Structural Rigidity and the 57-Token Predictive Window: A Physical Framework for Inference-Layer Governability in Large Language Models

This paper presents an empirical measurement framework for inference-layer governability in large language models, identifying a consistent pre-commitment window (~57 tokens) during which reasoning trajectories can be detected and influenced prior to irreversible commitment. We introduce trajectory tension (ρ = ‖a‖/‖v‖) as the primary measurement instrument and energy asymmetry (Σρₘisaligned / Σρₐligned) as the unifying governance metric. A five-regime spatial taxonomy is derived from decisive check sweep analysis: Authority Band, Late Signal, Inverted, Flat, and Scaffold-Selective. A 57-token pre-commitment window is identified in Phi-3-mini-4k-instruct under greedy decoding on arithmetic constraint probes — the only governable configuration found across the cohort. Key findings include: (1) chat template as a governance variable — 98% suppression of the authority band signal through prompt formatting alone with no change to model weights; (2) the distillation finding — reasoning distillation transfers output capability without transferring governance geometry; (3) the local-global decoupling finding — per-layer geometry and cumulative energy trajectory are independent axes that can produce opposite conclusions; (4) hallucination as an epistemically distinct failure mode — zero predictive signals across 72 test conditions, consistent with spurious attractor settling in the absence of world-model counter-force; and (5) a methodological null result establishing that only magnitude-based observables (ρ, Σρ) are discriminative — torque timing (τ = δ × κ) produces zero predictive signal across 488 layers and eight configurations. The theoretical framework connects inference dynamics to Hinton's energy-based account of neural computation as a motivating analogy. The Layer-Token Duality is introduced to reconcile simultaneous within-token settling (vertical axis) with sequential across-token prediction (horizontal axis). A hypothesis is stated that compliance optimization may create a fundamental tension with geometric governability. Extends arXiv: 2603. 21415. Submitted to NIST CAISI (Docket NIST-2025-0035).