Lapse-Induced Closure of the Discrete Bianchi Structure in Projection-Origin Geometry (Projection-Origin Gravity 3)

This work examines whether a projection-origin discrete geometryadmits an internal lapse choice under which the contracted Bianchistructure becomes numerically consistent in the weak-field regime. A scalar potential is first generated independently of generalrelativity using a projection-origin Poisson kernel defined by adiscrete spectral operator. The potential is embedded into a staticweak-field metric within an ADM-type framework with vanishingshift vector. All geometric quantities are evaluated using the same lattice-consistent spectral operator that defines the Poisson kernel.Within this unified discrete framework the bulk Bianchi residualis computed and a lapse-like reparameterization is introduced inthe form N(x) = exp(αΦs(x)). A systematic scan over α reveals a sharp minimum of the bulkBianchi residual near α ≈ 1, where the residual is suppressed byapproximately eight orders of magnitude relative to the baselineconfiguration. The location of the minimum and the magnitude ofsuppression remain stable under lattice refinement and variationsof spectral parameters. The analysis does not derive the Einstein field equations.Instead it provides a numerical consistency test indicating thatprojection-origin geometry can reproduce the conservationstructure associated with the contracted Bianchi identity withina static, shift-free weak-field sector. Note: Parts of the manuscript were linguistically and structurally refinedwith the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own.