Emergence I: A Deterministic Model from Wave Intersections on a Pre-Geometric Canvas

We present a deterministic model in which spacetime, quantum fields, and gravity emerge from open and closed waves on a pre‑geometric canvas. The fundamental entities are pulsating points (mathematical oscillators): a single time point and space points (one per spatial dimension). Their analog oscillations generate continuous space and time waves. When a space wave and a time wave intersect above a threshold, a closed wave — a spacetime particle — forms. These particles form a discrete voxel lattice, which is physical spacetime. Gravity arises from lattice compression. The model reproduces the Schrödinger, Dirac, Maxwell, Klein–Gordon, Yang–Mills, and Einstein equations, derives the Born rule, and makes testable predictions including a CMB cutoff and energy‑dependent speed of light. Generalization to 3+1 dimensions is straightforward.