Emergent Spacetime from Relational Coherence Dynamics: A Minimal Information-Theoretic Framework with Numerical Evidence

This preprint presents a minimal pre-geometric framework in which spacetime-like structure is investigated as an emergent phenomenon arising from relational coherence dynamics on a fully connected network of informational degrees of freedom.

The model introduces a scalar coherence variable assigned to each node and studies how nonlinear coherence dynamics on a fixed relational substrate can generate structured configurations, spontaneous symmetry breaking, stable attractor-like patterns, phase-transition-like variance growth, and an exploratory low-dimensional geometric representation based on multidimensional scaling (MDS).

Spatial distance, metric structure, and global temporal ordering are not assumed a priori. Instead, effective relational distance is defined through interaction strength, and geometric organization is examined through an MDS representation of the resulting distance matrix.

The numerical simulations use N = 100 nodes, fixed symmetric relational weights K_ij, and coherence-field dynamics with nonlinear amplification, saturation, and network-mediated coupling. The accompanying simulation code reproduces the representative figures discussed in the manuscript, including coherence-field evolution, variance evolution, and the exploratory MDS embedding colored by final coherence values.

The present work is intended as an exploratory theoretical and computational framework rather than a complete theory of quantum gravity or Lorentzian spacetime reconstruction. The model does not yet establish a Lorentzian metric, relativistic causal structure, or fixed emergent dimensionality. These limitations are explicitly discussed in the manuscript and are left for future work.

This Zenodo record includes the preprint manuscript, simulation code, and README file for reproducibility and scholarly discussion.