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[protocol spec] 4.17.2 (Spend statement): cm^old is not an auxiliary input
It's computed from other inputs.
Also Appendix A.4 says that $\mathsf{nk}$ needs to be on the curve, when it is already checked to be $[\mathsf{nsk}] \mathcal{H}$.
The same issue applies to the Orchard Action statement I think.