The Hermitian Discriminant and Algebraic Weil Classes of an Explicit G₃₄ Sixfold Family

This paper studies an explicit eighteen-branch G₃₄ paired-cover family of polarized abelian sixfolds of Weil type over K = Q(√−3). Building on the geometric monodromy and maximal rank-nine period variation established in the author's preceding Paper 4, we derive the Hermitian discriminant class [−1] using a maximal isotropic subspace arising from degeneration monodromy. Applying Markman's algebraicity theorem, we obtain algebraicity of the exceptional Weil classes throughout the family. For very general members, the maximal period variation and generic Mumford–Tate group yield the full Hodge conjecture through invariant-theoretic generation of Hodge classes. The accompanying ZIP archive contains computational inputs, verification scripts, authentication materials, and provenance documentation. AI-assisted mathematical review and verification are acknowledged in the manuscript; these materials have not undergone formal peer review. Related publication: https://doi.org/10.5281/zenodo.24073219