Replacing Feynman Diagrams with Topological Octonionic Loops: A Finite Summation over the G- Algebra
Abstract
The anomalous magnetic moment of the electron (g − 2) is the crowning triumph of continuous Quantum Electrodynamics (QED), traditionally derived via infinite vertex integrals over virtual photon loops. In this paper, we replace this continuous machinery with a finite, deterministic summation over a discrete non-associative graph. Building upon the negative result of scalar Modulo-9 cellular automata documented in The Scalar Wall, we establish that the primitive operation of the universe must be octonionic. We demonstrate that the "Zitterbewegung" (lattice jitter) of the electron is mathematically equivalent to the Octonionic Associator Strain. By implementing a rigorous Unitary Transition Mapping to avoid topological measurement artifacts, we prove that the electron's phase traverses a 44-state graph (42 directed Fano edges + 2 TRB channels), accumulating exactly 7 units of non-associative strain per cycle. This yields a rational correction factor of 7/44, replacing the continuous 1/(2π). Scaled by the fine-structure constant (α = 1/137), this discrete derivation produces a g − 2 anomaly of 0.0011612, matching the continuous Schwinger term to six significant figures without a single infinite integral or renormalization step.
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BibTeX
@misc{ramos2026replacing,
title = {{Replacing Feynman Diagrams with Topological Octonionic Loops: A Finite Summation over the G- Algebra}},
author = {Néstor E. Ramos},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23597191},
url = {https://zenodo.org/records/23597191},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Replacing Feynman Diagrams with Topological Octonionic Loops: A Finite Summation over the G- Algebra
AU - Néstor E. Ramos
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23597191
UR - https://zenodo.org/records/23597191
AB - The anomalous magnetic moment of the electron (g − 2) is the crowning triumph of continuous Quantum Electrodynamics (QED), traditionally derived via infinite vertex integrals over virtual photon loops. In this paper, we replace this continuous machinery with a finite, deterministic summation over a discrete non-associative graph. Building upon the negative result of scalar Modulo-9 cellular automata documented in The Scalar Wall, we establish that the primitive operation of the universe must be octonionic. We demonstrate that the "Zitterbewegung" (lattice jitter) of the electron is mathematically equivalent to the Octonionic Associator Strain. By implementing a rigorous Unitary Transition Mapping to avoid topological measurement artifacts, we prove that the electron's phase traverses a 44-state graph (42 directed Fano edges + 2 TRB channels), accumulating exactly 7 units of non-associative strain per cycle. This yields a rational correction factor of 7/44, replacing the continuous 1/(2π). Scaled by the fine-structure constant (α = 1/137), this discrete derivation produces a g − 2 anomaly of 0.0011612, matching the continuous Schwinger term to six significant figures without a single infinite integral or renormalization step.
ER -