Transport Papers T15. Neutrino Masses

T15 of the Transport Papers. Version 1.0. 21 pages. Epistemic status: Tier B/C. We identify the right-handed neutrino as the hypercharge-zero state of the framework's derived content, the empty twistor at grade zero, and prove that anomaly cancellation could not have fixed its hypercharge: with a fourth singlet free and Y_Q ≠ 0, the anomaly-free spectra are exactly the span of Y and B - L. The cosmological term of the deformed bracket cannot supply the neutrino mass (the sixteenth refutation: it lies below the flat term by Λ l²/6 at extent l). Gauge invariance makes the Majorana bilinear of the total singlet the one mass term needing no condensate, a textbook fact about which the framework's own bracket, computed only on slot states, says nothing; with its scale a premise, the seesaw follows. Indifference makes the Majorana matrix S_3-invariant, hence α·1 + βJ (J the all-ones matrix), aligned with the democratic Dirac matrix, and the light matrix is rank one at leading order with m_3 = m_D²/M_3: normal ordering, and, as consequences of m_1 ≈ 0 and real phases, the sum at the oscillation floor Σm_ν ≈ 0.059 eV and m_ββ at 1.5 or 3.7 meV. That sum is at the centre of the sharpest tension in cosmology, and the framework, which predicts w = -1, cannot relax the bound in the standard way: one joint prediction. Leptogenesis is suppressed under a reheating premise at the cost of a registered stance, δ_CP ∈ {0, π}. Tier B/C with every premise named, a prediction table, and exact machine verification. Position in the series: Within the series it relies on T10, T10, T11, T12, T13, T14. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T15.py checks every computational identity in the paper in exact rational arithmetic (50 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_T15.py. Files: T15_neutrino_masses.pdf; T15_neutrino_masses.tex; verify_T15.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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-12
DOI
https://doi.org/10.5281/zenodo.22723071
Primary Topic
Neutrino Physics Research
Type
preprint
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preprint

Transport Papers T15. Neutrino Masses

Leon Butler
Zenodo (CERN European Organization for Nuclear Research)
Neutrino Physics Research
preprint

Transport Papers T15. Neutrino Masses

Leon Butler
preprint en

Abstract

T15 of the Transport Papers. Version 1.0. 21 pages. Epistemic status: Tier B/C. We identify the right-handed neutrino as the hypercharge-zero state of the framework's derived content, the empty twistor at grade zero, and prove that anomaly cancellation could not have fixed its hypercharge: with a fourth singlet free and Y_Q ≠ 0, the anomaly-free spectra are exactly the span of Y and B - L. The cosmological term of the deformed bracket cannot supply the neutrino mass (the sixteenth refutation: it lies below the flat term by Λ l²/6 at extent l). Gauge invariance makes the Majorana bilinear of the total singlet the one mass term needing no condensate, a textbook fact about which the framework's own bracket, computed only on slot states, says nothing; with its scale a premise, the seesaw follows. Indifference makes the Majorana matrix S_3-invariant, hence α·1 + βJ (J the all-ones matrix), aligned with the democratic Dirac matrix, and the light matrix is rank one at leading order with m_3 = m_D²/M_3: normal ordering, and, as consequences of m_1 ≈ 0 and real phases, the sum at the oscillation floor Σm_ν ≈ 0.059 eV and m_ββ at 1.5 or 3.7 meV. That sum is at the centre of the sharpest tension in cosmology, and the framework, which predicts w = -1, cannot relax the bound in the standard way: one joint prediction. Leptogenesis is suppressed under a reheating premise at the cost of a registered stance, δ_CP ∈ {0, π}. Tier B/C with every premise named, a prediction table, and exact machine verification. Position in the series: Within the series it relies on T10, T10, T11, T12, T13, T14. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T15.py checks every computational identity in the paper in exact rational arithmetic (50 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_T15.py. Files: T15_neutrino_masses.pdf; T15_neutrino_masses.tex; verify_T15.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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