The Electron as an Octonionic Möbius Defect: An Algebraic Derivation Within Computational Finitism and an Evaluation of Competing Geometric Models

H. H. Otto (2026) has proposed using artificial intelligence to evaluate competing geometric models of electron structure and identify the most probable one. We argue that evaluation requires ground truth, not comparison. Computational Finitism provides this: a finite Modulo-9 causal substrate with Fano incidence, a 7-channel vacuum maintenance subspace, 137 active propagation channels, and an octonionic multiplication structure. We derive algebraically the electron's topological properties, Möbius (4π) closure, spin-1/2, charge from Fano chirality, mass from sub-channel bandwidth of the fine-structure constant, and the 11/137 transmutation coupling, from these axioms. We show that scalar Modulo-9 cellular automata cannot produce chirality or localized defects, because addition is commutative and mod-9 is not conservative; the substrate must therefore be octonionic, not scalar. We then evaluate the five competing models against eight Finitism criteria. Traill's helix-based wave function and Gauthier's double-helix photon fail the 4π closure requirement and are incompatible with the substrate. Otto, Guynn, and Markoulakis each capture part of the structure, Möbius topology, precession and g-factor, spinor fiber, but none is identical to Finitism; they are complementary effective descriptions at different resolutions. We close with falsifiable predictions and an honest list of what Finitism still does not derive.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22846055
Primary Topic
Algebraic and Geometric Analysis
Type
preprint
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preprint

The Electron as an Octonionic Möbius Defect: An Algebraic Derivation Within Computational Finitism and an Evaluation of Competing Geometric Models

Néstor E Ramos
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

The Electron as an Octonionic Möbius Defect: An Algebraic Derivation Within Computational Finitism and an Evaluation of Competing Geometric Models

Néstor E Ramos
preprint en

Abstract

H. H. Otto (2026) has proposed using artificial intelligence to evaluate competing geometric models of electron structure and identify the most probable one. We argue that evaluation requires ground truth, not comparison. Computational Finitism provides this: a finite Modulo-9 causal substrate with Fano incidence, a 7-channel vacuum maintenance subspace, 137 active propagation channels, and an octonionic multiplication structure. We derive algebraically the electron's topological properties, Möbius (4π) closure, spin-1/2, charge from Fano chirality, mass from sub-channel bandwidth of the fine-structure constant, and the 11/137 transmutation coupling, from these axioms. We show that scalar Modulo-9 cellular automata cannot produce chirality or localized defects, because addition is commutative and mod-9 is not conservative; the substrate must therefore be octonionic, not scalar. We then evaluate the five competing models against eight Finitism criteria. Traill's helix-based wave function and Gauthier's double-helix photon fail the 4π closure requirement and are incompatible with the substrate. Otto, Guynn, and Markoulakis each capture part of the structure, Möbius topology, precession and g-factor, spinor fiber, but none is identical to Finitism; they are complementary effective descriptions at different resolutions. We close with falsifiable predictions and an honest list of what Finitism still does not derive.

Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
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The Electron as an Octonionic Möbius Defect: An Algebraic Derivation Within Computational Finitism and an Evaluation of Competing Geometric Models — Néstor E Ramos · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS