Local Green, Global Red I - Evaluated Path Kernels for Composed Agent Reliability

Local Green, Global Red: Evaluated Path Kernels for Composed Agent Reliability introduces a finite calculus for measuring non-compositional verification in composed AI agent systems. The paper formalizes a central reliability failure mode in modern multi-stage agents: The paper formalizes the failure mode E(γ₁)=1, E(γ₂)=1 ⇏ E(γ₂⋆γ₁)=1: locally validated steps do not necessarily compose into globally correct behavior. That is, locally validated steps do not necessarily compose into globally correct behavior. The work defines Evaluated Path Kernels (EPK), proves a conditional finite kernel composition theorem under explicit factorization assumptions, and derives measurable residual defect terms when evaluator composition fails. The framework introduces quantitative diagnostics including: Evaluator Gluing Defect (Δₑ) Negative Gluing Defect Rate (NGD) Residual Kernel Error (RKE) Proposal-weighted hidden failure mass (wNGD) The manuscript connects finite path-space reliability, proposal-weighted trajectory modeling, Product-of-Experts vs. Mixture-of-Experts verification tradeoffs, and boundary sufficiency in multi-agent systems. It further develops a Proposal–Projection Representation (PPR) framework describing structural limits of systems whose outputs require external evaluator authorization. Primary application targets include: LLM agents repository-scale software repair hardware verification agents tool-augmented autonomous systems multi-agent orchestration The repository includes: theorem-consistent finite calculus formulations benchmark protocols synthetic diagnostics reproducibility fixtures LaTeX source and compiled manuscript This work is presented as a finite obstruction and compositional reliability framework rather than a claim of benchmark-complete empirical validation.