I dunno. Even in some fairly math-y situations, line solving sparse linear systems, we get stuff like BiCGStab which often will work well and converge in cases

I dunno. Even in some fairly math-y situations, line solving sparse linear systems, we get stuff like BiCGStab which often will work well and converge in cases where we can’t prove that it must. CS seems mostly good for proving that everything is hopeless in the rigorous general case and, hey, here are some heuristics to give you hope again.