A Symmetry-Based Heuristic Framework Toward the Hodge Conjecture Using 14-Fold Modular Decomposition

This work presents a symmetry-based heuristic framework toward the Hodge Conjecture, proposing a conjectural 14-fold modular decomposition of Hodge-theoretic data on smooth projective complex varieties. The manuscript does not claim a proof of the Hodge Conjecture; instead, it outlines a structured program in which harmonic representatives and period integrals are organized into 14 modular sectors, together with a conceptual folding operator intended to impose rational/algebraic constraints.The framework suggests testable directions, including numerical experiments on period integrals and Laplacian spectral patterns in low-dimensional varieties (surfaces) and explicit families such as Fermat hypersurfaces. This note is intended as an exploratory hypothesis document and a starting point for further formalization using standard tools in Hodge theory and algebraic geometry.