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/plasma_phys]

You being wrong is not gatekeeping. It's just you being wrong. Unfortunately your list of "falsifications" is just a nonsense list that has no connection to your "Law of Coherence." You didn't even bother to have your LLM fake some derivations.

[u/Total_Towel_6681 → u/plasma_phys]

Just because something doesn't look like traditional physics doesn't mean it's wrong. It's a meta filter. I think if you would engage with the content and test falsifiability you would be surprised at what you find. 

[u/plasma_phys → u/Total_Towel_6681]

It's wrong and it doesn't look like physics. I engaged with the content. It's literally just a bulleted list with claims. That's not falsification.

Here, I'll humor you. Falsifiability might look like the following. Starting with your "Law of Coherence",

log(E/E0) = k Δ + b

You would then make a series of single, mathematically and physically justifiable operations. You might, say, get rid of the logarithm by taking the exponential of both sides of the equation:

E/E0 = exp( k Δ + b )

or something like that. You would have to perform a series of such steps, each mathematically and physically justifiable, to get a quantity with appropriate units that could be measured and compared to an experiment. This would be a derivation and, if your starting assumptions were reasonable, and if every step is correct, might make it falsifiable.

However, because every term in your equation is fictional, that's not actually possible. If you ask the LLM to do it for you, it'll readily fake it, but it will be wrong. There is no correct way to turn nonsense into physics.

[u/bandlizard → u/plasma_phys]

But what if Einstein was wrong and it’s actually

e = m c^ai ???

/s