Dynamic Degenerate Fiber Bundle and Emergent Spacetime Model II: Lagrangian Action Principle, ADM 3+1 Emergence, and Stratified Environmental Boundaries

Abstract Building upon the exploratory framework of the Dynamic Degenerate Fiber Bundle and Emergent Spacetime (DDFB-EST) model [1, 2], this paper formalizes the topological phase transitions through a rigorous Lagrangian action principle. We decouple the singular control parameter into a kinetic evolution parameter (𝒓𝒕) and a spatial condensation parameter (𝒓𝒔), applying the Arnowitt-Deser-Misner (ADM) 3+1 formalism [3, 4, 5] to derive the emergence of the time metric (𝒈𝟎𝟎) and spatial metric (𝒈𝒊𝒋) dynamically. Furthermore, we introduce external gravitational gradients to break local 𝑺𝑶(𝟑)isotropy, establishing a stratified environmental manifold. By varying the geometric and non-linear kinetic action, we demonstrate how macro-environmental boundary constraints (the synergetic slaving principle) [10, 11] force the high-dimensional morphogenetic phase space to collapse into block-diagonal transfer matrices, yielding discrete, low-dimensional non-equilibrium limit cycles [12]. 中文摘要: 基于动态退化纤维丛与涌现时空(DDFB-EST)模型 [1, 2],本文通过最小作用量原理对其拓扑相变进行了严密的规范场论数学形式化。本文将单一控制参数解耦为动力学演化参数(𝒓𝒕)与空间凝结参数(𝒓𝒔),引入 ADM 3+1 分解 [3, 4, 5],从哈密顿约束中动态推导出时间度规与空间度规的涌现。同时,引入外部引力梯度打破空间各向同性,确立了垂向层级流形。通过泛函变分,本文证明了宏观环境边界约束(役使原理) [10, 11] 如何迫使高维形态发生相空间坍缩为分块对角转移矩阵,最终在物理时空中凝结为非平衡耗散极限环 [12]。