Vacuum as an Intrinsic Fixed Point and the Λ–ξ Correlation from Coarse-Grained

We develop an operational notion of cosmological vacuum within an intrinsic-density-matrix framework: vacuum is defined as the late-time fixed point selected by irreversible coarse-grained dynamics in the intrinsic reference basis (IRB). When coarse graining is controlled by a physical correlation length xi, unresolved degrees of freedom contribute a minimal residual vacuum-energy density of universal scaling form rho_vac(xi) = kappa_eff hbar c / xi^4, where kappa_eff is a dimensionless functional of intrinsic informational deficits (populations and coherences). Einstein's equations then yield the correlation Lambda = kappa_eff ell_P^2 / xi^4, mapping the observed cosmological constant to a laboratory length scale of order tens of microns (xi ~ 40 microns for kappa_eff ~ O(1)). What is structural (the xi^{-4} scaling and the composition law for the suppression functional) is isolated from what requires matching (the value and possible slow evolution of kappa_eff and xi). Falsifiable correlated tests in sub-millimeter gravity and dark-energy reconstructions are identified.