Reputation Sufficiency Criterion

Abstract

Reputation determines a target exactly by canonical target refinement.

Theorem 1.1 (Reputation sufficiency is target-relative factorization).

$$\begin{array}{c}\forall X,B_H,S,Y:\mathrm{Type},\\ H:X\to B_H,r:B_H\to S,T:X\to Y,\\ R:=r\circ H,\\ ((\exists p:S\to \mathrm{TargetImage}\left(T\right),\forall x,\mathrm{val}\left(p(R(x))\right)=T(x))\iff \mathrm{Refines}\left(\mathrm{canonicalTargetReadout}\left(T\right),R\right))\wedge \\ ((\exists x,y,R(x)=R(y)\wedge T(x)\ne T(y))\Rightarrow (\neg \mathrm{Refines}\left(\mathrm{canonicalTargetReadout}\left(T\right),R\right)\wedge \ker \left(R\right)\ne \ker \left(T\right))).\end{array}$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/Trust/ReputationSufficiencyCriterion.reputation_sufficiency_criterion (✓ std3). ∎

Source. Repository-derived.

Commentary.

Full history, the score map, and future trustworthiness are independent source channels. Reputation is constructed publicly as the score map composed with full history.

Exact determination exposes a predictor from score coordinates into the realized target image. Pointwise agreement of that predictor is equivalent to refinement of the canonical target readout by reputation.

A pair with the same reputation and different future trustworthiness publicly refutes target sufficiency and proves that reputation and the target induce different kernels.

The public construction R := r composed with H states directly that the score is a history compression. Its adequacy is relative to the chosen trustworthiness target.

The exact family collision theorem is applied directly. Repository and pinned-library searches found no theorem combining the target-image predictor, collision, and compression clauses.

References

• Truth anchor: D5/S3/ConceptDynamics/Trust/ReputationSufficiencyCriterion.reputation_sufficiency_criterion
• Dependency: D5/S3/ConceptDynamics/Governance/JudgmentRelativeAnalogyCriterion