rank 3: certificate verified exactly: 4 pairwise disjoint half-open dyadic boxes in [0,1)^1, total volume 1, each inside z+U+ for its z (36-form test per box: all 10 forms); 8 random/corner points re-tested from the statement (ii+).
rank 4: certificate verified exactly: 64 pairwise disjoint half-open dyadic boxes in [0,1)^3, total volume 1, each inside z+U+ for its z (36-form test per box: all 21 forms); 128 random/corner points re-tested from the statement (ii+).
rank 5: certificate verified exactly: 21484 pairwise disjoint half-open dyadic boxes in [0,1)^6, total volume 1, each inside z+U+ for its z (36-form test per box: all 36 forms); 42968 random/corner points re-tested from the statement (ii+).
rank 6 negative control: for L = 1..10 the requirement vector W of the dyadic box containing phi dominates floor(g(phi)); since {z integral : g(z) >= floor(g(phi))} is empty (Proposition 3.1), such a box is never accepted, as it must be.
