A Nash Point Origin for the Early Universe: Curvature Overshoot, Oscillatory Convergence, and the Emergence of Invariants

This work proposes a geometric origin for the universe based on the Primordial Curvature Overshoot Postulate. Instead of beginning at \kappa =0 or in a finely tuned symmetric state, the universe is framed as emerging from a Nash‑type point where multiple curvature modes were equally viable. Its first transformation overshot toward high curvature, recoiled toward lower curvature, and entered a sequence of diminishing oscillations that converged onto the narrow corridor of self‑sustaining geometry observed today. Because invariants, conservation laws, and persistent modes had not yet formed during this primordial phase, no information from that era could be encoded or preserved. The early universe was therefore thermally extreme but informationally barren, with physics emerging only after geometric stabilization. Observable features such as near‑flatness, slight positive expansion, the stability of matter, and the separation of forces are interpreted as fossilized consequences of this convergence process. The model replaces fine‑tuned initial conditions with a structural principle and offers a coherent, minimal framework for understanding how the universe learned its own geometry.