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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19954768 |
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Table of Contents:
- <p>Canon v30.1 explains entanglement through a shared Transaction ID (TxID) inherited from a common source and resolved atomically by A-Sync. However, the earlier language of “4D adjacency” risks being misread as the introduction of hidden non-local carrier edges, potentially conflicting with the strict 12-regularity of the FCC substrate.</p> <p>This paper replaces that language with a fully topological formulation. We propose that an entangled pair is not two separate particles linked by a hidden edge, but one <strong>fiber-supported defect</strong> in ℝP<sup>3</sup>, whose support is a discrete projective Hopf fiber. A low-bandwidth A0-observer does not see the whole fiber; it sees only two observer-visible access points of the same extended defect. These are interpreted as two spatially separated particles.</p> <p>The topological background is exact: ℝP<sup>3</sup> = S<sup>3</sup>/ℤ<sub>2</sub>, with projective Hopf fiber structure inherited from the Hopf fibration of S<sup>3</sup>. The discrete executable target is a partition of the 600-cell into 12 pairwise disjoint decagonal cycles, providing a candidate fiber basis for entangled defects. On that basis, the Transaction ID is refined to a geometric invariant of one fiber-supported defect:</p> <p><strong>TxID</strong>( <sub>α</sub>) = (α, θ, σ, η),</p> <p>where α is the fiber index, θ ∈ ℤ<sub>10</sub> the phase coordinate along the discrete fiber, σ ∈ ℤ<sub>2</sub> the spinorial parity / monodromy class, and η = (S(n), S(n−1)) the two-tick source memory.</p> <p>Within this framework, we derive the <strong>No-Extra-Edge Theorem</strong>: EPR correlations require no additional carrier edges beyond the original 12-regular FCC adjacency. Correlation is carried by shared support, not hidden connectivity. We also derive <strong>Atomic Fiber Commit</strong>: a local measurement at one visible point commits the state of the entire fiber-supported defect within one tick under A-Sync, so the correlated outcome at the distant point is produced by one atomic update of one shared object, not by superluminal signalling.</p> <p>The same geometric framework yields an architectural interpretation of tunnelling: a defect can re-localise its visible access point along its supporting fiber, so that an A0-observer records apparent transit through a classically forbidden barrier. Tunnelling is thus reformulated as <strong>fiber slide</strong>, not miracle transport and not a hidden shortcut edge.</p> <p>The central claim of this paper is deliberately modest but strong: <strong>entanglement can be reformulated geometrically in ORT without introducing any additional carrier edges beyond the original 12-regular FCC graph.</strong></p> <p><strong>Status discipline:</strong></p> <ul> <li><strong>Exact:</strong> topological background (ℝP<sup>3</sup>, π<sub>1</sub> = ℤ<sub>2</sub>, projective Hopf fiber existence).</li> <li><strong>Derived:</strong> no-extra-edge formulation and atomic fiber commit, conditional on the fiber-supported defect model.</li> <li><strong>Explicit / computational pending:</strong> decomposition of the 600-cell into 12 disjoint decagonal cycles.</li> <li><strong>Open:</strong> full no-signalling theorem, Bell-type calculation, and quantitative tunnelling amplitudes.</li> </ul> <p><strong>Keywords:</strong> ORT, quantum entanglement, EPR, projective Hopf fibration, ℝP<sup>3</sup>, fiber-supported defect, TxID, no extra edge, observer projection, tunnelling, 600-cell.</p>