Universal Coherent Response Closure of Weak Relativistic Observables in ECSM

This paper develops the weak clock-optical-rotational closure of the Emergent Condensate-Superfluid Medium (ECSM) framework using a strictly non-geometric physical description. ECSM contains no physical spacetime, no curvature, no metric field and no geodesic mechanism. Its primitive ontology is a three-dimensional coherent finite-response medium in which matter is represented by stable localized excitations and gravitational, inertial, optical, clock-rate and rotational phenomena arise from physical medium response. General-relativistic relationships are used only after the ECSM observables have been derived, as a comparison of predictions rather than as part of the underlying mechanism. Earlier ECSM work established a non-geometric weak-response framework containing static gravity-like response, inertial dressing, coherent clock-rate modification, split electromagnetic constitutive response, common propagation structure and a rotational/vorticity sector. Several coefficients required for complete weak relativistic recovery, however, remained as coherent closure conditions rather than consequences of one common physical principle. This work introduces the Universal Coherent Response Principle (UCRP) as the foundational closure principle of the coherent weak regime. The first part of UCRP states that a single dimensionless burden generator controls both stable matter-process rates and the reciprocal electromagnetic response amplitudes. The coherent clock response is written as R_tau = exp(-B), while the electric and magnetic response amplitudes vary reciprocally as exp(+B) and exp(-B). Because the electromagnetic constitutive coefficients are quadratic in these response amplitudes, the resulting constitutive responses are Z_E = Z_c exp(+2B) and Z_B = Z_c exp(-2B). Using the ECSM optical relation n_opt^2 = Z_E / Z_B gives n_opt = exp(2B), and therefore the exact relation n_opt x R_tau^2 = 1. The previously imposed weak-response coefficients then follow directly as zeta_tau = 1, q_tau = 1/2 and eta_B = 2. In the downstream relativistic comparison dictionary this gives gamma_eq = 1 and beta_eq = 1. The rotational sector is derived entirely from three-dimensional ECSM medium physics. The physical longitudinal response is represented by the gradient of the scalar response potential, while the rotational response is represented by Omega_W = 1/2 curl W. UCRP states that equal normalized longitudinal and rotational reconfiguration burdens carry the same coherent quadratic medium-response cost. This produces the transverse-to-scalar susceptibility relation C_T / C_E = 4 / c_R^2 without invoking spacetime geometry, trace reversal, four-dimensional stress-energy tensors or a spin-2 spacetime field. The resulting rotational closure gives R_W = 1 and Lambda_rot = 1. Combined with the ECSM matter-side result J = L + S, the coherent far rotational response becomes: W_far = (2 G_eff / c_R^2) (J x r) / r^3. The numerical weak-limit relationships therefore match the familiar relativistic results, but their physical interpretation is different. In ECSM they arise from the response and reconfiguration of a real three-dimensional coherent medium rather than from curvature of spacetime. The result is deliberately conditional. UCRP is treated as a foundational coherent-response principle and is not claimed to be derived from deeper constituent microphysics. Within that stated boundary, the weak clock, optical and rotational coefficients become consequences of one common ECSM response structure rather than independently assigned numerical closure values. Version 2 removes the previous response-space construction that used four-index notation, 00/0i components, trace-reversal normalization and massless spin-2 machinery. The revised derivation maintains the ECSM ontology throughout and uses only three-dimensional medium variables and physical response quantities before the final comparison with general relativity.