At any rate, as his expedition against Menahem is followed within (at the utmost) thirty-two years by an expedition of Tiglath Pileser against Pekah, his last year (if he was indeed a king of Assyria) cannot have fallen earlier than thirty-two years before Tiglath-Pileser's first.

In other words, if the Hebrew numbers are historical some portion of Pul's reign must necessarily fill into the interval assigned by the Canon to the kings for which it is the sole authority--Shalmaneser III., Asshur-dayan III., and Asshur-lush.
But these names are so wholly unlike the name of Pul that no one of them can possibly be regarded as its equivalent, or even as the original from which it was corrupted.

Thus the Assyrian records do not merely omit Pul, but exclude him: and we have to inquire how this can be accounted for, and who the Biblical Pul is, if he is not a regular and recognized Assyrian monarch.
Various explanations of the difficulty have been suggested.

Some would regard Pul as a general of Tiglath-Pileser (or of some earlier Assyrian king), mistaken by the Jews for the actual monarch.

Others would identify him with Tiglath-Pileser himself.