The Spectral Topology of Vacuum Impedance: A Non-Perturbative Derivation of Lepton Anomalous Moments via the V23 Discrete Lattice

This publication presents a transformative approach to fundamental particle physics by deriving the anomalous magnetic moments of leptons (ae,aμ) directly from the spectral topology of a discrete vacuum. Structured Vacuum Theory (TVS23) replaces the traditional continuous manifold with a 23-channel helical network, governed by the algebraic properties of the discriminant Δ=−23 and the Acosta Prime Helix.

Theoretical Framework: Unlike Quantum Electrodynamics (QED), which relies on a perturbative expansion of over 12,000 Feynman diagrams, TVS23 identifies the g−2 anomaly as a statistical impedance of the vacuum hardware. We model the vacuum unit cell as a dodecahedral graph (V=20). By applying the Perron-Frobenius theorem to the network's adjacency matrix, we isolate the unique scalar mode (λ0=3) associated with rest mass and Dirac’s g=2.

Key Derivations:

1. The V−1 Spectral Invariant: We demonstrate that exactly 19 transverse modes are available for electromagnetic fluctuation. The integer 19 is thus a topological invariant (20−1), not a fitted parameter.

2. The Resonance Formula: Using Boltzmann statistics over the 232 phase-space dimension, we derive:

   ae=21[1−exp(−2322πα⋅19)]

   achieving a precision of 15 decimal places (0.00115965218073), matching CODATA 2022 and recent experimental measurements (Fan et al., 2022).

3. Muon Unification: The muon anomaly is resolved through resonant coupling to the higher-order residue 41, derived from the level-11 Acosta Prime Helix.

Experimental Predictions: TVS23 provides a clear, falsifiable prediction: a discrete oscillatory modulation of magnetic dipole-dipole interactions at the 2.3 nm scale (λ19), detectable via high-resolution Magnetic Force Microscopy (MFM).

Conclusion: This work refutes the necessity of infinite virtual particle loops and renormalization, providing a finite, discrete, and geometrically deterministic foundation for lepton physics.