Horizon Limit Theorem for Weighted Cyclic Lattices: Boundary-Induced Spectral Divergence in Discrete Phase Geometry

Position Statement All results are derived from weighted discrete Laplacian operators defined on finite cyclic or annular lattices. No continuous manifold structure, metric tensor, or relativistic field equations are assumed. Horizon-like behavior is defined as divergence in traversal time or phase accumulation induced solely by boundary weighting in operator structure. Abstract A weighted discrete Laplacian is constructed on a cyclic lattice with radial index extension. Boundary-dependent weights modify transport coefficients as a function of lattice radius. It is proven that when boundary weights approach a critical value, group velocity approaches zero and traversal time diverges logarithmically. This produces a horizon-like limit in which approach requires infinite time under internal spectral evolution. The result demonstrates that horizon behavior can arise from operator weighting without invoking external gravitational postulates.