General Relativity as the Coherent Limit of a Finite-Response Medium: A Unified ECSM Parent Action, Strong-Field Completion, and Singularity Avoidance

This work presents a unified effective derivation of the gravitational sector of the Emergent Condensate-Superfluid Medium (ECSM) framework. A finite tensor response, medium amplitude, coherent phase, and coherence field generate an emergent metric through a matrix-exponential map. Assuming a coherent massless spin-2 Fierz-Pauli phase and universal coupling to total stress-energy, the nonlinear tensor sector closes onto Einstein-Hilbert dynamics. The coherent limit recovers Newtonian gravity, the general-relativistic post-Newtonian parameters, two luminal tensor polarizations, the exact Schwarzschild exterior, and the linear Kerr exterior. Finite strain capacity and finite response time terminate the formal coherent continuation at a threshold outside the divergent limit and replace it with a regular finite-response shell and finite-density core. Horizon-like behaviour may remain as a regular transport-characteristic boundary without degeneration of the metric determinant. The paper also reports the first quantitative tidal-deformability benchmarks for the regular ECSM compact-object branches. A compact-support benchmark with compactness C = 0.475 gives k2 approximately 3.74 x 10^-5 and Lambda approximately 1.03 x 10^-3. A coupled parent-field perturbation calculation recovers the reduced tidal equation in the frozen-field limit and demonstrates that parent-field corrections can shift or conditionally reverse the reduced Love-number zero crossing within explicit locally positive projected-Hessian closures. The construction is presented as a sufficient unified effective parent-action framework, not as a unique microscopic theory, a parameter-free prediction, or experimental confirmation. The publication record includes the executed N29R, N30R, and N31R notebooks and their complete evidence archives.