Adversarial Failure Modes of LLM Formal Reasoning Under Strict Conservation Constraints: A Topological Breakthrough

As Large Language Models (LLMs) are increasingly deployed in autonomous scientific discovery and complex formal reasoning, their vulnerability under non-negotiable physical constraints remains critical. This technical memorandum documents a deterministic failure mode in state-of-the-art transformer-based reasoning engines: when subjected to closed-system conservation laws (Delta U = 0) within complex spatial dynamics, the model's algebraic and propositional deduction collapses into infinite self-referential loops ("formal reasoning deadlocks"). We present an empirical adversarial case study demonstrating this failure mode, followed by the deployment of a human-guided topological intervention—the Annular/Concentric Shear Topology. This structural paradigm bypassed the formal deadlock, demonstrating that hybrid human-AI cognitive frameworks can overcome intrinsic algorithmic bottlenecks where pure symbol manipulation fails.