The Quark ER Dipole: A Minimal Ontology for Matter (XIII v4)

We propose a minimal ontology for matter within the Folded Crunch Dipole Reversed Big Bang (FCD-RBv4) pregeometric framework, extending the trans-brane Einstein-Rosen (ER) dipole structure down to the sub-hadronic scale. Three closely uni ed hypotheses are introduced: (1) up- and down-type quarks are not distinct fundamental particle species but the two lowestlying, quantized stable asymmetric mass-distribution modes of a single fundamental ER dipole, which we designate the Single-Quark Hypothesis; (2) electric charge is not an intrinsic scalar substance but a geometric signature of this trans-brane mass asymmetry (the Trans-Brane Mass-Asymmetry Rule or TBMAR), where visible charge corresponds to the negative of the mass fraction residing on the mirror brane; (3) the electron is not an independent fundamental lepton but the surface-con ned leptonic resonance (Rayleigh wave) of the minority-mass visible endpoint of the Mode-A dipole. We present the uni ed sub-hadronic taxonomy and details of how the Standard Model anomaly-cancellation condition emerges as a geometric constraint of three-dipole baryonic anchors. Finally, we integrate the v4 technical correction from Part XXVI, demonstrating how the elastic snap-through bistability of the double-well potential deforms the exact 1 : 2 mass ratio to the real minima λ − = 0.3163 and λ + = 0.6837, predicting m u /m d ≈0.46 in outstanding agreement with Particle Data Group values without free parameters.