The Electron in Computational Finitism: An Algebraic Derivation from a 9-Dimensional Fano- TRB Substrate and an Evaluation of Competing Geometric Models

H. H. Otto (2026) has proposed that artificial intelligence be used to evaluate the competing geometric models of the electron structure. We argue that evaluation requires ground truth, not comparison. Computational Finitism provides this: a finite causal graph of Planck voxels governed by a Modulo-9 alphabet, a Fano plane of 7 points and 7 lines, and a 9-dimensional algebra over ℤ/9ℤ whose structure we construct explicitly in this paper. Twenty scalar Modulo-9 cellular automata were tested across 1D, 2D, and 4D lattices. All failed to produce chirality or localized defects because addition is commutative and Modulo-9 arithmetic is not conservative. This negative result establishes that the Finitism substrate is algebraic, not scalar. We construct the correct primitive operation: the 9-dimensional Fano-TRB algebra over ℤ/9ℤ, with 7 Fano units, an identity, and a chiral nilpotent TRB element satisfying , , . We derive from these axioms: the Möbius (4π) topology of the electron, spin-1/2, the fine-structure constant , charge from Fano chirality, the transmutation coupling, the 12-vertex icosahedral shell from the D4 root system extended by the golden ratio, and a candidate formula for the anomalous gyromagnetic moment . We evaluate the five competing models, Gauthier, Markoulakis, Traill, Otto, Guynn, against eight Finitism criteria. Traill and Gauthier are incompatible because their helices close after 2π rather than 4π. Otto, Guynn, and Markoulakis are partial: each captures part of the structure without capturing the whole. We close with falsifiable predictions and an honest list of open problems. The path forward is algebraic, and the substrate remains computational finitism