DOI: 10.5281/zenodo.17238733
title: The Universal Law of Coherence: A Consolidated Framework and Empirical Validation
title: Law of Correspondence (LoC) V3 preregistered results
title: Law of Coherence v5 — preregistered endurance confirmation, scaling suggestive but inconclusive

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.
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 FALSI

 

FICATION_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.