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

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].