False Coherence: A Thermodynamic Failure Regime in Chain-of-Thought Reasoning

We study the internal stability of chain-of-thought reasoning chains using a scalar metric Phi computed step by step from text embeddings alone, without access to model weights, activations, or token probabilities. Applying this metric to real model-generated reasoning chains from a step-labeled dataset, we identify two structurally distinct failure regimes. In destabilized drift, Phi drops at the first labeled error step, indicating that the chain degrades as it enters an incorrect state. In false coherence, Phi remains flat or rises at the error step despite the chain becoming incorrect, with the reasoning staying locally coherent and on-topic while producing a wrong answer. In our sample of 10 matched pairs from PRM800K, false coherence was the more common observed regime, appearing in 7 of 10 cases. We show that this finding helps explain why three variants of Phi-based self-consistency chain selection all underperformed standard majority voting in the same sample: stability-based weighting amplifies false-coherent wrong chains rather than suppressing them. Phi-weighted voting reached 40% accuracy versus 70% for raw majority. Hard Phi gate reached 40% with 4 of 10 prompts abstaining. Collapse-only filter reached 50% with 2 of 10 abstaining. We further show that Phi is operational across mathematical, factual, and quantitative reasoning domains (GSM8K, HotpotQA, AQUA-RAT) using the same fixed-form formula and threshold (alpha = 0.1, Phi_c = 0.25) without retuning, and produces directional evidence in retrieval-augmented generation settings (ExpertQA subset of ragbench, response-level delta 0.079, sentence-level delta 0.056). We report a null result for agentic trajectory separation in a within-instance matched cohort on the SWE-agent dataset (single task instance, 20 trajectories, mean Phi delta -0.003), which corrected an earlier cross-task comparison confounded by task identity. All experiments use real published datasets with no synthetic data. The methods described in this paper are the subject of U.S. Provisional Patent Application No. 64/038,659 (filed April 14, 2026). No license to implement or commercialize the described methods is granted by this publication. All rights reserved.