Double-entry ledger content admits a finite gravitational construction based on the reciprocal cost J(x) = (x + 1/x)/2 - 1. We prove that every compatible collection of hinge contents has a unique shared-channel minimum, derive its exact stiffness, and establish quadratic small-content and linear large-content limits. With the stated geometric coupling, the construction supports the Regge action. Its midpoint-resolved second variation converges to the weak-field Einstein-Hilbert form with an explicit remainder; its interacting lattice branch carries exactly two physical modes at every nonzero on-branch momentum. Scalar constraint models recover the metric-dependent Hamiltonian bracket. The quantum construction includes the label-erasure measure, propagating Gaussian, and a one-hinge Lorentzian continuation. Separate cosmological readout premises give 13/12, w_0 = -0.9828, and Omega_dm = 0.2648981 without fitted continuous parameters. The Hubble and dark-matter comparisons are retrodictions; the dark-energy shape and photon-dispersion law supply prospective tests.