Every coordinate slice of every generic Christoffel symbol of Kerr is differentiable, with the closed-form derivative

For all real $M,a$, every point $x$ of the regular domain and all indices $l,i,j,k\in\{0,1,2,3\}$, the slice

of the generic Christoffel symbol christoffel (gKerr M a) (giKerr M a) i j k along coordinate $l$ has, at $u=x_l$, the derivative dGammaKerr M a l i j k evaluated at the atoms of $x$, in the sense of HasDerivAt.

This is the second differentiability certification of Layer II. It concerns the generic object, not the closed form, so that the second derivatives entering the Ricci formula are genuine derivatives of the Christoffel symbols defined in the specification layer. The pd-valued companion is pdchrKerr_all.