Local Green, Global Red III: EPK Generalized

Local Green, Global Red III: EPK Generalized — Evaluated Path Kernels as Authority-Free Diagnostics Across GTLA Paper 020 introduced Evaluated Path Kernels (EPK) as a finite path-kernel calculus for composed agent reliability, demonstrating that local evaluator success is not generally compositional ("local green, global red"). Paper 023 instantiated this pattern at organizational boundaries, where siloed local validators can pass while the global composed outcome fails. This paper provides the general GTLA (General Theory of Layered Authority) theory of EPK. It establishes EPK as a finite, authority-free diagnostic overlay that can be attached to every GTLA role—measuring proposal-trace mass, detecting composition failure, preserving residual structure, routing uncertainty, and deferring certification to finite descent authority. Key Contributions:• GTLA Integration: Defines the role of EPK across the six GTLA meta-roles (GTFOC, GTFDA, GTMUR, GTOR, GTTC, GTTA), ensuring EPK acts as evidence rather than laundering diagnostics into certification.• Clean Composition Locus: Provides the finite, replayable bookkeeping for exactly when composition is licensed via the G1–G4 boundary factorization hypotheses.• Defect Ledger: Formalizes the bookkeeping of composition failures (ΔE, ΔP, ΔC, ΔR) off the clean locus.• Finite Witnesses: Mechanizes the minimal local-green / global-red witness, the scalar proposal-defect criterion, and the NGD/PGD/ZDR defect partition in Lean 4. The resulting principle of the calculus is simple: EPK measures evaluated proposal composition. GTLA decides what, if anything, can be certified.