Two instruments on one null: the reported multifractality of the human heartbeat, re-audited

Abstract

A large clinical and complexity-science literature quotes multifractal detrended-fluctuation-analysis (MFDFA) widths of physiological signals as evidence of nonlinear, cascade-like dynamics, and reads a width that does not exceed its phase-randomised (IAAFT) surrogate band as evidence that a signal is monofractal, linear, or "not a cascade." We show, on the human heartbeat, that this reading is an artifact of the width estimator's own low power, not a property of the heart. We run two detection statistics on the byte-identical IAAFT null — regenerated from the same pinned surrogate seeds, so only the statistic differs — across four canonical PhysioNet RR cohorts. Instrument one is the field-standard MFDFA two-point width; instrument two is a wavelet-scattering-moment omnibus (sparsity, normalised second-order scattering, cross-scale modulus correlation, and one phase/modulus time-asymmetry coordinate proven exactly odd under time reversal), with a pre-registered specificity and power battery.

Under the width, healthy-cohort multifractality mostly collapses against the matched linear null (nsr2db: 19/54 records significant under NN editing, median IAAFT z = 0.60), while the congestive-heart-failure cohort retains it (chf2db: 18–25/29). Under the scattering omnibus, on the same surrogates, the healthy collapse does not harden — it inverts: decisive excess on 54/54 healthy records (both editing policies), carried predominantly by time-irreversibility (median aggregate z 73 under NN, significant on 53/54), with a real secondary intermittency component; the CHF cohort is 29/29, carried instead by the multiplicative sparsity / second-order families. The specificity battery places the linear-control false-positive rate at 0.010 (nominal 0.030) and the power curve reaches 16/16 at Holter length. The width's healthy null result was therefore a statement about the width estimator's power on this cohort; a sharper instrument, on the identical null, rejects the same records. This is the physiological instance of the program's finding that the width/IAAFT pairing is incoherent (canon §6.2): a null width-vs-IAAFT result is never, on its own, evidence of linearity. We read the live t_MF robustness counterclaim head-on against its own reported cascade split (§7). All results reproduce from a fresh clone behind a deterministic gate. Nothing here is clinical; time-irreversibility is a documented physiological feature, and every statement is a measurement about public, de-identified datasets.

Calibration note. The specificity battery is 96 exact rank tests of per-test size 1/33 with 1 significant: that is consistent with the nominal 0.030 (expected 2.9; P = 0.21). It certifies the instrument is not anti-conservative and has no power to establish that it is conservative.