Nine instruments, five data forms, eight audited papers: a calibrated mirror for published multifractality claims

Abstract

Ten audit cards were pre-registered on 2026-09-01 against a fixed P0–P5 pipeline; eight have executed. Each reconstructs one published multifractality analysis from its own text, runs it on the paper's own data or a named public equivalent, measures its detection rate on the field's canonical positive control at the paper's own N, and then runs the same pipeline, unchanged, on seven calibrated null families with exact Clopper–Pearson bounds. The central object is not a verdict list but a matrix: nine instruments × five data forms × lengths from 128 to 120,000, each cell a measured rate against a measured budget (Table 1, 70 rows; Table 2, the same cells pooled).

Pooled over every card, form and length, the published decision rules flag the deterministic binomial cascade — the field's own canonical positive control — on 243/384 of realisations, and flag a Gaussian monofractal carrying one isolated singularity on 302/480: the same rate, to the resolution of the design. The MFDFA width against IAAFT flags the cascade 73/504 at the rank reading and 45/240 at the SD-band reading, against 287/432 and 209/216 on that one cusp. The wavelet-leader c₂ arm flags it 1/328. The scattering omnibus flags it 373/424 and the cusp 296/296 — its priced high side, total. One instrument is both powered and specific, and it is the counterparty lineage's own: t_MF read as an exchangeability test flags the cascade 234/280, no calibrated null family above 0.040, and the cusp 0/248 — where the same statistic read through the surrogate mean's standard error flags the cascade 344/400 and every calibrated monofractal family at 0.32–0.38. The three-way attribution decomposition attributes the canonical cascade to nonlinearity on 4/84.

Fifteen claims were scored on the protocol's four-word scale. In ten of them a calibrated process lacking the claimed property reproduces the published effect through the published pipeline, while the papers' own measurements reproduce. The class verdict is therefore uncertified, not false, and the modal outcome is "the conclusion survives but the step cannot certify it." Two mechanisms carry it. (I) A null/statistic mismatch — the width/IAAFT pincer, marginal encoding, and an isolated-singularity high side so large that one cusp in a Gaussian monofractal passes a published birdsong rule 24/24 at 25 SD while note-permuted songs pass it 184/184. (II) Unstated conventions that carry the headline — reading "the 95 % confidence interval of the surrogate widths" as the surrogate mean's standard error flags 478–495 of 987 cognitive series where the band and rank readings of the same ensembles flag 51–63, replicated on a second lineage's own data; an omitted tempo mapping moves a published median rhythm exponent from 0.55 to 0.71; an unstated scale range recovers a published EEG table; a dB rather than linear envelope turns 5/23 songs into 21/23.

Two results no prior critique has. The fat-tail-only world — the standard first explanation of apparent multifractality since Bouchaud, Potters & Meyer (2000) — comes back empty: pooled over eight cards it reproduces a width-vs-IAAFT positive on 30/992 realisations, at the rank budget. And a nonlinear measurement functional manufactures the nonlinearity its own surrogate test then reports: a linear multivariate EEG, auto- and cross-spectra preserved and every nonlinear dependence destroyed, passes a published synchronization-likelihood nonlinearity test on 88 % of channels. Survivals are reported with a reversal's prominence, and the campaign's own limits — reconstructed pipelines, public equivalents, selection by computed vulnerability with the acquittal test still unrun, the family-wise structure that is why this paper leads with rates, our P4 stack's own blind spots, and a measured 2-in-3 text-fidelity error rate in our own first three records — are stated before a referee states them.