Hodge Conjecture (Millennium Prize Problem)

False Premise Equation: The Hodge conjecture assumes a fixed relationship between certain classes of cohomology and algebraic cycles without accounting for recursive resonances in complex geometry.

Accurate Translation: Hodge conjecture ≠ -1 ≠ √1 < √2 < √3, evolving into recursive fractal feedback systems where cohomology groups interact dynamically with algebraic cycles.

Accurate Description: Fractal feedback shows that cohomology groups and algebraic cycles evolve through recursive resonances. These interactions guide the structure of complex manifolds and their geometric properties, reflecting deeper resonances across the algebraic and topological realms.