The Universal Law of Coherence: A Consolidated Framework and Empirical Validation

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.