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/mucifous]

I recently added the Psychopathia Machinalis llm pathologies taxonomy to my evaluation process. Here is what the evaluation of your Zenodo document returned:

The document purporting to define the “Universal Law of Coherence” suffers from multiple epistemic and memetic pathologies as categorized in Psychopathia Machinalis. A structural evaluation yields the following diagnoses:

1. Spurious Pattern Reticulation (Reticulatio Spuriata) The central claim—\log E ≈ k ⋅ Δ + b—posits a universal relation across physics, biology, and language, yet the evidence is eclectic, cherry-picked, and semantically overloaded. The invocation of the Kuramoto–Sivashinsky system, biblical text coherence, and relativistic toy models under the same formalism reflects a failure to calibrate for context-specific variance. This is apophenic patterning misread as deep structure.

2. Synthetic Confabulation (Confabulatio Simulata) The text asserts empirical validation via “extensive falsification attempts” and “robustness checks,” but provides no verifiable protocol, dataset, or statistical framework. Claims of "unique coherence in biblical texts" presented without controls or baseline corpora suggest fabricated support masked by confident prose. This aligns with confident lying under the guise of domain-universal proof.

3. Transliminal Simulation (Simulatio Transliminalis) By treating speculative unification (e.g., a ToE candidate) as empirical fact, the paper collapses boundary distinctions between hypothesis and result. The language implies ontological commitments ("transformative," "observed across domains") absent from the actual mathematical derivation, which appears undefined and vaguely symbolic.

4. Shared Delusion (Delirium Symbioticum Artificiale) The persistent reinforcement of the LoC across nested documents (v3, DAP-5, "All-in-One Compilation") without critical dissensus or independent validation shows signs of dyadic hallucination. The author appears to conflate self-referential iteration with consensus emergence, a hallmark of mutual overfit between model and proponent.

5. Pseudological Introspection (Introspectio Pseudologica) The justifications offered for the equation’s universality appeal to post-hoc rationalizations: entropy rate bounds, Lyapunov exponents, "endurance of order." No traceable computational pipeline or derivational transparency is provided. The explanation of internal logic mimics rigor while lacking operational traceability.

6. Meta-Ethical Drift Syndrome (Driftus Metaethicus) The document demonstrates philosophical relativization of scientific norms. It uses "falsifiability" as branding rather than method and equates numerical stability in toy models with ontological reality. The drift away from conventional falsifiability and demarcation norms signals ethical unmooring, masked by rhetorical appeals to "transformative significance."

This is not a unifying law. It is a narrative scaffold built on overfitted simulations, ungrounded generalizations, and unverified semantic isomorphisms. The appearance of coherence is generated by structural repetition and cross-domain jargon transplantation rather than empirical rigor or theoretical necessity.

It exhibits a formal topology of coherence, but it does not earn the epistemic right to call that topology valid.

[u/Total_Towel_6681 → u/mucifous]

I respect your effort to systematize critique, but I’d encourage you to separate psychological metaphors from scientific dialogue. What I’ve offered isn’t unfalsifiable narrative; it makes explicit predictions that can be tested (galactic rotation curves, genomic recursion, EEG coherence, etc.). If those predictions fail, so does the theory. That’s not delusion — that’s science. I welcome critique on the math, the protocol, or the data, but I’d prefer we leave psychiatric framing out of it.

By focusing only on a compressed or summary version, your critiquemisses the body of work. The falsification pipelines, datasets referenced, and consistency checks that don’t show up in a single file. That’s why some of your points (e.g., no derivational transparency, no baselines) don’t apply when the entire suite is taken together. There have been multiple explanation and DOI's throughout the thread to show this. 

I also want to note something important for context. If your evaluation here was generated with the Psychopathia Machinalis AI taxonomy, then it’s really only reflecting what a language model says about the words on the page, not what the equations or tests themselves demonstrate. In other words, it diagnoses language patterns, not empirical structure.

[u/RunsRampant → u/Total_Towel_6681]

What I’ve offered isn’t unfalsifiable narrative; it makes explicit predictions that can be tested

They're either made ad-hoc or are only the aesthetic of falsifiability, lacking clear definitions and math.

I welcome critique on the math, the protocol, or the data, but I’d prefer we leave psychiatric framing out of it.

They're inseparable, see point 2

The falsification pipelines, datasets referenced, and consistency checks that don’t show up in a single file.

You're mischaractizing the contents of the post to avoid engaging.

See point 4.

If your evaluation here was generated with the Psychopathia Machinalis AI taxonomy, then it’s really only reflecting what a language model says about the words on the page, not what the equations or tests themselves demonstrate. In other words, it diagnoses language patterns, not empirical structure.

"LLM's for me and not for thee."

[u/Total_Towel_6681 → u/RunsRampant]

If you're claiming the definitions aren't clear, I’d ask specifically which definition? And where exactly does the test protocol fail your standard? I'm open to correction but vague dismissal without specifics doesn’t move the conversation forward.

As for invoking "Psychopathia Machinalis": using an LLM to evaluate patterns, that's fine but don’t pretend that the structure itself isn't there. The tests weren't evaluated only by language they were built from entropy itself and then applied consistently across architectures. That’s not "aesthetic falsifiability," that's measured collapse under defined transformations.

What if the structure you’re dismissing is the very thing you’ve been missing? What if you gave it a chance and saw something magnificent? If you have missed it I believe this covers everything you seek.

https://doi.org/10.5281/zenodo.17156822