Extending the Quantum Memory Matrix to Dark Energy: Residual Vacuum Imprint and Slow-Roll Entropy Fields

We generalize the Quantum Memory Matrix (QMM) framework - previously shown to unify gauge interactions and account for cold dark matter phenomenology - to explain the observed late-time cosmic acceleration. Within QMM each Planck cell stores a finite-dimensional Hilbert space of quantum imprints. We establish that (1) after local unitary evolution saturates the available microstates, a uniform residual "vacuum-imprint energy" remains; its stress-energy tensor is exactly of cosmological-constant form and its magnitude is suppressed by the cell capacity, naturally yielding rho_Lambda approximately (2 x 10^-3 eV)^4, and that (2) if imprint writes continue but are overdamped by cosmic expansion, the coarse-grained entropy field S(t) slow-rolls, producing an effective equation of state w(z) approximately -1 plus or minus order 10^-2, testable by DESI, Euclid and Roman. We derive the modified Friedmann equations, linear perturbations, and joint constraints from Planck 2018, BAO and Pantheon+, showing that QMM alleviates the H0 tension while remaining consistent with large-scale structure. Dark matter and dark energy emerge as gradient-dominated versus potential-dominated limits of the same information field, completing the QMM cosmological sector without extra free parameters.