degraded-evidence allowance does not define n(2). Likewise, an idempotence claim needs composability and n(n(x))=n(x) on the named domain; a function’s fibers do not prove it.

Show (P2W and transformation flow). Missing/stale inputs:

• A selector (or comparator) requires comparability under normalization-based mode.
• UNM finds that a required coordinate value is missing/stale for the current slice and the instance validity window.
• UNM returns GuardDecision = abstain (fail-closed) and identifies the missing current measurement. The receiver may reuse an adequate existing result, choose a justified acquisition, or leave this comparison unresolved; any acquisition has its own planning and enactment basis.