A Deterministic Arithmetic Perspective on Hodge Structures

We explore a deterministic, arithmetic-inspired framework for organizing cohomologyclasses of smooth projective varieties. By partitioning cohomology intosequentially generated “bands” and introducing a band-amplitude admissibility principle,we identify structural constraints on the emergence of Hodge decomposition.A canonical band-structured Hamiltonian is introduced to realize admissible spectralmodes. While this approach does not constitute a proof of the Hodge conjecture, itprovides a conceptual perspective in which admissible Hodge classes arise naturallyfrom arithmetic propagation and band-level balance.