Future as Dark Energy, Present as Decoherence, Dark Matter as Past Gravitational Memory: A Testable Framework for DESI DR2 and Euclid

What if dark energy, decoherence, and dark matter are not three independent cosmological puzzles — but three temporal roles in a single irreversible process? The Cosmology of Time (CT) framework proposes that the dark sector emerges from the thermodynamic cost of the universe's irreversible quantum-to-classical transition. Dark energy is the engine that continuously generates genuinely open quantum possibilities and erases every alternative not selected — two inseparable thermodynamic costs of the same irreversible cycle, the second grounded in the Landauer principle. Decoherence is the irreversible selection — the process by which quantum possibilities become classical facts. Dark matter is the cumulative gravitational archive of past selections — not a passive record but an active causal rail that progressively constrains where and how the next cycle of collapses will unfold. The archive only grows. Erased branches do not return. This is the cosmological arrow of time. The cosmic acceleration at z ≈ 0. 7 is interpreted as the thermodynamic phase transition at which the rate of possibility generation overcame the gravitational weight of the accumulated archive. The current proportions — 70% DE, 25% DM, 5% baryons — are the thermodynamic snapshot of this ongoing process. The paper derives analytic solutions for a minimal baryon-mediated DE→DM coupling with a single free parameter (ξ₀), demonstrates Planck consistency, and produces an effective equation of state wₑff (z) = −1 + ξ₀ S (z) whose morphology is set entirely by the development of the gravitational rail — not by a scalar field potential. Dark matter is decomposed into a primordial seed component and a late-time archive generated by the irreversible cycle. The framework is structurally constrained to w ≥ −1, providing an explicit falsifiability condition against phantom crossing. Dimensional analysis links the Landauer identification to the Gibbons–Hawking horizon temperature, showing quantitative consistency between the erasure bit-rate and the cosmological horizon entropy density. Testable predictions for DESI DR2, Euclid, Roman, and Rubin are provided, including environment-dependent assembly bias, characteristic sigmoid curvature of w (z) near the activation redshift, and weak-lensing signatures in diffuse systems. The model reduces to ΛCDM when ξ₀ → 0.