Jain cosmology places its twenty four Tirthankaras across immense cycles of cosmic time, called utsarpini and avasarpini, each lasting far longer than recorded human history. Within this scheme, most scholars of Jainism treat only the twenty third Tirthankara, Parshvanatha, and the twenty fourth, Mahavira, as having any plausible claim to a datable historical existence, generally placed somewhere in the middle of the first millennium BCE or a little earlier.
Ajitanatha, second in the sequence, is set by the tradition in a vastly more remote age, and no evidence outside Jain religious literature itself exists to corroborate or date such a figure, which places him entirely within the internal chronology of the tradition rather than within any framework historians can independently test. This is not treated by Jain scholarship as a problem to be resolved, since the function of the earlier Tirthankaras within the tradition is primarily cosmological and doctrinal, establishing that the teaching of right conduct and liberation has been renewed across countless ages rather than originating only once, a claim that does not depend on external historical verification the way a claim about a specific datable person would. Ajitanatha's own biographical material beyond his name, emblem, and place in the succession is correspondingly thin.