DOI: 10.5281/zenodo.17165772
title: Law of Coherence v7.2 (Cross-Domain Evidence Pack): Empirical Tests across Gravitational-Wave, Mechanical and Bioelectric Domains
title: Law of Correspondence (LoC) V3 preregistered results
title: Law of Coherence v5 — preregistered endurance confirmation, scaling suggestive but inconclusive
title: The Universal Law of Coherence: A Consolidated Framework and Empirical Validation

description: This deposit contains the full cross-domain evidence package for Law of Coherence v7.2 (LoC V7.2), an empirical preregistration testing the proposed universal relation: \log E = k Δ + b where Δ is the short-lag information surplus (mutual information over IAAFT surrogates) and E is signal endurance (windowed decay rate or variance persistence).

 

Positive k implies coherent structure; k ≈ 0 or negative k marks chaotic or structure-free regimes.

 

Domains included

 

Gravitational-wave ringdowns (LIGO H1/L1 pairs × 4) — k_meta ≈ 0.86, 95% CI [0.70, 1.02] (positive).

 

Double pendulum simulations — positive k under weak damping; negative k as damping → 0 (chaotic).

 

EMG bioelectric signals — Gesture 9: k ≈ 12.5 [10.3, 14.8]; Gesture 10: inconclusive (CI crosses 0).

 

Lorenz chaos control — expected negative slope used as contrast domain.

 

Outcome Cross-domain agreement supports the claim that sustained, structured dynamics obey a monotonic Δ–log E relation, suggesting coherence as a necessary condition for endurance in physical and biological processes.

 

V7.2 is frozen under the tight preregistration (Δ ≥ 0.1, τ = 1–256 ms windows, R² ≥ 0.1, 95 % bootstrapped CI).

 

Contents

 

LoC_V7_2_CrossDomain_Master.zip – full data + JSON summaries + manifest

 

Domain packs: LIGO, Double Pendulum, EMG Gestures 9–10, Lorenz control

 

Preregistration PDF and README (MD)

 

Methods log and hash integrity manifest

 

Author – Aaron Cole Nailer

License – Creative Commons Attribution 4.0 (CC-BY 4.0)

Keywords – information theory, mutual information, gravitational waves, electromyography, chaos, coherence, universality, signal endurance

 

📚 Citations / Data Sources

 

Please cite the following primary sources used in LoC V7.2:

Gravitational-Wave Data

 

Abbott et al. (2018). Open Science Center (LOSC) O1–O2 strain data. LIGO Laboratory. doi:10.7935/CA75-FM95

(Pairs used: GW150914, GW170104, GW170814, GW170823; H1/L1 4096 Hz segments 32 s.)

 

 

Double Pendulum Simulations

 

Generated with custom numerical solver (v7.2 implementation, damped and undamped runs). No external data used.

 

EMG Bioelectric Signals

 

PhysioNet: A. Khushaba et al., Surface EMG Hand Gesture Dataset (Ninapro Subset 1). doi:10.13026/C2XG7C

 

Lorenz System

 

Synthetic Lorenz ODE

integration (scipy v1.11 solve_ivp, σ = 10, ρ = 28, β = 8/3).
description: > LoC v3 (minimal prereg archive).

This package documents the preregistered necessary-condition outcome for the Law of Coherence: Δ > 0 versus strict IAAFT surrogates on valid dynamics, with endurance τ measured via the log-Hilbert envelope on the same window as Δ.

Scope: v3 is a minimal archive (Δ and τ). Pooled scaling statistics (Δ vs ln τ) are not included/claimed here; broader pooled analyses and cross-domain rows are provided in v4/v5 records.

Contents:

– results_v3/loc_v2_results.csv — per-row Δ and τ (same window) with validity flags.

– results_v3/loc_v2_stats.json — run details for necessary-condition checks (not pooled scaling).

– docs/RUN_LOG.txt, docs/CHECKSUMS.txt — reproducibility metadata.

– Two background PDFs for context.

Methods (brief): KSG MI (k=5), IAAFT null (M=100), max-over-lags with L = min(80, ⌊0.05N⌋); τ via log-Hilbert envelope; validity gate: R² ≥ 0.2 and positive decay.

Claim: Endurance supported; necessary condition holds. Scaling not supported/inconclusive in v3; s

ee v4/v5.
description: What this is.

