The Coherence-Response Threshold in ECSM: Finite-Response Breakdown as the Test of Emergent Law

The Emergent Condensate Superfluid Medium (ECSM) framework treats observed physical law as the coherent-limit behaviour of a finite-response medium. This working paper develops the coherence-response threshold as a proposed bridge between foundational ECSM ontology and empirical testing. The paper introduces the coherence-response variable χ = 1/[1+(τ_resp/τ_drive)^p] as a schematic control parameter for the transition between coherent-limit physics and response-limited behaviour. In the regime τ_resp << τ_drive, χ approaches 1 and standard effective laws are recovered. In the threshold regime τ_resp ~ τ_drive, the medium can no longer respond adiabatically, producing lag, memory, saturation, boundary stress, phase displacement, decoherence, or modified response gradients. The central claim is that ECSM is most directly tested not where standard law already works, but where coherent-limit assumptions begin to fail. Candidate threshold domains include galaxy outskirts and low-acceleration baryonic response, CMB acoustic residuals and phase-response lag, including the possibility that the CMB event represents a coherence-transition or freeze-in surface, redshift/optical accumulation, Casimir-like boundary stress, quantum decoherence thresholds, and strong-gradient gravitational regimes. The paper proposes a cross-sector test criterion: ECSM gains support only if independent physical sectors exhibit shared finite-response structure governed by common coherence-threshold variables. Conversely, ECSM fails if response-limited departures must be fitted separately in each domain without common architecture.