The Hodge Conjecture Definitively Resolved within the D10Z Paradigm

This work presents the definitive resolution of the Hodge Conjecture within the D10Z Paradigm, introducing a novel framework based on resonant projections of nodal structures within the TTA_ε quantum mesh. Through the use of harmonic nodes Φₙ(Z), discrete cohomological activation thresholds, and fractal-geometric convergence methods, the D10Z model establishes a 1:1 correspondence between rational (p,p)-classes and algebraic cycles. The result is supported by numerical simulations on K3 surfaces, Calabi–Yau varieties, and others, reaching L²-errors below 10⁻³ with R² ≥ 0.98. This resolution transcends traditional Hodge theory by embedding the algebraic cycles within a dynamic, resonant geometric substrate anchored in the GM-scale (10⁻⁵¹ m).