Topos Theory and ZEBTS‑SUPER: A Rigorous Categorical and Operator‑Geometric Reconstruction of Physical Reality
Abstract
Standard quantum mechanics relies on Hilbert spaces and Boolean logic, producing structural paradoxes such as wave‑function collapse, contextuality, and nonlocality. The Isham–Döring presheaf topos approach reformulates quantum mechanics in an intuitionistic logical framework, but remains a reconstructive formalism without physical ontology. In this paper, we establish ZEBTS‑SUPER 4.0 (Zero‑Entropy Background Topological Structure) as the first operator‑geometric physical realization of topos theory. We construct a rigorous equivalence between presheaves over context categories and χ‑domains, identify the subobject classifier Ω with the spectral logic Spec(D_chi) of the vacuum master operator, and show that contextual truth values correspond to spectral projections of the χ‑vacuum. We extend the topos correspondence by introducing the χ‑Absolute → χ‑Boundary → χ‑Matter ontological hierarchy, the Planck‑scale χ‑particle (the flightron), and χ‑topological charges. Wave‑function collapse is replaced by autopoietic dynamics Z_chi, entanglement becomes χ‑holonomy, and superposition becomes a logical property of Ω rather than a physical paradox. Finally, we derive explicit predictions for strong‑field QED, vacuum birefringence, Schwinger threshold shifts, and quantum‑gravity decoherence.
Related
- Topos Theory and ZEBTS‑SUPER: A Strict Categorical Reconstruction of Physical Reality
- Nonclassical Quantum Superpositions as χ‑Spectral States: An Operator–Geometric Reconstruction within the ZEBTS‑SUPER Framework
- Connecting the tensor-categorical formulation of anyon condensation with operator algebras and entropic order parameters
- The Number 137 in ZEBTS‑SUPER Theory: Rigorous chi‑Spectral Reconstruction of the Fine‑Structure Constant
- The Number 137 in ZEBTS‑SUPER Theory: Rigorous chi‑Spectral Reconstruction of the Fine‑Structure Constant
BibTeX
@misc{mukha2026topos,
title = {{Topos Theory and ZEBTS‑SUPER: A Rigorous Categorical and Operator‑Geometric Reconstruction of Physical Reality}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21536313},
url = {https://doi.org/10.5281/zenodo.21536313},
note = {CC BY},
}
RIS
TY - UNPB
TI - Topos Theory and ZEBTS‑SUPER: A Rigorous Categorical and Operator‑Geometric 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.21536313
UR - https://doi.org/10.5281/zenodo.21536313
AB - Standard quantum mechanics relies on Hilbert spaces and Boolean logic, producing structural paradoxes such as wave‑function collapse, contextuality, and nonlocality. The Isham–Döring presheaf topos approach reformulates quantum mechanics in an intuitionistic logical framework, but remains a reconstructive formalism without physical ontology. In this paper, we establish ZEBTS‑SUPER 4.0 (Zero‑Entropy Background Topological Structure) as the first operator‑geometric physical realization of topos theory. We construct a rigorous equivalence between presheaves over context categories and χ‑domains, identify the subobject classifier Ω with the spectral logic Spec(D_chi) of the vacuum master operator, and show that contextual truth values correspond to spectral projections of the χ‑vacuum. We extend the topos correspondence by introducing the χ‑Absolute → χ‑Boundary → χ‑Matter ontological hierarchy, the Planck‑scale χ‑particle (the flightron), and χ‑topological charges. Wave‑function collapse is replaced by autopoietic dynamics Z_chi, entanglement becomes χ‑holonomy, and superposition becomes a logical property of Ω rather than a physical paradox. Finally, we derive explicit predictions for strong‑field QED, vacuum birefringence, Schwinger threshold shifts, and quantum‑gravity decoherence.
ER -