# Verification of the Hadamard certificate

The six-page English manuscript specifies every rational polynomial
multiplier as a finite sum. Summing the leaf identities gives the literal
identity 1 = A_L L + sum_d A_d s_d + sum_i Q_i q_i.

Exact checks completed:

- All 262144 compressed rows were checked; exactly 36 survive.
- All 78732 lifts were checked; none is a common zero.
- A second sign-mask implementation agrees with every fine residual count.
- All 32 local and generic polynomial identities pass exact rational expansion.
- Normal Python and Python -O reports are identical.
- The paper contains a standalone complete finite check in Appendix A.

The source package also includes the written algebraic proof, the source and
novelty review and the programs. The finite calculation is exhaustive; random
substitution is not used as proof of a polynomial identity. The degree bound
29 is an upper bound and is not asserted optimal.

This is an originating-researcher self-audit, not external independent review
or formal proof-assistant certification. AI assistance is disclosed in the
body of the manuscript. The nonexistence theorem is classical. Only the
explicit certificate challenge is answered; the other questions concatenated
in the dataset record are not answered.