Secant Characters, Hochschild Evaluation, and Geometric Obstructions for Weil-Type Abelian Eightfolds

We investigate secant Chern characters and deformation constraints in the search for exceptional Weil classes on abelian
eightfolds. For positive secant data, the cohomological contraction has rank twelve and a sixteen-dimensional kernel; an
exact rational projector isolates the two-dimensional Weil plane. We establish scoped obstructions for smooth-surface
ideals, line-bundle resolutions, nef rank-three constructions, smooth theta containment, and elliptic pullbacks. Exact
genus-217 controls distinguish a class-correct disconnected six-curve scheme from a smooth connected embedded curve
whose mixed pairing is 36 rather than the target value zero. Lean O2–O7 certificates verify finite pairing and polarization
identities; a separate Eisenstein G34 boundary calculation has a nonzero rank-sixteen minor. These results sharpen the
geometric and deformation tests, but do not construct the required curve/surface/Ueda package or establish all-order
semiregularity.