A Minimal Lattice Laboratory for Emergent Gravity: Binding from Capacity Superadditivity and a Newtonian 1/r Field from Update-Bandwidth Dilution

A toy-model computational study of emergent gravity on lattices and graphs. Two information-theoretic ingredients are tested separately and together: (I) a space ledger, in which matter carries a volume-desire entropy while geometry supplies capacity proportional to connectivity, and (II) a time ledger, in which a fixed per-node update bandwidth dilutes the effective clock rate of crowded regions. Main results, obtained with local Metropolis rules only and no force or metric written into the dynamics: (i) attraction requires both a responsive geometry and a superadditive capacity term, the discrete analogue of the area law A ∝ M²; frozen geometry or saturating capacity yields pure diffusion. (ii) The time ledger alone turns a conserved diffusing gas into a mediator field obeying Laplace's equation: the steady-state drawdown around a dense core is logarithmic in 2D and follows a clean 1/r law in 3D (power-law exponent p = -1.02 ± 0.01, 16 seeds), with logarithmic and screened alternatives rejected by ΔAIC and a band-split curvature test. (iii) Two-body approach times obey τ ∝ d³ in 3D (γ = 2.96 ± 0.47), consistent with a flux-product conjecture linking the static field to the kinetics; a massless-marker vacuum control bounds the metric-contraction confound. (iv) Lensing exhibits a dichotomy: independent tracer particles show only an absorber shadow, while a minimally bound composite deflects toward the mass, overcoming a repulsive entropic wall. (v) A growing-ring version reproduces the FRW particle-horizon integral and shows, by varying bandwidth at fixed geometric growth, that the horizon resides in the time ledger. Negative results (vacuum crumpling reproducing the Euclidean-dynamical-triangulations pathology), one retraction, and the measurement-artifact audits that shaped the final protocol are documented in full in the released laboratory notebooks. Each ingredient is explicitly attributed to known physics (zero-range-process defect condensation, Ito-type accumulation, Smoluchowski absorption, EDT/CDT, and the Wolfram Physics Project's computational time), and novelty claims are limited accordingly. The deposit contains the manuscript in English and Japanese, the LaTeX and HTML sources, all figures, all simulation code (pure Python/NumPy, seeds recorded), two laboratory notebooks, and two design documents. Status: preprint, not yet peer-reviewed and not yet read by a specialist in the field. Known issues (v1): §2 defines Mechanism II with a per-node update budget, while §7 adopts a fixed global bandwidth; these are distinct normalizations and the paper does not flag the switch. Fixed-N results (§3–§6) are unaffected. The relation c(t)=B/N in §7 is a varying-speed-of-light cosmology and should cite Moffat (1993) and Albrecht this attribution is missing in v1 and will be added in v2.