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 abelianeightfolds. For positive secant data, the cohomological contraction has rank twelve and a sixteen-dimensional kernel; anexact rational projector isolates the two-dimensional Weil plane. We establish scoped obstructions for smooth-surfaceideals, line-bundle resolutions, nef rank-three constructions, smooth theta containment, and elliptic pullbacks. Exactgenus-217 controls distinguish a class-correct disconnected six-curve scheme from a smooth connected embedded curvewhose mixed pairing is 36 rather than the target value zero. Lean O2–O7 certificates verify finite pairing and polarizationidentities; a separate Eisenstein G34 boundary calculation has a nonzero rank-sixteen minor. These results sharpen thegeometric and deformation tests, but do not construct the required curve/surface/Ueda package or establish all-ordersemiregularity.