What is the ruling if the third-party possessor admits ownership to both claimants?

Primary text

If the possessor acknowledges ownership to both claimants, the matter is treated as if the item was in their joint possession from the outset. Each claimant is required to swear to the other concerning the half judged in favor of that other claimant, and similarly, each must swear to the other regarding the half judged in their own favor, implying division of the item or its value between them.