The Hodge Architecture: Stability, Selective Freedom, and Structural Necessity

This preorint proposea an architectural reformulation of the Hodge conjecture based on three structural principles: global damping, selective release, and explicit constraint. By integrating Resonant Operator Calculus (ROC), Resonant Operator Architecture (ROA), Leue Modulation Coefficients (LMC), and Arithmetically Modulated Resonance Dynamics (AMRD), we construct a stability framework for cohomological state spaces. For p=1 (divisors), this recovers the Lefschetz (1,1)-theorem. For p>1, the framework localizes the Hodge conjecture to a single, sharply defined obstruction: the existence of a canonical arithmetic discretization principle (LMC-realizability) for flat rational Hodge classes. All operator-theoretic and variation-theoretic constraints are enforced; the remaining gap is purely algebraic. This work does not prove the Hodge conjecture but isolates its precise location within a coherent stability architecture. Linked foundational components Leue Modulation Coefficients (LMC) https://doi.org/10.5281/zenodo.17764669 Resonant Operator Calculus (ROC) https://doi.org/10.5281/zenodo.18142920 Resonant Operator Architecture (ROA) https://doi.org/10.5281/zenodo.18361337 Arithmetically Modulated Resonance Dynamics (AMRD) https://doi.org/10.5281/zenodo.18361505