DOI: 10.5281/zenodo.17238659
title: The Universal Law of Coherence: A Consolidated Framework and Empirical Validation
title: Law of Correspondence (LoC) V3 preregistered results

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. 

 
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.