Deriving the Born Rule from Boundary–Induced Alignment in Chronon Field Theory

This paper presents a rigorous derivation of the Born rule—the cornerstone of quantum probability—within the framework of Chronon Field Theory. By modeling measurement as boundary-induced alignment, we show that outcome probabilities emerge dynamically from stochastic chronon fluctuations, without postulating collapse. Using tools from stochastic analysis, martingale theory, hydrodynamic limits, and large-deviation principles, we prove that single-shot absorption probabilities coincide with Born weights and that empirical frequencies obey Sanov’s theorem. The work bridges microscopic chronon dynamics with macroscopic measurement statistics, establishes robustness bounds under realistic imperfections, and outlines falsifiable experimental signatures. It provides a mathematically complete route from chronon microphysics to quantum probabilities, offering new insights into the measurement problem and quantum foundations.