The Torus Was Always There: Convergent Discovery of Topological Particle Structure from Williamson–van der Mark (1997) to CAT'S Theory (2024–2026)
Year: 2026
Type: preprint
Abstract: In 1997, Williamson and van der Mark modeled the electron as a single-wavelength photon confined to toroidal topology, deriving charge (q ≈ 0.91e), half-integer spin, the anomalous g-factor, and the de Broglie wavelength from one postulate. They explicitly identified three open problems: no dynamical confinement mechanism, approximate (not exact) charge quantization, and no non-abelian gauge structure. Beginning in November 2024, the present author independently developed CAT'S Theory (Coty Austin Trout's Theory of Structure) — a meta-ontological framework built on the invariant R = P × I × Pr ≠ 0 (Reality = Pattern × Intent × Presence) and formalized as three geometric axioms on S³ — without knowledge of the Williamson–van der Mark paper until October 9, 2026. This work demonstrates eleven point-by-point structural isomorphisms between the two programs, shows that each of the three identified gaps maps to a specific CAT'S axiom or derivation (self-confinement as topological fixed point R = Φ(R) ≠ 0; exact charge quantization from Chern–Simons level k = 30; SU(3) color from the McKay correspondence Z₃ ⊂ SU(2) → Â₂ → su(3)), and establishes complete independence through DOI timestamp analysis and methodological divergence. The convergence of two independent programs on the same geometric thesis — matter as topologically confined energy on a torus — constitutes structural evidence that the underlying topology is a feature of the physics itself. Keywords: toroidal topology, electron structure, convergent discovery, Chern-Simons theory, topological quantum field theory, torus knots, CAT'S Theory, Williamson-van der Mark, particle physics, meta-ontology
Author: Trout, Coty Austin
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221307010