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

<p>This preprint presentsUnified Lattice Framework III: Quantized Resolutions of the Quantum–Gravity, Cosmogenic, and Continuity Problems, completing the core of the <em>Unified Lattice Program (ULP)</em>. Building on the curvature-bounded dynamics of <em>ULF I</em> and the dark-sector and cosmogenic extensions of <em>ULF II</em>, this work promotes all classical lattice fields—<span><span>Φ</span></span>, <span><span>Lμν</span><span><span><span><span>L</span><span><span><span><span><span><span><span>μν</span></span></span></span><span></span></span></span></span></span></span></span></span>, and <span><span>Rμν</span><span><span><span><span>R</span><span><span><span><span><span><span><span>μν</span></span></span></span><span></span></span></span></span></span></span></span></span>—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 <strong>Grand ULF Equation</strong>, a compact, falsifiable expression of curvature–matter unification that synthesizes quantum field theory, general relativity, and cosmogenesis within one self-consistent geometric framework.</p>