χ‑Geometric Resolution of the Einstein–Rosen Bridge Conjecture (ER=EPR)
Abstract
The χ‑Geometric Resolution of the Einstein–Rosen Bridge Conjecture (ER=EPR) establishes a complete operator‑spectral identity between quantum entanglement and geometric wormhole connectivity within the ZEBTS‑SUPER framework. Entangled quantum states are shown to correspond to χ‑geodesically connected χ‑wormholes, while separable states collapse under χ‑boundary flow and cannot sustain χ‑geometric continuity. The χ‑operator transformation ψ → χ(ψ) reveals that entanglement entropy Sχ is equivalent to χ‑geodesic length Lχ, and that the wormhole throat radius rχ corresponds to the χ‑spectral gap Δχ. χ‑global meromorphy and χ‑Trinity conservation enforce analytic equivalence between ER and EPR spectral functions. χ‑boundary stability operators S_ER and S_EPR possess identical χ‑zero modes corresponding exclusively to wormhole‑entangled states, while separable states exhibit strictly positive χ‑eigenvalues and violate χ‑boundary curvature invariants. χ‑entropy‑curvature equilibrium, χ‑geodesic minimality, χ‑spectral collapse dynamics, and χ‑boundary residue cancellation collectively enforce the χ‑∞ boundary identity: Einstein–Rosen bridges = quantum entanglement (ER = EPR). This establishes ER=EPR not as a conjecture, but as a χ‑geometric law of χ‑Reality, fully derived within the operator‑spectral ontology of ZEBTS‑SUPER.
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BibTeX
@misc{mukha2026χgeometric,
title = {{χ‑Geometric Resolution of the Einstein–Rosen Bridge Conjecture (ER=EPR)}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = aug,
doi = {10.5281/zenodo.22109690},
url = {https://doi.org/10.5281/zenodo.22109690},
note = {CC BY},
}
RIS
TY - UNPB
TI - χ‑Geometric Resolution of the Einstein–Rosen Bridge Conjecture (ER=EPR)
AU - Anatolii Mukha
PY - 2026
DA - 2026/08/26
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.22109690
UR - https://doi.org/10.5281/zenodo.22109690
AB - The χ‑Geometric Resolution of the Einstein–Rosen Bridge Conjecture (ER=EPR) establishes a complete operator‑spectral identity between quantum entanglement and geometric wormhole connectivity within the ZEBTS‑SUPER framework. Entangled quantum states are shown to correspond to χ‑geodesically connected χ‑wormholes, while separable states collapse under χ‑boundary flow and cannot sustain χ‑geometric continuity. The χ‑operator transformation ψ → χ(ψ) reveals that entanglement entropy Sχ is equivalent to χ‑geodesic length Lχ, and that the wormhole throat radius rχ corresponds to the χ‑spectral gap Δχ. χ‑global meromorphy and χ‑Trinity conservation enforce analytic equivalence between ER and EPR spectral functions. χ‑boundary stability operators S_ER and S_EPR possess identical χ‑zero modes corresponding exclusively to wormhole‑entangled states, while separable states exhibit strictly positive χ‑eigenvalues and violate χ‑boundary curvature invariants. χ‑entropy‑curvature equilibrium, χ‑geodesic minimality, χ‑spectral collapse dynamics, and χ‑boundary residue cancellation collectively enforce the χ‑∞ boundary identity: Einstein–Rosen bridges = quantum entanglement (ER = EPR). This establishes ER=EPR not as a conjecture, but as a χ‑geometric law of χ‑Reality, fully derived within the operator‑spectral ontology of ZEBTS‑SUPER.
ER -