Topos Theory and ZEBTS‑SUPER: A Strict Categorical Reconstruction of Physical Reality
Abstract
Topos theory provides a fundamentally new mathematical language for describing physical systems, replacing set‑theoretic and Boolean foundations with intuitionistic logic, presheaves, and morphisms. In quantum mechanics this eliminates conceptual paradoxes such as superposition, wave‑function collapse, contextuality, and nonlocality. This work demonstrates that the ZEBTS‑SUPER framework (Zero‑Entropy Background Topological Structure — SUPER 4.0) implements the topos approach at the level of operator geometry: χ‑domains, χ‑morphisms, and χ‑spectral logic form a physical realization of the topos of observables. The subobject classifier Ω is realized as the spectrum of the master operator Dχ, and quantum effects become consequences of the topological structure of the χ‑Boundary and its morphisms. The article establishes a strict equivalence between the Isham–Döring topos approach and the χ‑spectral geometry of ZEBTS‑SUPER, and derives experimentally testable predictions for strong‑field physics, quantum gravity, and high‑energy processes.
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BibTeX
@misc{mukha2026topos,
title = {{Topos Theory and ZEBTS‑SUPER: A Strict Categorical Reconstruction of Physical Reality}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21534025},
url = {https://doi.org/10.5281/zenodo.21534025},
note = {CC BY},
}
RIS
TY - UNPB
TI - Topos Theory and ZEBTS‑SUPER: A Strict Categorical Reconstruction of Physical Reality
AU - Anatolii Mukha
PY - 2026
DA - 2026/07/24
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21534025
UR - https://doi.org/10.5281/zenodo.21534025
AB - Topos theory provides a fundamentally new mathematical language for describing physical systems, replacing set‑theoretic and Boolean foundations with intuitionistic logic, presheaves, and morphisms. In quantum mechanics this eliminates conceptual paradoxes such as superposition, wave‑function collapse, contextuality, and nonlocality. This work demonstrates that the ZEBTS‑SUPER framework (Zero‑Entropy Background Topological Structure — SUPER 4.0) implements the topos approach at the level of operator geometry: χ‑domains, χ‑morphisms, and χ‑spectral logic form a physical realization of the topos of observables. The subobject classifier Ω is realized as the spectrum of the master operator Dχ, and quantum effects become consequences of the topological structure of the χ‑Boundary and its morphisms. The article establishes a strict equivalence between the Isham–Döring topos approach and the χ‑spectral geometry of ZEBTS‑SUPER, and derives experimentally testable predictions for strong‑field physics, quantum gravity, and high‑energy processes.
ER -