
Description / 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 from three prior inputs within the Self-as-an-End (SAE) framework: (1) SAE foundational axioms (remainder ineliminability and conservation), (2) a complex-amplitude modeling postulate, and (3) a discrete minimality postulate n(Q_L) = 1. Main results: color triplet states arise from the complexification of the 3-dimensional orthogonal complement to the timelike direction in 4DD (dim = 4−1 = 3); SU(3) = Aut(C_x, h_x, Ω_x) with 8 gluons as a downstream consequence and baryon number B = 1/3 as a geometric corollary; quarks and leptons are two boundary-resolution images of the same trans-dual family object; the hypercharge quantum 1/6 arises from six 4DD facets within one 3DD via an equal-weight theorem; all five known hypercharge values of one generation are exactly reproduced with no continuous free parameters. Predictions: right-handed neutrino exists with zero hypercharge; within each completed family sector, quark-like and lepton-like readouts must pair; proton does not decay through gauge-mediated channels. The Higgs is reinterpreted as an effective field-theoretic description of DD-level charge transfer, not a fundamental prior structure. 四力篇(DOI: 10.5281/zenodo.19342106)建立了nDD↝SU(n)的结构对应。本文在此基础上,从SAE框架的三条先验输入出发,推导一代费米子的完整色结构和超荷值。核心结果:色三态来自4DD时间方向三维正交补空间的复化(dim = 4−1 = 3);SU(3) = Aut(C_x, h_x, Ω_x),8个胶子为下游结果,重子数B=1/3为几何推论;夸克和轻子是同一trans-dual family object的两种边界分辨像;超荷基本量子1/6来自等权定理;一代费米子全部五个已知超荷值精确复现,无连续自由参数。预言:右手中微子存在且超荷为零;每个completed family sector内quark-like与lepton-like readouts必须成对出现;质子不通过规范介导通道衰变。Higgs被重新诠释为DD层级荷转移的有效场论描述。 Keywords Self-as-an-End; SAE; four forces; color charge; hypercharge; trans-dual; fermion; gauge symmetry; SU(3); SU(2); U(1); baryon number; right-handed neutrino; seesaw; Higgs; DD hierarchy; boundary resolution; remainder conservation Related Identifiers Is supplement to (SAE Foundational Papers) DOI: 10.5281/zenodo.18528813 (Paper 1: Systems, Emergence, and the Conditions of Personhood) DOI: 10.5281/zenodo.18666645 (Paper 2: Internal Colonization) DOI: 10.5281/zenodo.18727327 (Paper 3: Complete Framework) Is continuation of (Four Forces Series + Cosmo Series) DOI: 10.5281/zenodo.19342106 (Four Forces Paper I: nDD ↝ SU(n)) DOI: 10.5281/zenodo.19341042 (Four Forces Prequel: DD Breakthrough and DD Splitting) DOI: 10.5281/zenodo.19329771 (Cosmo Paper V v2: Dual-Frame Resolution) References DOI: 10.5281/zenodo.18842450 (Methodology Paper I: Chisel-Construct Cycle) DOI: 10.5281/zenodo.19245267 (Cosmo Paper I: Cosmological Constant) DOI: 10.5281/zenodo.19276846 (Cosmo Paper II: Dark Matter) Subjects Physics — Particle Physics — Theoretical Physics Philosophy — Metaphysics Mathematics — Mathematical Physics Notes Chinese text is authoritative; English text is an independent rewrite, not a translation. This paper resolves two open problems from the Four Forces Paper I: (1) 1DD gauge landing fixed as U(1)_Y; (2) Higgs repositioned from breakthrough mediator to effective description of DD-level charge transfer. Derivation employed four-AI collaborative method (Claude/Zilu, ChatGPT/Gongxihua, Gemini/Zixia, Grok/Zigong).
