Cartesian-product slack matrices: complexity-six polygon products

For convex polygons $P,Q$ with $\operatorname{xc}(P)=\operatorname{xc}(Q)=6$,
the note proves $\operatorname{xc}(P\times Q)=12$ by a finite,
certificate-based support argument. Every such polygon has between six and
nine vertices. A hypothetical eleven-term nonnegative factorization of the
complete product slack matrix must satisfy explicit row-degree, vertex-slice,
edge-slice, pure-column and coverage conditions. These give ten Boolean
formulas, one for each unordered pair of polygon sizes, and each has a
deletion-free LRAT refutation, checked by separate Python and C++
implementations and by a hint-free unit-propagation check. Together with
proofs from the author's preceding notes, the result gives additivity for
every pair of polytopes with extension complexities at most six. The note
also gives an integer octagon of complexity six with an exact twelve-term
factorization of its square, and a higher-complexity support pattern that
admits no numerical weights.