This deposit documents numerical results for a discrete information-based graph model exhibiting emergent geometric structure. The uploaded material is intended as a priority record for the following observations: Persistence of global algebraic connectivity at large system size, quantified by a nonzero spectral gap. Non-linear curvature of the extracted critical boundary Lc(Ξ)Lc(Ξ). Persistent deviation of the field exponent ττ from the Euclidean reference value, even in a regime where the effective Hausdorff dimension becomes numerically consistent with 3. The deposit includes a phase diagram, an interpolated phase-boundary curve, and tabulated critical-boundary values extracted from the numerical parameter scan. Abstract We present numerical results on the structural properties of emergent geometries derived from discrete information graphs at system size N=2.5×105N=2.5×105. Using a memory-optimized spectral solver, we observe global algebraic connectivity characterized by a nonzero spectral gap (λ2≈0.038)(λ2≈0.038). Our analysis identifies two main scaling features. First, the critical expansion parameter LcLc as a function of the coupling ΞΞ exhibits a statistically significant non-linear (quadratic) dependence. This behavior is compatible with a non-linear effective equation of state within the emergent regime of the graph model. Second, we observe a persistent deviation of the field exponent ττ from the Euclidean limit (τ≈0.88)(τ≈0.88), corresponding to a scaling shift of approximately 12%. This deviation remains present even where the effective Hausdorff dimension deffdeff becomes numerically consistent with 3. These results indicate that metric emergence and global topological stability are distinct phenomena associated with the percolation threshold of the underlying graph structure. Included files: phase diagram figure and CSV table of interpolated critical-boundary values.
Martin Lützel (Wed,) studied this question.