extended_proof< ppT, snarkT > prove(const Field &root, const std::array< joinsplit_input< Field, TreeDepth >, NumInputs > &inputs, const std::array< zeth_note, NumOutputs > &outputs, const bits64 &vpub_in, const bits64 &vpub_out, const bits256 &h_sig_in, const bits256 &phi_in, const typename snarkT::proving_key &proving_key, std::vector< Field > &out_public_data) const