The surrogate band and its three readings

The surrogate band and its three readings — a paper of the Feno program. Abstract. The multifractality test this literature has run since 2010 compares a series' singularity-spectrum width to the widths of its IAAFT surrogates and rejects when the original lies outside "the 95% confidence interval" of the surrogate widths. That phrase is not one test. On one and the same ensemble it admits at least three: a band (the surrogate mean plus 1.96 SD of the surrogate widths), a standard error of the surrogate mean (the mean plus t × SD/√n_surr — the construction the successor instrument t_MF standardised), and a rank or exchangeability test (the original must out-rank its surrogates at p < 0.05). The readings differ by a factor of √n_surr — about 5.5 at the 30 surrogates the 2010 precedent fixed — and the difference is not cosmetic. On 987 public lexical-decision session series, the reconstructed 2010 rule flags 51/987 under the band reading and 63/987 under the rank reading — the nominal rate — while the same thirty surrogates read through the surrogate mean's standard error flag 478/987, and the successor instrument's published rule flags 495/987 significant-positive plus 252 significant-negative. On identical ensembles at the same length, the standard-error reading fires significant-positive on 8/24 realisations of a fitted fGn, 8/24 of a fitted AR(4), 8/24 of a Gaussian monofractal carrying the cohort's own response-time marginal and 10/24 of one carrying a single lapse episode, where the band readings of the same ensembles fire 0–2/24 and the rank readings 0–1/24 — at full power on the canonical cascade. The same behaviour replicates on a different lineage member's own published recording. The convention, not the statistic, is the cost: the sealed flag says so, and the fix is one line of a methods section. Report the band, the standard error and the rank side by side, both tails, and state n_surr. Deposit note. All seven Feno-program repositories are private and remain private, so this deposit is standalone: it carries its own reproduction materials, its metadata contains no repository link, and sibling work is referenced by DOI rather than by repository path. Part of the Feno program. The source repository is private; the reproduction materials are contained in the record itself.