History witness certificates 451–500

Exact checker for witnesses 451 through 500; nine tensor Bernstein coefficients each. Each witness carries a lower threshold, an upper threshold, a parameter rectangle and an array of Bernstein coefficients over that rectangle, together with a rational lower bound for every coefficient; validity asserts that the thresholds are correctly oriented, that the rectangle is nondegenerate and lies in the positive quadrant, that the recorded coefficients are exactly the Bernstein transform of the cross polynomial of the two thresholds over the rectangle, and that every coefficient dominates its recorded bound.

This is the sub-range $[450,500)$ of the platform node Freiman.lowerHistory_witnesses_0400_0500, split so that the exact rational verification fits inside a single compile.