The Four Forces Paper II: Color, Hypercharge, and Dual-4DD Boundary Resolution
From SAE Priors to the Complete Hypercharge Table of One Generation of Fermions

Writing Declaration: This paper was independently authored by Han Qin. All intellectual decisions, framework design, and editorial judgments were made by the author.

Abstract

The Four Forces Paper (DOI: 10.5281/zenodo.19342106) established the structural correspondence nDD ↝ SU(n). Building on that foundation, this paper derives the color structure and complete hypercharge values of one generation of fermions. The main results are: (1) color triplet states arise from the complexification of the three-dimensional orthogonal complement to the timelike direction in 4DD, with dim = 4−1 = 3; (2) SU(3) = Aut(C_x, h_x, Ω_x), with 8 gluons as a direct downstream consequence of localization, and the global U(1) phase stripped during the U(3) → SU(3) reduction identified as the geometric origin of baryon number conservation; (3) quarks and leptons are two boundary-resolution images of the same trans-dual family object — native readout yields the color triplet (quark), while remote readout through an unreadability quotient yields the color singlet (lepton); (4) the fundamental hypercharge quantum of 1/6 arises from the equal-weight theorem on six 4DD facets within a single 3DD block, combined with primitive normalization; (5) the complete hypercharge values of one generation of fermions are derived from one discrete minimality input and two structural priors, with no continuous free parameters, exactly reproducing all five known values.

Predictions: a right-handed neutrino exists with zero hypercharge (consistent with the seesaw mechanism); within each completed family sector, native and remote readouts must appear in pairs; the proton does not decay through gauge-mediated channels.

Keywords: Self-as-an-End, four forces, color charge, hypercharge, trans-dual, fermion, gauge symmetry, Standard Model, SU(3), quark, lepton