An Explicit Nullstellensatz Certificate for the Seventh Hadamard Ideal

The nonexistence of a Hadamard matrix of order 28 with one circulant core is classical. A separate AIM workshop challenge asks for an explicit polynomial combination of the 41 generators of the seventh Hadamard ideal that equals one. We give this combination over the rationals in factored finite-sum form, with total degree at most 29. Compression from length 27 to length 9 leaves 36 compressed rows and 78732 Boolean lifts. Boolean projectors and ordered polynomial differences convert the exhaustive finite computation into explicit multipliers for the original generators, using 340840 leaf identities. The package includes integer enumeration, exact symbolic identity checks and a separate bit-mask replay. The contribution is the explicit reproducible certificate, not a new Hadamard nonexistence theorem, a new general Nullstellensatz method or a claim of optimal degree. The other workshop questions concatenated in AIM-COMPUTATION-0052, including the contingency-table cell-spectrum question, are not resolved. This is a self-audited, AI-assisted, unrefereed preprint.