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

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22760550
Primary Topic
Complex Systems and Time Series Analysis
Type
preprint
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preprint

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

Evan Tabak Atlas
Zenodo (CERN European Organization for Nuclear Research)
Complex Systems and Time Series Analysis
preprint

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

Evan Tabak Atlas
preprint en

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. Companion preprint. The program-level mechanism, the pincer, and the synthetic known-truth power/specificity certificate are not re-derived here; they are owned by the sibling methods-core preprint "The width and the null" (Zenodo DOI reserved; publication pending), of which this paper is the physiological instance. The reference list was verified against Crossref on 2026-08-30 and is fully discharged; three bibliographic errors were corrected in that pass. Part of the Feno program. The source repository is private; the reproduction materials for this record are contained in the record itself. Version 2 (2026-09-01): reference-list publication-status notes corrected (the program's reserved DOIs were published 2026-08-31); content otherwise unchanged. Version 3 (2026-09-15). The paper now cites the Feno-program records it reads by their concept DOIs, records the deposit of Fenosoma record v5 (10.5281/zenodo.22759709) and record v10 (10.5281/zenodo.22759711, the recovery floor re-measured as the pair (N, fit grid)), and is rebuilt from the repository source so the deposited copy matches it. No measured number changes.

Zenodo (CERN European Organization for Nuclear Research)
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Complex Systems and Time Series Analysis
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