On a lattice whose adjacent faces share their corner bits, the face records of an M × N patch carry exactly MN independent bits, one per face, while the configurations hidden behind a fixed record grow only with the perimeter. Under a heat-posting rule (the heat crossing a cut is a fixed quantum times the change in what the cut posts), with each posted bit carrying Landauer’s heat k_B T ln 2, the Clausius relation (heat over temperature equals entropy change) charges the record ln 2 per posted bit and the hidden configurations nothing, so the entropy per area is η = ln 2/λ_rec². Identifying the cut with Jacobson’s local horizon, his relation G = c³/(4ℏη) then gives ℓ_P = λ_rec/(2√(ln 2)): for a cut along lattice faces the Planck length is 0.6006 lattice edges, with no free area coefficient and no dependence on the action quantum; a tilted cut counts up to √3 more faces per unit area, and how that is to be read is left open. With the same G on both sides, the quarter in black-hole entropy is an identity, and a free area coefficient is a second definition of G. With the measured G the edge is 2.69 × 10⁻³⁵ m; a prediction of G itself waits on the duration of one tick.