Bubble Theory: A Deterministic Field Model for Emergent Quantum-Like Phenomena

This document presents the first complete technical formulation of the Bubble Theory, a deterministic field model in which particle‑like events, probabilities, and measurement collapse emerge from classical soliton dynamics. The monograph introduces the static bubble solution, derives the linear mode spectrum, defines a modal detector model, and demonstrates how discrete events and Born‑like statistics arise from threshold dynamics. Numerical simulations of bubble motion, collisions, and detector responses are included. This version establishes the foundational framework for future extensions toward multi‑field systems, spin‑like degrees of freedom, and higher‑dimensional geometries.