Local Lorentz Recovery in ECSM: Special Relativity as the Coherent Propagation Limit

Special relativity is among the most precisely tested structures in modern physics. Any deeper framework in which spacetime is not fundamental must therefore explain why local observers recover Lorentz-invariant kinematics to very high accuracy. This paper develops the ECSM interpretation of special relativity as the local coherent propagation limit of a finite-response medium. In this view, the invariant speed c is not taken as a primitive property of empty spacetime, but as the limiting coherent response speed of the underlying medium. Stable clocks, particles, fields, and measurement devices are treated as excitations of the same coherent substrate, so internal observers cannot define operational procedures that bypass this response limit. Under the conditions χ → 1, kξ ≪ 1, and τ_resp ≪ τ_drive, the ECSM excitation spectrum reduces to the Lorentz-invariant dispersion relation E² = p²c² + m²c⁴, and the standard time-dilation law follows as a consequence of response-limited internal phase evolution. Finite-response corrections are suppressed by powers of 1 − χ, kξ, and τ_resp/τ_drive, ensuring that ordinary local experiments recover special relativity while leaving open the possibility of small deviations in non-coherent or high-drive regimes. The result clarifies that ECSM is not anti-relativistic: it treats special relativity as an emergent but mandatory local limit.