B.3/A.2.6/C.2.2 ontology inconsistency: G as characteristic vs scope object

[iqdoctor]

Outcome (Ontology-first)

The ontology in the current FPF-Spec.md is locally inconsistent (categorical failure): G is typed both as a CHR “characteristic” and as a USM set-valued scope object.

1) Terms and normalization (scholastic)

• U.Characteristic: a measurable aspect with declared scale kind and CHR legality (A.17/A.18 family).
• U.ClaimScope (G): a set of U.ContextSlice values with set algebra; not a numeric scale.
• R: warrant-strength (ratio, or declared ordinal proxy), aggregated pathwise.
• CL: edge/crossing property that penalizes R, not F/G.
• GateDecision: {abstain, pass, degrade, block}.
• GuardDecision: {pass, degrade, abstain}.

Normalization used in this issue: G is treated only as a USM scope object, not as a CHR characteristic.

2) Ontology validation (ontology-first)

Failure type: categorical.

Evidence

• B.3 still frames F–G–R as characteristics and gives G a scale-style treatment:
  • FPF-Spec.md:23560
  • FPF-Spec.md:23595
  • FPF-Spec.md:23606
• A.2.6 explicitly forbids typing scope entities as CHR characteristics:
  • FPF-Spec.md:3892
  • FPF-Spec.md:4015
• C.2.2 states ⟨F,G,R⟩ is not U.CharacteristicSpace:
  • FPF-Spec.md:26087
• A.2.6 also contains wording that reintroduces G as a characteristic in the same normative area:
  • FPF-Spec.md:4030

Concrete counterexample

If G is interpreted as “larger is better” (scale intuition), a bridge translation can lawfully narrow scope in the target context. Then the smaller translated scope is the only valid one for admissible use. So monotone “bigger G is better” is not invariant under bridge transport. This is a categorical error, not an empirical one.

3) Logical analysis

• Hidden assumption: all triad members must live in one CHR regime. This is false for G.
• Hidden assumption: G admits scalar/ordinal monotonicity. This is false if G is set-valued.
• Explicit inconsistency: B.3 versus A.2.6/C.2.2 (see evidence above).
• Salvage by trivialization is present: saying “the tuple is not a CharacteristicSpace” limits consequences but keeps characteristic language for G; this blurs the type boundary instead of repairing it.

4) Modalities separated

• Deontic: MUST/SHALL rules for publication, gates/checks, bridge use.
• Alethic/typing: what each entity is (G as set object; R as warrant-strength).
• Epistemic: unknown-folding, degrade/abstain, evidence freshness/decay.
• Pragmatic: SHOULD-level profile and operational guidance.

5) Structured argument (premises → steps → conclusion)

Premises

• P1 (established): G is defined as set-valued scope object in USM.
• P2 (established): B.3 still types/frames G under characteristic language.
• P3 (established): C.2.2 denies that the triad is a CharacteristicSpace.

Steps

• S1: P1 and P2 are type-incompatible in one ontology.
• S2: P3 does not remove that contradiction; it only fences one consequence.

Conclusion

The current triad layer is internally inconsistent at the ontology/type level (categorical inconsistency).

6) Minimal repair + re-run

1. In B.3, replace “three characteristics F–G–R” with:
   • “two characteristics (F,R) + one scope object (G)”.
2. In A.2.6:4030, replace “set-valued characteristic” with:
   • “set-valued scope object”.
3. Introduce explicit projection CoverageMetric(G) as a report-only proxy when a scalar is required, with a normative ban on substituting G by this projection in norms/gates.

Re-run expectation after repair

• F and R remain CHR-compatible measurements.
• G remains an applicability object governed by set algebra.
• CL penalizes R only.
• Gate logic remains typed without cross-type collapse.