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July 13, 20260 citationsOpen Access

Universality and Topological Attractors in Quantum Graph Emergent Field Theory: The Inevitability of the Fractal Ground State

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YCYaniv Cohen

Key Points

  • The aim is to explore the behavior of quantum graphs under specific parameters and their resultant fractal ground state.
  • Utilized phase-mapped resonant coupling at $J=0.55$ and $=kappa=0.05$ with an $N=512$ gauge-coupling sweep.
  • Applied a four-point finite-size scaling series across varying sizes $N=1024$ to $N=3072$ to analyze light-cone fit and diagnostics.
  • Calculated the triangle-Ricci correlation and Einstein-Hilbert action fit to assess gravity-facing diagnostics.
  • Achieved consistent high emergent light-cone fit ($R^2$ range from 0.877 to 0.914).
  • Observed triangle-Ricci correlation improve from $R=0.355$ to $R=0.535$, with a p-value of $p<3.11 imes10^{-227}$.
  • Spectral dimension remained anchored in the fractal band, illustrating stability in the ground state despite temporary 3D configurations.

Abstract

The current Paper 70 benchmark does not claim that fine-tuning-independence has been established across the full (N, J, , Rₒ₏₀₍) parameter space. It does show that, at one independently phase-mapped resonant coupling point (J=0. 55, =0. 05, identified from a "causal ridge" in an N=512 gauge-coupling sweep peaking at dₛ2. 171), a genuine SU (3) four-point finite-size scaling series across N=1024204825603072 (3 volume growth) leaves the emergent light-cone fit consistently high (R²0. 877, 0. 914) while both gravity-facing diagnostics strengthen *monotonically* (triangle-Ricci correlation R=0. 3550. 4660. 5190. 535, p3. 1110^-227; Einstein-Hilbert action fit R²=0. 0420. 1420. 1740. 205), even as the measurement-averaged spectral dimension itself remains anchored in the fractal band (dₛ1. 552. 0) rather than drifting toward a smooth continuum, despite burn-in-phase live diagnostics transiently touching a near-3D configuration (dₛ3. 40, dH3. 21 at N=3072) before settling back into the fractal ground state.

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Cite This Study

Yaniv Cohen (2026) studied this question.

synapsesocial.com/papers/6a548195475c38bf615a5a02https://doi.org/10.5281/zenodo.21306025
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Emergent Gravity, Matter Condensation, and Spectral Geometry in Quantum Graph Emergent Field Theory2026
  2. 2Spacetime Emergence, Causal Structure, and Local Gravity in QGEFT from Pure Gauge-Field Dynamics2026
  3. 3Spacetime Emergence, Causal Structure, and Local Gravity in QGEFT from Pure Gauge-Field Dynamics2026
  4. 4Emergent Area Laws and Entropic Attraction in a Bare Graph Dynamics Surrogate2026
  5. 5The Topological Hooke's Law and Emergent Cosmology in Quantum Graph Emergent Field Theory (QGEFT)2026