An imperceptible incorrectness in deriving data consistency condition from John's equation for cone-beam CT imaging

A John's equation-based consistency condition (JECC) and restoration of corrupted projection had ever been proposed for the circular trajectory cone beam CT (CBCT) imaging. They attempted to derive the so-called JECC, i.e., a data consistency condition (DCC) from John's equation. Unfortunately, there is an imperceptible incorrectness in their derivation, which is disproved here by following the line of their thought. The basic cause leading to the imperceptible incorrectness is that John's equation was incorrectly applied to a characteristic manifold.