Unified Lattice Framework III: Quantized Resolutions of the Quantum–Gravity, Cosmogenic, and Continuity Problems

This preprint presentsUnified Lattice Framework III: Quantized Resolutions of the Quantum–Gravity, Cosmogenic, and Continuity Problems, completing the core of the Unified Lattice Program (ULP). Building on the curvature-bounded dynamics of ULF I and the dark-sector and cosmogenic extensions of ULF II, this work promotes all classical lattice fields—Φ, LμνLμν, and RμνRμν—to operator-valued quantities obeying an intrinsic curvature algebra. The resulting quantized Hamiltonian unites gauge, gravitational, and cosmological sectors within a single finite-geometry formalism, yielding discrete curvature spectra, bounded vacuum energy, and continuity across classical and quantum limits. The paper culminates in the Grand ULF Equation, a compact, falsifiable expression of curvature–matter unification that synthesizes quantum field theory, general relativity, and cosmogenesis within one self-consistent geometric framework.