Defect-Two V4 Positivity for Powers of Ordinary Abelian Sixfolds

Let $A$ be an ordinary geometrically simple abelian sixfold over an algebraic closure of a finite field. Assume that the multiplicity of $A$ is $1$, that its Frobenius rank is $4$, and that the Galois image on the two-dimensional rational quotient of its Frobenius relation lattice is the Klein four-group $V_4$. We prove that every power of $A$ satisfies the standard conjecture of Hodge type. The proof is structural. The two one-dimensional characters of the $V_4$ relation representation occur in the embedding permutation module of the Frobenius field, so Frobenius reciprocity forces two imaginary quadratic subfields. After a finite extension of the field of definition, the corresponding relations become exact determinant norm relations. A $\bmod\ 2$ weight invariant excludes the unique nonsplit index-two integral over-lattice in dimension $6$. On the ordinary canonical CM lift, each determinant relation forces Weil signature $(3,3)$. A field-only computation of the Weil discriminant, together with an odd-degree discriminant-norm lemma, makes discriminant $-1$ attainable. Markman's algebraicity theorem for Weil classes on abelian sixfolds then supplies algebraic ownership of the two determinant motives. These motives form a full positive tensor generator, and Agugliaro's comparison of real fiber functors propagates positivity to every numerically nonzero simple Lefschetz block on every power. A general by-product is that in the multiplicity-one $V_4$ relation chamber of even dimension $g$, the unique nonsplit saturation coset has weight parity $g/2 \pmod 2$; hence $g \equiv 2 \pmod 4$ forces integral splitting. The paper does not treat primitive $C_4$ or $D_8$ rank-four relation types, nor the nonordinary case.