Emergency Evidence Necessity

Abstract

Evidence collisions force an authorization error and block necessity recovery.

Theorem 1.1 (Evidence-only authorization must err on a collision).

$$\forall X,B_E,E:X\to B_E,N:X\to Bool,\forall x,y,(E(x)=E(y)\wedge N(x)\ne N(y))\Rightarrow ((\forall A:B_E\to Bool,(\exists z,N(z)=false\wedge A(E(z))=true)\vee (\exists z,N(z)=true\wedge A(E(z))=false))\wedge \neg (\exists R:B_E\to Bool,N=R\circ E)).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/EmergencyEvidenceNecessity.emergency_evidence_necessity (✓ std3). ∎

Source. Repository-derived.

Commentary.

The public hypotheses expose the evidence interface and Boolean necessity target, together with an equal-evidence, unequal-necessity pair.

For every Boolean rule on evidence, the theorem explicitly exhibits an unnecessary authorization or a necessary rejection. The same collision also prevents any recovery map from factoring necessity through evidence.

The nonfactorization conjunct directly applies the repository’s informed_disclosure_defect theorem.

References

• Truth anchor: D5/S3/ConceptDynamics/EmergencyEvidenceNecessity.emergency_evidence_necessity
• Dependency: D5/S0/Rewriting/Quotients/InformedDisclosureDefect