Flytron Electrodynamics and the ZEBTS Framework: From Spectral Primacy to Circuit Theory
Year: 2026
Type: preprint
Abstract: We introduce Flytron Electrodynamics (FED), a discrete framework in which electromagnetic structure emerges from a network of coupled oscillators — flytrons — carrying U(1) phases on edges, conjugate momenta, and an evolving kinetic metric. The framework is built from a minimal set of primitives: an evolving graph, an incidence structure satisfying the chain-complex identity BC = 0, and a canonical dynamical system in which the metric weights are slow dynamical variables. The electromagnetic sector requires no additional ontology: the field observables are intrinsic to the discrete U(1) connection, and the homogeneous field laws — the Faraday identity and the absence of magnetic charges — are exact identities of the incidence structure, holding for arbitrary dynamics, parameters and topology. Three results carry the paper. First, topological protection of a spectral invariant: the index I₀ = dim ker L_F of the amplitude-weighted face Laplacian L_F = C^T A^(−1) C is exactly conserved under a working gap hypothesis — a one-directional implication, proved for the canonical class, verified numerically in the proved direction over 5·10⁶ integration steps, and shown to fail exactly when the gap is destroyed (a deliberate no-dealiasing control run). Second, a bifurcation of classical limits: under two metric calibrations, one discrete structure converges to the quasi-static circuit regime (Ohm's law as leading order, telegraph relaxation as first correction) or to the radiative wave regime, both at rate O(h²) on the flat torus — the circuit/wave hierarchy is recovered as a theorem rather than assumed as a phenomenology. Third, a status discipline: every claim of the framework is assigned the weakest status class that supports it — exact, proved, verified, derived within model, assigned, postulate, conditional — with two hypotheses (drift persistence, ζ-correlation) left assigned with pre-announced protocols, and two postulates (dark-sector supremacy, spectral primacy of transport) explicitly delimited. Applications are presented as declared models with graded statuses: a DC-motor model in which the classical characteristic is derived within the declared assumptions; a structural necessary criterion for room-temperature superconductivity (gap above thermal scale, stated in dimensionless form); and a heuristic correspondence for the low-temperature superconducting state, with phase slips modeled by index events. The framework does not replace classical circuit theory or Maxwell theory; classical theories are its two exact limits, and its domain is the regime classical theory does not cover: networks whose geometry itself evolves.
Author: Mukha, Anatolii
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225340980