Transport Papers T11. The Origin of Mass

Abstract

T11 of the Transport Papers. Version 1.0. 24 pages. Epistemic status: Tier B. Mass enters a conformally invariant theory where scale does: as coupling to the frozen point, the parallel scale tractor of squared norm Λ/3. We prove the mass-weight dictionary: a density of conformal weight w coupled to the frozen point through the Thomas operator obeys the Klein-Gordon equation with m² = -w(w+n-1)⟨I,I⟩, in dimension four m² = -w(w+3)Λ/3, the de Sitter formula Δ(3-Δ)H² with Δ = -w, H² = Λ/3. A real weight gives a nonnegative m² only on w ∈ [-3,0], and there at most m = 3H/2; every known massive particle has complex weight -3/2 ± iν with ν ≈ m/H, about 3 × 10^(38) for the electron. We prove the twistor counterpart, m² = 2|[π¹π²]|² for a two-twistor composite, and compute its exact de Sitter extension: the composite's grip on the frozen point, P = M(I_Λ) with M the conformal moment map, is its de Sitter momentum, with squared length m² = 2 |B_Λ|² + ⟨I_Λ,I_Λ⟩ C, where B_Λ = [π¹π²] + (Λ/6)[ω¹ω²] is the composite's pairing against the frozen point and C the internal su(2) Casimir of the constituents' Gram matrix. Relative to the deformed bracket the correction is one term, with coefficient exactly Λ/3, and the massless locus is computed. The dictionary then assigns the composite its weight; it does not explain the observed masses but relocates the question: the hierarchy is the size of an imaginary weight. The paper is Tier B; every computational identity is verified in exact arithmetic by a deposited script. Position in the series: Within the series it relies on T00, T01, T06, T09, T10. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T11.py checks every computational identity in the paper in exact rational arithmetic (39 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_T11.py. Files: T11_origin_of_mass.pdf; T11_origin_of_mass.tex; verify_T11.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.