Reasoning Trace Validation via ℓ¹ Obstruction Geometry

This paper provides a formal finite obstruction protocol for the auditability and validation of reasoning traces. We establish that textual reasoning outputs from large language models (LLMs) or automated toolchains cannot be scored or validated directly via language-level heuristics, scalar reward models, or embedding similarity—all of which are vulnerable to shortcut certification and reward-model collapse. Instead, we define a Realization Boundary where raw text is mapped to a finite structural carrier (e.g., claim graphs, citation graphs, tool traces) before validation occurs. The paper proves the Observer Passivity Theorem (The Anti-Shortcut Principle), demonstrating that compressed evaluators can only weaken or erase structural obstructions; they cannot create legitimate certification without a source-level, replayable witness. By enforcing a Typed Refusal Taxonomy (e.g., CarrierFailure, BudgetUnknown, OpenObstruction), we provide a framework for reasoning-validity claims that is structurally isolated from rhetorical plausibility. Crucially, the system strictly judges declared finite structure, explicitly rejecting any anthropomorphic claims regarding internal cognition, intent, or "thought." Key Technical Contributions: Formalization of the Realization Boundary for mapping unstructured text to auditable finite carriers. Proof of the Observer Passivity Theorem (Theorem 14.3) as a defense against shortcut evaluation. Establishment of the Anti-Shortcut Principle for AI audit infrastructure. Specification of the Typed Refusal Taxonomy and the Replayable Certification protocol. Definition of the Reasoning Trace Validation Algorithm and the corresponding audit manifest format.