Path-Additive Coboundary Defects for Reasoning Trace Validation

This paper connects finite obstruction calculus to reasoning trace validation through path-additive coboundary defects. A reasoning trace is modeled as a directed graph P, a section s, and a manifest of typed morphism claims, restriction maps, path-evaluation rules, and observer specifications. Each inference step adds or modifies a vertex, edge, path, or diagram claim, and validity is evaluated only relative to the declared graph and manifest. The central result is an observer-relative commutativity defect bound. Given two paths with common endpoints, their observed noncommutativity defect |Δ| is bounded by the summed local edge defects along the induced closed walk W and by the observer-measured inconsistency ObsO (δ|W). Thus, a failed diagram supplies a certified lower bound on the structural inconsistency that must be present somewhere along the audited walk, relative to the chosen observer. The framework defines structural reasoning failure as the inability to add an induced vertex, edge, path, or diagram claim to the current reasoning state without producing nonzero observer-measured defect, increasing current defect, or requiring an unlicensed structural refinement. The paper explicitly does not claim that all reasoning failure is graph non-embeddability, that one commutative diagram implies global consistency, or that reasoning error is inherently scalar or ℓ¹. Its claim is narrower: reasoning traces can be audited as path diagrams in a specified constraint graph under a declared observer model. The paper also situates this path-additive validation layer within the broader guarded evaluator architecture. It addresses path-additive defect detection and Φ₁-level obstruction interpretation, while leaving full Γ₂ closure diagnostics, Rcl gating, and Ξ representative-distortion refinement to the corresponding obstruction, operator, and representation layers.