This paper derives the ECSM coherence parameter from the linear response of a compressible finite-response medium. Starting from a density-phase order parameter, the medium is shown to support coherent long-wavelength propagation with a characteristic propagation speed and healing length. The finite time required for the medium to reorganise over this coherence length defines an intrinsic response time, tauᵣesp. When the medium is driven on a timescale comparable to or shorter than this response time, the response amplitude is suppressed by the transfer function of a finite-relaxation system. This yields the ECSM coherence law: chi = 1 / (1 + (tauᵣesp / taudrive) ²) showing that chi is not an arbitrary phenomenological modifier, but the effective response efficiency of a finite-relaxation medium. The derivation provides a bridge between the microscopic ECSM scaffold and the macroscopic coherence parameter used in gravitational, optical, inertial, localisation, and cosmological applications. In the coherent limit, chi approaches 1 and standard propagation behaviour is recovered. In the response-limited regime, chi becomes small and the medium may exhibit lag, saturation, localisation, confinement-like behaviour, or coherence-dependent propagation corrections. This paper therefore provides a core derivational basis for the ECSM programme by linking its central control parameter to compressible medium dynamics rather than treating it as a free phenomenological insertion.
Adam Sheldrick (Tue,) studied this question.