From a Unified Finite-Response Parent Action to Gravity–Electromagnetic Propagation and Strong-Field Saturation in ECSM

This paper presents a constructive finite-response completion of the Emergent Condensate–Superfluid Medium (ECSM) framework, linking a unified parent action to coherent-limit gravity, electromagnetic gauge structure, quantised response cells, domain-boundary networks, causal propagation and a bounded strong-field continuation. The construction begins with finite parent variables, a matrix-exponential emergent metric, an internal-orientation connection and an antisymmetric response tensor. A massless spin-2 coherent branch with universal stress-energy coupling recovers the Einstein closure in the long-wavelength limit, while a normalised complex orientation doublet produces a Berry-type gauge connection and gapped orientation modes induce a Maxwell kinetic coefficient. A common microscopic response scale is recovered from the gravity and electromagnetic coefficients, with E_star = 7.4173075 × 10^17 GeV and ell_c = 2.6603586 × 10^-34 m. A compact parent phase produces integer cell action, and a repulsive charging Hamiltonian selects one elementary action quantum, Xi = 1. Finite domain walls suppress occupation transfer while retaining weak phase communication, and a disordered three-dimensional benchmark produces a system-spanning coherent cluster with 99.78% protected sites. Network homogenisation introduces an essential distinction between local and observed projection coefficients. A microscopic derivative-mixing Hamiltonian then forces temporal and spatial response to share one causal kernel, preserving a common gravity–electromagnetic propagation cone despite strong amplitude renormalisation. Finally, the coherent geometric branch is terminated at a finite coherence threshold and continued by a bounded density, pressure, response and transport regime rather than a physical singularity. The supporting N47R–N70R notebook programme contains 23 linked derivation notebooks, an end-to-end audit and 628 passed upstream internal-consistency tests. These tests establish mathematical and numerical consistency within the stated assumptions; they are not independent empirical validation.