Testing the Factuality of the Conquest of Ai Narrative in the Book of Joshua

Summary of the problem. The gamut of views concerning the conquest of Ai narrative in the 7th and 8th chapters of the Book of Joshua can be summarized as follows: the narrative is factual, having the weight of eye witness testimony; or, it is an aetiological legend, compiled long after the fact, either just before or during the Babylonian exile for the purpose of justifying Israel’s presence in the land of Canaan; or, it is a pernicious myth, deceptively and skillfully fabricated to correspond with the material time-space context in which it is alleged to have occurred. Is there a method that is capable of objectively arbitrating among these three views?