[MST-EUT Theory Series #18] Unified Origin of Natural Constants from Entropic Field Phase Transitions - 熵場相變與自然常數的統一起源 (v1.0-zh)

This paper presents the first part of the MST-EUT Trilogy, establishing a unified theoretical framework in which fundamental physical constants emerge from phase-transition structures of an underlying entropic field. Instead of treating constants such as the fine-structure constant, the speed of light, or spectral normalization factors as externally given parameters, this work formulates them as fixed-point projections of a nonlinear response function governing the entropic field near critical density. A central phase-response function is introduced to characterize the transition between sparse, stable regimes and critical configurations where structural reorganization occurs. Within this framework, quantum decoherence is reinterpreted as a structural phase transition rather than an environment-induced stochastic process, and sparsity is identified as a necessary condition for topological stability and solvability across scales. The resulting construction provides a coherent ontological and dynamical basis linking vacuum structure, phase transitions, and the origin of physical constants. This work serves as the conceptual and structural foundation of the MST-EUT Trilogy, upon which subsequent papers develop rigorous dynamical derivations, relativistic field equations, and electromagnetic structures. 本文為 MST-EUT 三部曲(Trilogy)之第一篇,建立一套以熵場相變結構為核心的自然常數統一起源理論框架。 在此架構中,自然常數不再被視為外加的實驗參數,而被重新詮釋為熵場於臨界密度附近,其非線性響應函數所對應之固定點投影。本文引入一個相變響應函數,用以刻畫熵場由稀疏穩定態過渡至臨界結構時的動力學行為。 基於此結構,量子退相干被重新理解為一種結構性相變現象,而非傳統觀點中的環境隨機噪聲;同時指出稀疏性乃拓撲穩定性與可解性得以維持的必要條件,並具備跨尺度的普適意義。 本文件作為 MST-EUT 三部曲的理論基礎與結構總覽,為後續關於動力學方程、相對論場結構與電磁起源之嚴格推導奠定整體框架。