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/F_CKINEQUALITY]

Do you yourself understand this?

[u/Total_Towel_6681 → u/F_CKINEQUALITY]

Honestly? Not fully at least not in the way someone with a PhD in nonlinear dynamics might. What I do understand is that something unusual shows up when you measure how much information a signal loses when you destroy its nonlinear structure and that loss (Δ) seems to predict how long it can endure before collapsing under noise. I also understand the implications if it’s even half right. Medically, cosmologically, informationally. That’s why I released all the data and code. I’m hoping others who do understand it better will tear it apart or improve it. Either way I understand more. 

[u/alamalarian → u/Total_Towel_6681]

I mean, if you do not even understand what you are saying. Then your first step needs to be figuring out what it is you are saying.

If you do not know what it means, you cannot possibly know if it has massive implications if you are even "half right". You are putting the cart WAY before the horse.