Coordination Number Independence of Dimensional Information Loss: A Pre-Registered Study

Prior research identified a consistent ≈ 86% information loss when embedding binary patternsfrom 2D into 3D space. Based on the geometric properties of the hexagonal lattice used inthose observations, it was hypothesized that information loss (L) scales with the coordinationnumber (k) of the lattice according to the function L(k) = 100 × k/(k + 1). To test this, a pre-registered study (DOI: 10.5281/zenodo.18287219) was conducted comparing Von Neumann(k = 4), Hexagonal (k = 6), and Moore (k = 8) topologies. Experimental results from static pattern embedding (Phase 1, n = 30 total, 10 per topology) showed no significant difference in loss between topologies (Mean: 83.01%, Max Diff: 0.15%). Further testing with dynamic patterns evolved via Conway’s Game of Life (Phase 4, n = 90) yielded higher total loss (≈89%) but similarly failed to show k-dependence across any individual component of the Φ metric (R, S, or D). The coordination number hypothesis is definitively falsified. We conclude that dimensional information loss is driven by volumetric space dilution and Shannon entropy reduction, independent of lattice connectivity.Keywords: dimensional embedding, information loss, dimensional boundaries, Shannon entropy, pre-registration, hypothesis falsification.