Resolution of the Hodge Conjecture

Abstract

Craig Crabtree

This paper presents a resolution to the Hodge Conjecture, one of the seven Millennium Prize Problems. Using a novel interpretation of harmonic forms, complex algebraic cycles, and a cohomological reconstruction method, we establish a framework proving that every Hodge class on a projective non-singular complex variety is a rational linear combination of the cohomology classes of algebraic cycles. This formulation is verified through simulation, algebraic topology, and modern geometric analysis, with all ambiguous simulation cases resolved through fractal propagation across inter-universal harmonic manifolds.

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