Superluminal Correlations in Ensembles of Optical Phase Singularities: Direct Experimental Evidence for Information-Mediated Nonlocality

This paper formalizes Bucher et al. 's (Nature, 2026) experimental observation of superluminal correlations in optical phase singularities into a rigorous information-physics framework, introducing Information Topology (Definition 15. 0) as the study of conserved informational structures localized at zero-energy loci of quantum fields. MAIN RESULTS Five bridging definitions (Definition Set 15) map the empirically measured properties of phase singularities to the information-physics framework of Papers 8–11: (1) quantized topological charge (q = ±1) to a discrete Shannon bit; (2) zero field amplitude to the Landauer existence-erasure dichotomy; (3) topological charge conservation to the information continuity equation; (4) superluminal velocity divergence to EPR nonlocal correlation; and (5) macroscopic substrate independence to the universality theorem (Axioms A1–A4). Two theorems are formally proven: Theorem 15. 1 (Reverse Derivation) establishes that continuous complex wave fields satisfying Landauer-Shannon-Unitarity host topological structures with the five measured properties, closing the logical loop from theory to experiment. Theorem 15. 2 (A2 Cancellation) demonstrates that the algebraic cancellation of the group velocity (vg) in singular optics shares an identical structural origin with the cancellation of basis energy (ℏω0) in the neural information dynamics of Paper 10 — both deterministic consequences of the quadratic separable interaction (Axiom A2). Key numerical results: η = ng·λ/ (4π·d) ≈ 121. 5 ± 11. 1 at d = 5 nm for hBN phonon polaritons; superluminal spatial threshold dc ≈ 5. 07 nm; universal divergence exponent β = 1 across four distinct wave substrates; Information Flash duration Δtflash = 1–10 fs predicted within Bucher et al. 's 3 fs experimental resolution. The Interpretive Verification Protocol (IVP) yields 5/5 consistency against Bucher et al. 's single-source dataset, 15/15 across three independent wave systems (Bucher 2026 optical; Embon 2017 superconducting; Sachkou 2019 superfluid), with two Framework-Specific alignments (vg cancellation; A1–A4 universality) that exceed purely classical topological-defect predictions. PREDICTIONS AND FALSIFICATION Nine quantitative predictions (P1–P9) and five explicit falsification conditions (F1–F5) are formalized with strict numerical thresholds. Four predictions (P3, P5, P6, P8) are directly testable on Bucher et al. 's existing trajectory data. Prediction P9 (CHSH |S| = 2√2 ± 0. 1 via OAM mode-sorting Bell test) requires a new experimental campaign. The entanglement interpretation (§5) is framed as logically modular: its hypothetical empirical rejection leaves the six structural equation correspondences, the IVP scoring matrices, and all non-entanglement predictions intact. PACKAGE CONTENTS (12 files) - Paper15ᵥ25₉SuperluminalCorrelations. docx — main manuscript (~100 pages, 9 figures, 10 tables, 13 appendices A–M, 39 references) - README. md — usage guide- 01ₛimₚhase1ₜheoretical. py — Phase 1 simulations (Bekenstein bound, Landauer energy, β universality, vg independence, Fröhlich efficiency) - 02ₚhase2calibration. py — Phase 2 calibration of hBN superluminal threshold and η (d) - 03ₚhase2ₚipelineAppendixKLM. py — Complete Appendix K+L+M analysis pipeline (mutual information from g² (r), η uncertainty propagation, composite IVP scoring, JSON export) - 04bellₜestCHSH. py — CHSH Bell-test derivation for OAM singlet state- fig3bell. png, fig4ᵥelocity. png, fig5ₛuperluminal. png, fig6building. png, fig8crossdomain. png, fig9ₚhase2ᵥalidation. png — supplementary figure files All Python scripts require only NumPy, SciPy, and Matplotlib. Execution is <5 seconds per script on standard hardware. Synthetic benchmark achieves 6/6 composite IVP verdict, confirming pipeline readiness for direct application to digitized Bucher et al. data. KEY FEATURES - Zero new axioms, zero fitted free parameters- Epistemic independence: framework F (Papers 8–11) archived with registered DOIs prior to publication of Bucher et al. (2026) - Strong falsifiability: every prediction carries a specific numerical threshold- Cross-domain corroboration: identical framework passes IVP evaluation against Paper 14's 23 biomedical datasets (combined 38/38; interpretable as a Jeffreys-scale consistency metric, not a posterior probability of theory truth) - Complete reproducibility pipeline included KEYWORDS phase singularity, Information Topology, quantum entanglement, Information Physics, topological charge, superluminal correlation, substrate independence, Landauer principle, Unitarity, ER=EPR, Interpretive Verification Protocol, OAM entanglement, CHSH Bell test, hBN phonon polariton, Bucher et al. 2026 RELATED WORK Companion paper in the Information Physics Series: - Paper 14 (Qi as Information Flow): DOI 10. 5281/zenodo. 19587732- Paper 13 (Karma as Condensation): DOI 10. 5281/zenodo. 19534060 License: CC BY-NC 4. 0 Correspondence: dfdfgo92@gmail. com