Entropy–Phase Closure of Λ, Horizons, and Cosmological Budgets

Entropy–Phase Closure of Λ, Horizons, and Cosmological Budgets Author: Radu Necsanu ORCID: https://orcid.org/0009-0009-1281-9180 DOI: https://doi.org/10.5281/zenodo.18437431 Abstract We present a fully operational, strictly standard-physics framework (QM/GR/EFT) in which (i) phase-accessible entropy is defined via the maximal set of mutually phase-resolvable alternatives Ω_acc, and (ii) a separate horizon-inclusive entropy ledger is tracked when horizon area terms are intentionally included. We demonstrate a closure-rigidity result: under diffeomorphism-invariant, CPTP coarse-graining that preserves ∇^μT_μν = 0, the late-time horizon-inclusive entropy computed from (A) the Einstein equations with Λ, (B) horizon thermodynamics via the observed Hubble scale H₀, and (C) the standard cosmological entropy census must agree if and only if the second cumulants of action-phase dispersion match across the declared window. In homogeneous and isotropic windows, Λ is the unique local zeroth-derivative covariant term that preserves this closure. All three routes converge to S_hor / k_B ≈ 10¹²² for late-time ΛCDM parameters. The result is non-trivial, falsifiable, and introduces no new postulates. We provide explicit numerical evaluation and a scale-localized closure-defect diagnostic suitable for observational falsification.