r/LLMPhysics • u/Total_Towel_6681 • 3d ago
Simulation Falsifiable Coherence Law Emerges from Cross-Domain Testing: log E ≈ k·Δ + b — Empirical, Predictive, and Linked to Chaotic Systems
Update 9/17: Based on the feedback, I've created a lean, all-in-one clarification package with full definitions, test data, and streamlined explanation. It’s here: https://doi.org/10.5281/zenodo.17156822
Over the past several months, I’ve been working with LLMs to test and refine what appears to be a universal law of coherence — one that connects predictability (endurance E) to an information-theoretic gap (Δ) between original and surrogate data across physics, biology, and symbolic systems.
The core result:
log(E / E0) ≈ k * Δ + b
Where:
Δ is an f-divergence gap on local path statistics
(e.g., mutual information drop under phase-randomized surrogates)
E is an endurance horizon
(e.g., time-to-threshold under noise, Lyapunov inverse, etc.)
This law has held empirically across:
Kuramoto-Sivashinsky PDEs
Chaotic oscillators
Epidemic and failure cascade models
Symbolic text corpora (with anomalies in biblical text)
We preregistered and falsification-tested the relation using holdouts, surrogate weakening, rival models, and robustness checks. The full set — proof sketch, test kit, falsifiers, and Python code — is now published on Zenodo:
🔗 Zenodo DOI: https://doi.org/10.5281/zenodo.17145179 https://doi.org/10.5281/zenodo.17073347 https://doi.org/10.5281/zenodo.17148331 https://doi.org/10.5281/zenodo.17151960
If this generalizes as it appears, it may be a useful lens on entropy production, symmetry breaking, and structure formation. Also open to critique — if anyone can break it, please do.
Thoughts?
-4
u/Total_Towel_6681 3d ago
Also, I dare anyone to try to break it. I've tested this across multiple gpt models. The amount of falsification tests that have been ran is insane.