A cellular absolute motivic ring spectrum representing Hermitian K-theory

In the Morel-Voevodsky motivic stable homotopy category of a quasi-compact quasi-separated scheme S, several candidates exist for a motivic spectrum representing hermitian K-theory. This note shows that the cellular absolute motivic spectrum constructed in the thesis of the first author via the geometry of orthogonal and hyperbolic Grassmannians over any scheme coincides with the motivic ring spectrum constructed recently by Calmès, Harpaz, and Nardin.