Standard-Model Flavour as a Typical Draw: Hierarchies, Mixing and CP Violation from a Record-Localised Overlap Measure

Abstract

We test the hypothesis that the flavour parameters of the Standard Model are not selected by any dynamical mechanism but are a typical draw from a canonical probability measure on Yukawa overlap data. The measure is not fitted: Yukawa matrices are overlap integrals of generation zero-mode packets whose positions are uniformly distributed on their carrier manifolds, whose localisation follows a heat-kernel law with a bandwidth quantized on a spectral-truncation ladder, and whose complex phases are monopole holonomies weighted by the hypercharge decomposition Y=k/3+q. Two structural correlations are inherited from the underlying geometric model rather than imposed: the up- and down-type right-handed sectors share one internal bundle, and the up-type sector couples through the conjugate Higgs doublet, whose action on coherent packets is the antipodal map. An additive (harmonic-fluctuation) measure is excluded at the outset: its 99th-percentile hierarchy depth is 1.6 decades against the observed 5.1. Under the multiplicative record-localised measure, a pre-specified joint test of seventeen basis-invariant flavour observables — three hierarchy depths, the up–down depth split, three middle-mass placements, three CKM angles, the Jarlskog invariant, three PMNS angles, the neutrino mass-squared ratio, and two inter-sector scales — is not rejected (p_T=0.084, p_S=0.667 under minimum-margin and Fisher statistics with empirical nulls). Within-sector structure is uniformly typical, including sin^2 θ_13=0.022 at the 51st percentile, where pure anarchy places it at the 4th. The test isolates a single correlated tension: the up-sector normalisation log_10 (y_t/y_b )=1.78 lies at the 99.7th percentile while the dependent diagnostic log_10 (y_b/y_τ ) is central — the one number the ensemble does not explain is the overall scale of the top Yukawa. The realisation predicts normal neutrino mass ordering with probability 0.97, stable across the admitted Majorana structures, and an uninformative (near-uniform) leptonic δ_CP. All discrete modelling choices, one undischarged basis identification, and a pre-specified follow-up protocol for the top-scale tension are catalogued in a freedom audit.