Flavour as a Boundary Test of Geometric Reconstruction Homogeneous Family Carriers, Majorana Backreaction, and Topological Zero Modes in the Geometric Block Universe

Abstract

The Geometric Block Universe (GBU) programme seeks to reconstruct quantum probability, relational time, gauge–Higgs structure and gravitational dynamics from one constrained geometric ontology. This volume asks whether the same discipline can derive three-family fermion hierarchies, quark and lepton mixing, and CP violation without inserting Yukawa matrices in disguise. Ten independently motivated routes are audited with carrier content, incidence structure and stiffness data frozen before their flavour consequences are inspected. The principal analytic result is an abelian-commutant flavour obstruction. Homogeneous equivariance places the left-handed Gram operators in the carrier commutant; for the multiplicity-free carriers audited here that commutant is abelian. Minimal common-left-node determinants instead compress the incident arms into one aggregate operator; stationarity under independent frame rotations forces the up and down Gram operators to commute on nondegenerate branches. Such vacua have aligned quark frames and a vanishing Jarlskog invariant, while degeneracies leave mixing unresolved rather than predicted. Under a separate single-root radial condition, active singular values are equal within each irreducible block. The theorem unifies the real and complex homogeneous carriers, the graded one-plus-two carrier, homogeneous zero-mode overlaps and the minimal common-left determinant; a graph-separation corollary formalises the quark blindness of disconnected neutrino additions. It does not subsume the Majorana quintet source, vector-like bridge, complex sextet or unrestricted multi-Higgs routes: those mechanisms escape at least one theorem hypothesis and retain route-specific analytic or numerical dispositions. Across all ten explicit constructions, none selects the simultaneous observed pattern. The GBU can nevertheless accommodate empirical Standard-Model Yukawa matrices as finite Dirac-operator input. What fails is the stronger claim that the audited minimal geometries derive flavour. A measure-theoretic typicality programme is identified as one distinct GBU-native alternative, not as a logical consequence of invariance alone.