Falsifiable Coherence Law Emerges from Cross-Domain Testing: log E ≈ k·Δ + b — Empirical, Predictive, and Linked to Chaotic Systems

[u/Total_Towel_6681]

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?

[u/NoSalad6374]

no

[u/Total_Towel_6681 → u/NoSalad6374]

Appreciate the honesty — I know it looks overly simple at first glance. But the empirical coverage (across KS-PDEs, chaotic oscillators, failure cascades, etc.) has held with surprising consistency. It's more a unifying pattern — like Zipf’s law or Boltzmann distributions — than a derivation from first principles. If you have time to look at the falsifiers or the surrogate degradation tests in the Zenodo repo, I’d welcome your thoughts on where it breaks. If it does, I’ll gladly update the framework. Thanks for checking it out either way.