Theoretical analysis demonstrates the emergence of Standard Model gauge symmetries in minimal twistor hierarchies, indicating a geometric origin for particle multiplets.
T12 of the Transport Papers. Version 1.0. 64 pages. Epistemic status: Tier C (with Hypothesis (S) declared). Mass first exists at two twistor constituents (the series' mass paper); this paper computes the composite's symmetries and finds the Standard Model. The minimal massive hierarchy is C² ⊗ C³; its automorphism algebra is su(2) ⊕ su(3) ⊕ u(1) with global form S(U(2) × U(3)), four dimensions is pair count three, and only a two-by-three hierarchy has this algebra. Hypercharge is the weight of the abelian generator: the quark doublet at Y = 1/6 and the four singlets at 0, -2/3, 1/3, 1, unconditionally; the lepton doublet needs one declared hypothesis, slot statistics, without which the state space holds no lepton. Under it the anomalies cancel, the generation is the half-spinor of Spin(10), and sin²θ_W = 3/8 at unification; the one-loop run refutes the desert and demands partner-like content. That demand is made exact: no other tower contributes, complete multiplets are inert, the demand is split content, and the supersymmetric row, undecided at one loop, is admissible at two, at record level. The mass mechanism is computed on the state space, under the same hypothesis where a species is named: the frozen point is insensitive to the slots; the Higgs doublet's representation is the directions transport adjoined, a vector there has the Standard Model's Yukawa pattern, and the transported frozen point lands there; three no-go theorems show the Georgi-Jarlskog factor cannot come from the frozen point, the family structure or the bracket. The smallness problems are powers of N = M_P/H. Every identity is verified in exact arithmetic. Position in the series: Within the series it relies on T01, T03, T06, T07, T08, T09, T10, T11, T13, T14, T15. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T12.py checks every computational identity in the paper in exact rational arithmetic (206 checks, all passing at deposit). It imports GA.py, the series' shared exact-arithmetic library, deposited alongside so the record is self-contained. Run with a bare Python 3: python verify_T12.py. Files: T12_standard_model.pdf; T12_standard_model.tex; verify_T12.py; GA.py; LICENSE-CODE.txt. Licence: the paper (PDF and LaTeX source) is CC BY 4.0. The code files in this record are additionally released under the MIT licence; see LICENSE-CODE.txt. Authorship and disclosure. The founding idea of the series is the author's: that division by zero in a Clifford algebra should be read not as a prohibition but as a transport into a higher-dimensional algebra, and that the transported division need not be accompanied by an inverse operation. The direction of investigation and the critical review of the results are likewise the author's. The mathematical development and the drafting of the text were carried out in extended collaboration with Claude Fable 5 (Anthropic), an AI system.
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