https://youtu.be/uHYGlIcybDw?si=acVvUMw_tQyMmaTb https://youtu.be/03vu8u6jvyo?si=sT8QporYD5x897M2 This work proposes a structural theory of wave dynamics in which quantum, statistical, and cosmological phenomena emerge from a single underlying principle: whether a wave process achieves phase closure or remains phase-open. Within a discrete conservative framework, wave evolution is shown to admit two qualitatively distinct regimes. Phase-closed processes generate stationary normal modes and localized particle-like states, whereas phase-open processes produce dispersive envelope dynamics and persistent background fluctuations. In this framework, Schrödinger-type evolution is not postulated as a fundamental law but arises universally as the effective continuum description of structurally incomplete (phase-open) wave processes. A central result of this paper is that Heisenberg-type uncertainty relations emerge as a structural consequence of phase openness rather than measurement postulates or operator non-commutativity. Persistent background fluctuations, including vacuum noise and cosmological background phenomena, are likewise interpreted as unavoidable residuals of incomplete phase closure in conservative wave systems. The theory further introduces a probabilistic structural law governing phase closure, predicting that particle-like states are rare events in a dominantly phase-open universe. This leads to falsifiable scaling relations connecting microscopic phase dynamics to macroscopic cosmological matter fractions. The framework is integrated with the JS–SH discrete geometry and the SRCD ratio coordinate, providing a unified structural interpretation of quantum mechanics, particle formation, and cosmic background structure. Unlike conventional approaches, this work does not modify quantum mechanics by additional axioms or stochastic assumptions. Instead, it derives quantum and cosmological phenomena from structural properties of discrete wave dynamics, offering a unified conceptual and mathematical foundation linking Schrödinger evolution, uncertainty, and cosmic background fluctuations.