The physics
shows up in the data.

A single scalar feature — the fractal-scaling exponent of beat-to-beat intervals — separates severe heart failure from normal sinus rhythm at AUC 0.942 on public PhysioNet data. The multivariate HRV model hits 0.947 ± 0.052, five-fold cross-validated.

The Wike Coherence Law predicts this collapse before it's measured: as γ_eff rises toward the critical threshold γ_c, cross-scale phase locking fails — and fractal structure with it. This page shows the prediction matching the data.

The numbers.

DFA α — the coherence signature.

A healthy heart sits near α ≈ 1.0 — pink noise, long-range correlations, coherent organization across time scales. In severe CHF, α collapses toward 0.65. The distribution separation is what the framework predicts: decoherence is fractal-exponent collapse.

Figure 1. DFA α distribution overlay. Dashed lines mark group means: Normal α = 1.104, CHF α = 0.649. Single-feature AUC 0.942, p < 0.0001.

Every feature, one row.

Six HRV features computed per 5-minute segment. Cohen's d measures standardized effect size; AUC is the rank-based probability a CHF segment's value exceeds a normal segment's for that feature.

Figure 2. Per-feature AUC. Gold bars exceed 0.85; the dashed reference line marks the multivariate ceiling.

Where coherence lives. Where it breaks.

Plotting DFA α against RMSSD lays the two cohorts on different manifolds. Normal sits in a narrow fractal band with moderate vagal tone. CHF fans out toward both α-collapse and RMSSD inflation — classic autonomic dysregulation on top of fractal failure.

Figure 3. RMSSD vs DFA α, per-segment scatter. Teal circles: Normal. Red triangles: CHF.

This is what the math said would happen.

As γ_eff rises toward the critical threshold γ_c, coherence decays exponentially. The prediction is that decoherence is not just a loss of amplitude — it is a loss of structure across scales. A coherent biological system shows pink-noise (1/f) fluctuations; a decoherent one loses that scaling and drifts toward uncorrelated noise. DFA α measures exactly that fractal exponent.

CHF is a sustained γ_eff excursion at the cardiac level. The prediction: α should collapse from ~1.0 toward ~0.5–0.7 as the coherent attractor is lost. The data: Normal α mean = 1.104; CHF α mean = 0.649. That's the prediction, measured.

How the numbers were made.

Reproduce it. Dispute it. Extend it.

What we're already building.

Phase 1 answers "does HRV discriminate?" Phase 2 answers the real clinical question: does adding C-reactive protein push the discrimination ceiling above 0.947 in a cancer cohort? That requires paired HRV + inflammation + outcome data, which lives in MIMIC-IV.