A logarithmic redshift drift template for the fine-structure constant and its multi-messenger signatures

We propose a phenomenological template for testing an effective vacuum-relaxation framework through a logarithmic redshift drift of the fine-structure constant. While the bulk electromagnetic vacuum is assumed to remain impedance-protected, bound atomic states may retain a screened elastic mismatch with the relaxing background. This yields Δα/α(z)-κscr\,Δ dL/dL(z) where Δ dL/dL≡(dLEM-dLGW)/dLGW is the fractional electromagnetic-versus-gravitational-wave luminosity-distance offset. Adopting the benchmark closures εᵣₑₗ=πα₀/2 and κscr=2α₀², the model predictsΔα/α-πα₀³ln(1+z)-1.22ln(1+z)\ ppm.The signal reaches $-1.34$ ppm at $z=2$, within the target range of ESPRESSO and ELT-ANDES, and is correlated with a sub-percent to percent-level standard-siren offset. This provides a fixed falsifiable consistency benchmark between quasar spectroscopy and gravitational-wave cosmology.