PFUSRC-148 Spatial Hierarchical Nesting Dynamics Coupling Mechanisms of L4 Bicone Respiratory — Coupling Mechanisms of L4 Bicone Respiratory Rhythm, L5 PNRMTS Nodal Response, and L6-L7 Receiving-Layer Feedback

Abstract

PFUSRC-146 defines the observable L5 spacetime substrate as Prime-Node Rigid Morphing Topological Space (PNRMTS), while PFUSRC-147 identifies large-scale cosmic filaments as global spacetime damped topological imprints. However, the bidirectional dynamical coupling between the L4 parent double-cone ontology, L5 prime-node network and L6-L7 solidified receiving layers has not been systematically elaborated. This paper fills this gap by establishing a complete set of interlayer hierarchical nesting dynamical equations. Independent dynamical variables are defined for each hierarchical layer: the L4 layer is characterized by bicone respiratory period, 55-anchor stress tensor and 12/11 gauge ratio constraint; the L5 layer contains nodal displacement field, interstitial morphing tensor and damping gradient tensor (the geometric equivalent of dark matter gravitational fields); the L6-L7 receiving layer is described by solidification stress, cognitive information flux and technological feedback coefficient. Four core coupling equations are derived to describe L4→L5 respiratory driving, L5→L4 negative nodal feedback, L5→L6-L7 damping projection and L6-L5 solidification backreaction. This work analyzes simultaneous steady-state fixed-point solutions of the coupled system, elaborates multi-stage perturbation propagation paths and three-tier self-repair mechanisms (nodal rearrangement, interstitial relaxation, global respiratory rhythm adjustment). Three observationally testable corollaries are proposed: the power-law spacing distribution of cosmic filament nodes with exponent −12/11, dark energy density attenuation driven by bicone rhythm drift, and fixed pendulum resonant frequency coupled to fundamental L4 topological periodicity. The core conclusion: universal steady state is dynamic respiratory equilibrium rather than static balance. The L4 bicone rhythm acts as the global driving source, the L5 PNRMTS nodal network serves as the spatial response carrier, and the L6-L7 receiving layer provides solidified feedback constraints. Together they form a complete three-layer nested dynamical system, which constitutes the PFUSRC fundamental answer to how the universe maintains long-range ordered large-scale structures.