  We show that the hermitian K-theory space of a commutative ring R can be
identified, up to A^1-homotopy, with the group completion of the groupoid of
oriented finite Gorenstein R-algebras, i.e., finite locally free R-algebras
with trivialized dualizing sheaf. We deduce that hermitian K-theory is
universal among generalized motivic cohomology theories with transfers along
oriented finite Gorenstein morphisms. As an application, we obtain a Hilbert
scheme model for hermitian K-theory as a motivic space. We also give an
application to computational complexity: we prove that 1-generic minimal border
rank tensors degenerate to the big Coppersmith-Winograd tensor.
