The ichinomiya of Oki Province

What the Japanese sources say

Two shrines are treated as the ichinomiya of Oki Province: Mizuwakasu Jinja (水若酢神社) and Yurahime Jinja (由良比女神社). This is not a contest between rival claimants; the two divide the ground island by island.

Oki Province consists of two island groups separated by sea, Dōgo (島後) and Dōzen (島前). Mizuwakasu Jinja stands on Dōgo (Kōri, Okinoshima-chō) and Yurahime Jinja on Dōzen (Urago, Nishinoshima-chō).

For Mizuwakasu Jinja, Shimane Kankō Navi (the official tourism site of Shimane Prefecture) calls it “the ichinomiya of Oki” and says that the Engishiki (延喜式, a law code completed in 927 that lists the official shrines) has the entry “Mizuwakasu Jinja, myōjin tai”. For Yurahime Jinja, the Shimane Prefecture Shrine Agency says that “the Engishiki Jinmyōchō, the shrine register of that code, has it as Yurahime Daimyōjin of Junior Third Rank, Upper”, and that “at the end of the Heian period it was fixed as the ichinomiya of Oki Province”.

Dōgo also has, separately, Tamawakasumikoto Jinja (玉若酢命神社), the sōsha of Oki Province — a shrine where the deities of a whole province were worshipped together — so even within Dōgo the roles of ichinomiya and sōsha are divided between shrines.

Written from Japanese sources, each quoted. The Japanese page has the same discussion with the original wording.