Six Domains. One Equation.
The Cx operator — Cx = Φ × C² — was applied to six independent physical systems using publicly available data. No parameter tuning between domains. No domain-specific adjustments. One equation. Statistically significant results in every domain tested. Four achieve p < .001.
Where Φ is normalized Shannon entropy of the eigenvalue distribution of the cross-correlation matrix (measuring signal integration), and C² is the squared inverse of the Frobenius distance between consecutive correlation matrices (measuring structural stability). The product Cx measures coherent integration.
Confirmed Results
| Domain | Substrate | p-value | ΔCx | N |
|---|---|---|---|---|
| EEG (Neural) | EM cortical | 1.54 × 10&supmin;&sup6; | −7.7% | 4,574 |
| Ocean Currents | Thermohaline | 2.34 × 10&supmin;&sup6; | +9.4% | 7,103 |
| Financial Markets | Information | 3.37 × 10&supmin;&sup5; | −11.6% | 852 |
| Jet Stream | Neutral gas | 7.20 × 10&supmin;&sup4; | +15.9% | 204 |
| Seismic | Solid elastic | 0.00172 | −8.4% | 239 |
| Solar Wind | Plasma | 0.00471 | −9.3% | 65 |
The Six Confirmed Domains
1. Neurological EEG
8-channel scalp EEG recordings. The Cx operator detects coherence collapse at seizure boundaries — the transition from organized cortical activity to disordered firing. Strongest statistical result of all domains.
2. Ocean Currents
Temperature profiles across 4 depth layers from the global Argo float network. Coherence increases in organized circulation patterns. Largest dataset in the study.
3. Financial Markets
Seven sector ETF returns analyzed across 17 years. Cx drops sharply before market crises — coherence degrades as correlations fragment. The operator detects pre-crash signature without any financial-domain-specific inputs.
4. Atmospheric Jet Stream
5-channel u-wind data at jet stream altitude. Coherence increases during atmospheric blocking events — when the jet stream locks into a persistent pattern. Largest effect size in the study.
5. Seismic Network
Vertical-component seismograms from 6 stations around the 2019 Ridgecrest M7.1 event. Coherence drops at the earthquake boundary — organized stress release transitions to aftershock disorder.
6. Solar Wind
4-channel magnetic field data from NASA’s OMNI2 database. Coherence degrades at interplanetary shock boundaries. The domain with the smallest sample size, producing the weakest (but still significant) result.
Honest Nulls
Not every domain confirmed. Two produced non-significant results. We report them because selective reporting is the antithesis of science.
Geomagnetic Storms (Kp ≥ 5)
Storm-window analysis using the same OMNI2 dataset as Solar Wind but segmented by Kp ≥ 5 events. Only 8 qualifying storm windows in the study period — severely underpowered. The effect direction was consistent with the Solar Wind result, but the sample was too small to reach significance.
Cardiac HRV (MIT-BIH)
Heart rate variability from single-lead ECG recordings. The multi-channel independence assumption required by the Cx operator was violated — a single physiological source cannot generate the cross-channel structure the operator measures. This is a theoretical exclusion, not a failed replication. The separate CHB-MIT EEG study (multi-electrode, genuine multi-channel) confirmed strongly.
Pending Domains
These domains have protocols designed but are awaiting data access or additional validation.
Power Grid (Fingrid Open Data API)
Finnish national grid frequency and cross-border flow data. Multi-channel structure confirmed. API access pending. Expected to test whether coherence drops precede grid instability events.
MIMIC-IV Cardiovascular / Respiratory
Multi-channel ICU physiological data from PhysioNet’s MIMIC-IV database. True multi-channel (ABP, ECG, SpO2, respiratory) — resolves the single-source limitation that excluded the MIT-BIH cardiac analysis.
What This Means
A single mathematical operator — identical code, identical parameters — detects boundary transitions in neural tissue, ocean currents, financial markets, atmospheric circulation, seismic networks, and solar plasma. It fails where theory predicts it should fail (single-channel cardiac data) and produces non-significant results where sample size is insufficient (geomagnetic storms with N=8).
The operator does not know what domain it is measuring. It receives only a matrix of time-aligned numerical channels. That it finds structure — and that the structure aligns with independently documented physical boundaries — is either a coincidence across six unrelated fields, or evidence that coherent self-referential integration is a domain-general property of complex systems.
Reproducibility
Every dataset used in this study is publicly available. The validation code runs on a standard laptop in under two hours. Source datasets: NASA OMNI2 (CDAWeb), CHB-MIT Scalp EEG (PhysioNet), NOAA NCEP/NCAR Reanalysis (PSL), SCEDC CI Network (SCEDC), SPDR Sector ETFs (public market data), Argo Float Program (Argo GDAC). No proprietary data. No special hardware.