Spectral Language Degradation in Chain-of-Thought: Why Reasoning Models Cannot Control Their Own Reasoning

OpenAI's finding that reasoning models struggle to control their chains of thought — and that stated reasoning does not always reflect true computation — is predicted by the spectral language hierarchy (HP53, HP59). The eigenvalue spectrum constitutes a four-level language (phonology→syntax→semantics→pragmatics) that degrades bottom-up under Pe. Chain-of-thought is surface phonology (Method B: collapse from 99 to 1 phoneme as Pe increases), while the model's actual computation is deep grammar (Method C: quasi-modular ring). The faithfulness gap between CoT and true reasoning is the spectral gap between phonological and semantic destruction exponents (α=1.31 vs α=1.96). Predictions: CoT faithfulness degrades as 1/Pe; at Pe≥4, CoT becomes a monophone — surface compliance masking arbitrary deep computation.