QDL Cosmological Closure as a Horizon-Screened Curvature Ansatz: Vacuum-Energy Residuals, Horizon Ledgers, Dark-Sector Separation, and the Cosmological Constant Scale

The Quantized Dimensional Ledger (QDL) program treats physical theory construction as a problem of structural admissibility, closure completion, transformation stability, and residual survival. Earlier QDL work developed conditional spectrum selection, electroweak numerical closure, flavor-rank closure, SMEFT operator governance, and classical gravitational closure. The cosmological constant is the most difficult remaining numerical target because it is not merely a local particle-physics parameter. It is a global curvature-scale residual. This paper develops the QDL cosmological-closure layer in a deliberately bounded form. It does not claim to derive the cosmological constant as a completed hard-physics result. It does not solve the full vacuum-energy problem, compute the cancellation of all quantum-field zero-point contributions, derive the bare cosmological constant, prove w = -1, resolve the Hubble tension, replace Lambda-CDM parameter fitting, solve dark matter, or derive inflation. Its contribution is more limited: it identifies the correct QDL target for Lambda, separates the distinct ledgers usually conflated under dark energy, formulates a horizon-screening interpretation, and presents a first numerical ansatz that reconstructs the observed Planck-normalized curvature scale. The cosmological constant has dimension L^-2. Therefore QDL cannot derive Lambda as an isolated raw number such as 10^-52 m^-2 without specifying the length scale relative to which it is measured. The admissible dimensionless target is lambda_Lambda = Lambda l_P^2, or equivalently the logarithmic curvature ledger H_Lambda = -log10(Lambda l_P^2). Using the observed Lambda-CDM-scale curvature, Lambda of order 10^-52 m^-2, and the Planck length, one obtains Lambda l_P^2 of order 10^-122 and therefore H_Lambda of order 121.5 to 122. The central interpretation is that the observed cosmological constant is not a raw sum of local quantum-field vacuum energies. It is treated as a horizon-screened curvature residual. A positive cosmological constant defines a horizon scale R_Lambda of order Lambda^-1/2 and a horizon-area ledger N_Lambda of order A_Lambda / l_P^2. Since A_Lambda is of order R_Lambda^2 and therefore of order Lambda^-1, one obtains N_Lambda of order 1 / (Lambda l_P^2), or Lambda l_P^2 of order N_Lambda^-1. Thus cosmic curvature is interpreted as the inverse of a horizon-area ledger. The paper then presents a first horizon-screening ansatz. Let H_v = -log10(G v^2 / hbar c) be the Planck-electroweak hierarchy ledger. Let T_alpha = 9 + 1/27, C_W = 53/18, and C_lambda = 49/72. The proposed QDL horizon-screening ansatz is H_Lambda^QDL = 4 H_v - sqrt(alpha^-1) + (T_alpha + C_W - C_lambda + 1/18) / sqrt(alpha^-1) - log10(4 pi). Using representative QDL values H_v approximately 33.38 and alpha^-1 approximately 137.035999177, this gives H_Lambda^QDL approximately 121.7, and therefore Lambda_QDL l_P^2 approximately 10^-121.7, of order 10^-122. This reconstructs the observed Planck-normalized cosmological-constant scale at ansatz level. It is not yet a hard derivation. The formula must eventually be derived from a deeper QDL horizon action, entropy principle, global curvature-source closure theorem, or vacuum-screening mechanism. Until then, its correct status is: first-pass horizon-screened curvature ansatz, not a completed solution to the cosmological constant problem. The paper also separates the cosmological constant from dark matter, dynamical dark energy, inflation, H0, Omega_Lambda, and vacuum-energy bookkeeping. It identifies residual tests and limitations, including the dimensionless-target test, horizon-formula derivation test, vacuum-energy cancellation test, equation-of-state test, cosmological-dataset test, Hubble-tension test, dark-matter separation test, Planck-electroweak hierarchy dependency test, and ansatz robustness test. The final bounded result is that QDL reduces Lambda to a dimensionless horizon-screened curvature residual and reconstructs its observed scale at first-pass ansatz level. The next hard-physics step is to derive the horizon-screening formula from a QDL action, entropy principle, or global curvature-source closure theorem, or else downgrade it to numerical compression.