Spacetime Memory and Cosmic Expansion: Deriving Dark Energy and Dark Matter Signatures from a Single Geometric Kernel

The standard cosmological model assumes that spacetime curvature is strictly reactive — that when gravitational sources move or dissipate, spacetime returns to a neutral state. This assumption is foundational but unproven. This paper extends the LALA framework introduced in Paper One by challenging that assumption directly. If spacetime retains geometric memory of past curvature events, decaying at the local expansion rate rather than instantaneously, photons propagating through the resulting distributed residual curvature accumulate a logarithmic correction of the form Δμ = A·ln (1+z). We show that this single mechanism naturally produces both the kinematic photon path correction previously attributed to dark energy and a dynamic contribution to H (z) scaling as (1+z) ^ (3/2) — identical to the Hubble rate scaling in a matter dominated universe — producing expansion history behaviour observationally consistent with what cold dark matter describes without requiring non-baryonic matter — two geometric projections of the same underlying spacetime memory. Paper 1 Doi https: //doi. org/10. 5281/zenodo. 18912383