There are so many variations on the ninja’s kuji-kiri and kuji-in, huh? I believe people are hoping to find the “one and only authentic kuji system”, and they are confused by the differing deities and states assigned to the various mudra and cuts depending on where and from whom one learns the kuji.
This makes sense to me. Just like there are variations in all the martial art systems, so there are variations (sometimes radical) in the kuji systems. I think above all, regardless of system, it is necessary for one to absolutely believe in the power of kuji, unquestioningly, just as a Catholic believes in the power of making the cross or an Islamic believes in touching the 3 centers.
The 9 (actually 10…) “deities” associated with the kuji are in truth more accurately experienced as “states” or “experiences” or perceptions, personified as named deities. For example Fudo Myo-Oh is a symbol for kuji 1’s state of imperturbable physical, mental, and spiritual strength, as the antidote to what decreases those strengths. It is totally possible to link to that strength directly, without having to reference or identify with the character Fudo Myo-Oh. Though we usually do teach kuji 1 with a reference to Fudo and his sword and rope, it is more important to use the mudra to link to the actual state of strength.