Dark Energy as Future, Irreversible Selection as Present, and Dark Matter as Past: A Lagrangian Model with Implications for the BAO–CMB Tension

Preprint and supplementary verification code for the paper: Dark Energy as Future, Irreversible Selection as Present, and Dark Matter as Past: A Lagrangian Model with Implications for the BAO–CMB Tension submitted to Foundations of Physics. The Cosmology of Time (CT) interprets dark energy, baryonic matter, and dark matter as three temporal roles — Future, Present, and Past — within a single irreversible information-processing cycle. This paper develops an effective Lagrangian realization of that cycle with potential V(φ) = Vcc + V1 tanh²(φ/M) and conformal baryon coupling A(φ) = exp[−κ sech²(φ/M)], producing a thawing equation of state with w(0) = −0.938 and w ≥ −1 at all redshifts. The model is confronted with DESI DR2 BAO and BOSS DR12 data, yielding Δχ² = −20.9 (ΔAIC = −16.9) at Planck fiducial parameters. Under profile likelihood, CT accommodates BAO data at h = 0.680 (1.2σ from Planck), whereas ΛCDM requires h = 0.685 (2.2σ). The deposit includes: (1) the preprint PDF, (2) an independent verification script that reproduces all 35 numerical claims in the paper (35/35 PASS), (3) a figure generation script for all 6 paper figures. The code requires only Python, NumPy, and SciPy. The full reproducibility chain additionally requires CLASS v3.3 for the sound-horizon computation.