( HC ) Structural Closure of the Hodge Conjecture: Degeneration, Infinitesimal Rigidity, and the Absence of Hidden Algebraic Classes

This work applies the Structural Variance Control (SVC) framework to the Hodge Conjecture, reframing it as a problem of structural admissibility rather than one of explicit algebraic construction. Instead of attempting to produce algebraic cycles corresponding to Hodge classes, the paper investigates whether the defining structure of Hodge theory itself permits the existence of genuinely non-algebraic rational Hodge classes. By enforcing simultaneous constraints from Hodge decomposition, rationality, polarization, degeneration behavior, and infinitesimal variation of Hodge structures, the analysis shows that no admissible structural variance allows such non-algebraic classes to persist. The result is a demonstration of structural closure: within its defining framework, the Hodge Conjecture admits no internally consistent failure mode.