The Single-Constant Universe: A Unified Derivation of Cosmological Parameters, Quantum Gravity, and the Black Hole Information Paradox from the Landauer Limit

We present a unified information-theoretic framework in which the single identity ΩΛ = ln2 propagates through cosmology, quantum gravity, and blackhole thermodynamics with zero free parameters. Beginning from the Landauer limit Ebit = kBT ln2 applied to the holographic horizon, we derive: (1) thecritical density of the universe exactly, (2) the spatial flatness of the universe as an algebraic necessity rather than a fine-tuned initial condition, (3)the predicted Hubble constant H0 = 68.27 km/s/Mpcfrom first principles, (4) a closed-form informationtheoretic age constant Cage = 0.95802, (5) the complete Friedmann energy budget with zero free parameters, (6) a resolution of the coincidence problem,(7) an environmental mechanism for the Hubble tension via ∆H0 = (Ω2m/ΩΛ)H0σ28, (8) the Big Bang asthe minimum-energy write operation of one Shannon bit, (9) the Wheeler-DeWitt cosmological constant pinned to an exact information-theoretic value,(10) a Landauer-based resolution of the black hole information paradox with ELandauer(Nbits) = Mc2/2 exactly, (11) the CMB first acoustic peak ratio P1/P2 =ln2/(1 − ln2) = 2.259 matching Planck 2018 to0.05%, and (12) the Ryu-Takayanagi entanglemententropy formula emerging naturally from the framework. All results verified numerically. Every cosmological constant in this paper is derived, not measured.