A frozen, rerunnable evidence pack for the Law of Coherence (LoC), a meta-criterion (necessary condition) for lawful dynamics in real time-series. Under a preregistered pipeline, a coherence gap (measured against strict phase-randomized surrogates, with permutation as a robustness check) scales with the system’s endurance (a physical lifetime in seconds, e.g., ringdown , qubit ).

Not a curve—this is a preregistered test. The contribution is a fixed, cross-domain test: Δ is computed against strict phase-preserving surrogates (permutation reported for robustness) and E is a physical lifetime in seconds. The Δ→ln(E) line is a descriptive summary, not the claim; the core result is that Δ_phase stays > 0 vs the strict null where real nonlinear structure exists and ~0 where an almost-linear system should not pass.

 

How to falsify 

 

Show a large-E measured system with Δ_phase ≈ 0 under the frozen spec.

 

Add datasets (same prereg); if pooled Δ vs ln(E) slope ≤ 0, LoC fails.

 

Under prereg robustness (lags/k/window ±), drive 5× CV R² ≤ 0 or flip the sign.

 

Contents.

 

core/ — Frozen spec (SPEC_LoC_v1.md), PREREGISTRATION_v1.md, FALSIFICATION_PLAN.md, CITATIONS.md

 

code/ — Reference Δ implementation + helpers (compute_delta_full.py, compute_delta.py, estimate_tau.py)

 

results/ — JSON/CSV outputs for three measured systems:

 

Gravitational waves (GW150914, H1) Superconducting qubit (Ramsey ) Nanomechanical ringdown (MHz beam) plus a pooled summary table robustness/ — Bootstrap/CV/permutation summaries (compute-friendly) data_instructions/ — DOIs/links to fetch raw data (we do not redistribute copyrighted data)

 

Reproduce (minimal).

 

1. Fetch raw data via data_instructions/DOIs_and_links.md.

 

2. Use the fixed window rule; compute E (seconds) and Δ on the same segment.

 

3. Record Δ_phase, Δ_perm, and aggregate into the provided table.

 

4. Fit Δ vs ln(E) (shared-slope test), 5× CV; see FALSIFICATION_PLAN.md for pass/fail.

 

LIGO/Virgo/KAGRA (GWOSC). GWTC-1 open data catalog. DOI: 10.7935/82H3-HH23. (Open-data hub and event pages indicate usage & acknowledgement.) 

 

Abbott, B.P., et al. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett. 116, 061102 (2016). DOI: 10.1103/PhysRevLett.116.061102. 

 

Abbott, R., et al. Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo. SoftwareX 13 (2021) 100658. DOI: 10.1016/j.softx.2021.100658. 

 

Superconducting qubit dataset & paper

 

Arnold, G.M., et al. All-optical superconducting qubit readout. Nature Physics (2025). DOI: 10.1038/s41567-024-02741-4. Dataset: Zenodo 10.5281/zenodo.14033026. 

 

Methods

Kraskov, A., Stögbauer, H., Grassberger, P. Estimating mutual information. Phys. Rev. E 69, 066138 (2004). DOI: 10.1103/PhysRevE.69.066138. 

 

Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., Farmer, J.D. Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 77–94 (1992). DOI: 10.1016/0167-2789(92)90102-S. 

 

Schreiber, T., Schmitz, A. Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77, 635–638 (1996). DOI: 10.1103/Ph

 

ysRevLett.77.635. 
description: This version (V5) extends preregistered testing of the Law of Coherence (LoC) to additional domains (GR ringdown and NMR FID).

 

Key outcomes:

 

Endurance supported: In all valid datasets, Δ > 0 versus strict IAAFT surrogates, confirming LoC’s necessary condition.

 

Scaling suggestive but inconclusive: The pooled Δ vs ln(τ) regression shows a negative slope (≈ –0.3) with moderate explanatory power (R² ≈ 0.49). However, the 95% confidence interval crosses zero and permutation testing does not reject the null (p ≈ 0.26). With only 4 valid rows, the analysis is underpowered.

 

Contents:

 

Public package — Δ and endurance results only (minimal, for readers).

 

Archival package — full reproducibility metadata (logs, checksums, environment).

 

Unified addendum — pooled Δ vs ln(τ) regression results, 95% CI, permutation p, CV-R², and figure.

 

Scope:

 

V5 confirms endurance across domains under preregistration, but pooled scaling remains underpowered. Earlier V3 suggested positive scaling trends under looser preregistration; V5 tightens definitions, demonstrating robustness but leaving

 

 

 

scaling unresolved.