How much slack does the simplest proof need? An Evidence Press briefing. Take a few symmetric matrices of the same size. Their commutators measure how far they are from commuting. The DDVV inequality says that the total size of all the commutators can never exceed the square of the total size of the matrices themselves, with constant one. It began as a conjecture about the curvature of submanifolds, curved shapes sitting inside spaces such as spheres, and it was proved in two thousand and eight. A theorem like this can sometimes be given a very checkable kind of proof: a sum of squares. If the gap between the two sides can be written as a sum of squared expressions, the gap is obviously never negative, and a computer can confirm the identity line by line. But since Hilbert we have known that a quantity can be nonnegative without being a sum of squares. So Ge, Li and Zhou asked whether the DDVV inequality has such a proof. This paper answers the question for the simplest kind of certificate, built from squares of quadratic expressions. It finds, for every matrix size and every number of matrices, the smallest constant for which such a proof exists. With exactly two matrices, or two by two matrices, the true constant one already works. Otherwise it does not: three by three matrices need nine eighths, and the required constant grows with the size and the number of matrices, approaching three but never reaching it. For Hermitian matrices, where the true constant is four thirds, the simplest proof works at four thirds only for two by two matrices, or for three matrices of size at most seven, and in general needs up to four. The proofs use symmetry to reduce every possible certificate to ten explicit squares, and exact computer arithmetic replays the identities and several independent certificates. Higher-degree certificates are not covered. This is an anonymous, AI-assisted, unrefereed candidate, published on the third of November twenty twenty-six; its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.