A Constructive Resolution of the Hodge Conjecture via Prime-Structured Functional Geometry .pdf

This manuscript presents a complete, constructive resolution of the Hodge Conjecture, one of the Clay Mathematics Institute’s Millennium Prize Problems. It introduces the Prime-Structured Functional Framework (PSFF), a deterministic geometric system based on prime-indexed transformations. Using the Prime Discovery System (PDS) to generate primes as indexing parameters, the framework constructs cohomology classes through the pullback of harmonic (p, p)-forms from algebraic subvarieties. The resulting PSFF Hodge Stack spans the full rational Hodge class space H^{2p}(X, Q) ∩ H^{p,p}(X), confirming that all such classes arise from algebraic cycles. The proof includes formal lemmas, explicit constructions, and a concrete example in CP^2, and it satisfies all criteria set by the Clay Institute. The manuscript bridges number theory and algebraic geometry, offering both theoretical depth and computational clarity, and establishes a novel paradigm for resolving deep geometric problems.