Constraint-Driven Coherence in LLM Output: Token-Entropy and Surprisal as CPA Signatures Across Models

Dynamic Present Theory (DPΦ) posits that only the present is physically real and that reality unfolds via Continuous Present Actualization (CPA): a dynamical process in which constraint progressively narrows the lawful possibility space, driving actualization along paths of minimal cost. 

We test whether this principle manifests in artificial language systems. Across four independent large language models (GPT-4o, GPT-4 Turbo, Mixtral-8x7B-Instruct, and Llama-3.1-70B-Instruct), we measure per-token surprisal under three externally imposed constraint levels (Low/Medium/High). 

CPA predicts monotonic uncertainty reduction with increased constraint, yielding statistically separable Low versus High distributions. All models exhibit the predicted directionality; Mann-Whitney tests show significant separation (p < 0.05) across all architectures:

- GPT-4o: z = -5.74, p = 9.4 × 10⁻⁹
- GPT-4 Turbo: z = -2.58, p = 0.010
- Mixtral-8x7B: z = -2.66, p = 0.008
- Llama-3.1-70B: z = -6.00, p = 2.0 × 10⁻⁹

Complete data, figures, and statistical analyses are included for independent verification and replication.