Topological network at the Planck scale in the ZEBTS framework: flytrons, triune substance, and foundations of quantum physics

02 November 2026, Version 1
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

We submit “Flytrons in ZEBTS: a Planck‑scale topological network and the emergence of quantum principles” for consideration. The paper presents the ZEBTS framework: quantum features and the Yang–Mills mass gap are derived from discrete topology, APS‑type index theory, and spectral geometry without free parameters. Key contributions: construction of APS‑triunities and the Flytronus operator on discrete networks; proofs of the spectral gap and APS‑index stability (yielding an analytical route to the mass gap); derivation of core quantum principles from network geometry; explicit 𝑁 = 3 , 4 N=3,4 examples with matrix analysis; geometric realization of arithmetic structures as curvature perturbations. The work offers a unified, parameter‑free model linking topology, spectra, and arithmetic to physics. All arguments are self‑contained; we welcome reviewers’ feedback and are ready to revise.

Keywords

Flytron
ZEBTS
topological network
Planck length
triunity of substance
Flytronus operator
discrete geometry
quantum foundations
APS index
Lichnerowicz formula.

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Comment number 1, Anatolii Mukha: Nov 02, 2026, 11:18

Mukha, A. (2026). Spectral invariants and spectral calibration in the ZEBTS model: zeta-determinant, topological index, and mass gap. Zenodo. https://doi.org/10.5281/zenodo.23769530 Mukha, A. (2026). Discrete Gravitational Field in the ZEBTS Framework: Canonical Construction, Convergence, and Reproducible Examples. Zenodo. https://doi.org/10.5281/zenodo.23856148 Mukha, A. (2026). Unified Framework of Space, Time, Gravity and Quantum Phenomena in ZEBTS: A Topological and Spectral Construction via Flytron Dynamics. Zenodo. https://doi.org/10.5281/zenodo.23859028 Mukha, A. (2026). ZEBTS: From Flytron Networks to Quantum Physics. Zenodo. https://doi.org/10.5281/zenodo.23882642