Correct me if I am wrong The cholas alternated the Parakesari,Rajakesari titles after Parakesari and Rajakesari of the early cholas and called themselves Sembiyan as they were descendands of SIBI
My mail was comprising of the two view points of the learned ones w.r.t. the foreigner, who have conducted research in-situ. We will make effort and get their written opinion on this and try to put across.
Re Rajakesari & Parakesari, I am not competent to suggest anything absolute. You yourself are well-informed. There are only gaps - like Adithakarikalan - Rajakesari - succeeding Sundara - Rajakesari - paving way to Rajaraja - again Rajakesari. This was explained as "a Yuvaraja- designate (or would-be designate) might have been identified as Rajakesari.
I remember to have something to this effect in the History of Cholas, a collective works published before World Tamil Conference held in Tanjore.