Why Spacetime Is (3+1)-Dimensional: Polygon Transcendence via V=N/D — Paper 2 of 3D Theory Series

This paper is part of the TheYKHC Theoretical Series: 'From Duality to Field: A Three-Dimensional Evolution of Universal Theory' Paper 1: Dual-Layer Light Invariance (2D — The Discovery of Duality) Paper 2: Why Spacetime is (3+1)-Dimensional (2.5D — Polygon Transcendence) Paper 3: Ki-Net Field Evidence (3D — Universal Field Completion) Related: Genki Particle Dance (DOI: 10.5281/zenodo.20955834) The series demonstrates that V = N / D governs reality from the quantum vacuum to the cosmic scale. Paper 2 of 3 — 2.5D: Polygon Transcendence Polygons approximate curved surfaces with flat faces — discrete patches that never truly merge. Standard physics faces the same problem: discrete quantum events stitched into continuous spacetime with unresolved seams. This paper proposes that V = N / D resolves this discontinuity. Where density gradient (N/D) is continuous, spacetime is continuous. The (3+1)-dimensional structure of our universe is not arbitrary — it is the unique dimensional configuration where V = N / D achieves stable propagation. Spacetime has (3+1) dimensions because that is the geometry required for the dance to continue.