My question is specifically to break the tie between an ethynyl group and a specific connectivity of cyclopentadienyl group where the chiral center is bonded to one of the sp2 carbons. I attached a picture of my analysis, which I am unsure about.
I do not know which one is higher priority. Specifically, it seems like I can go out in two directions on the ring. If I continue along the "winning" side of the ring, then the cyclopentadienyl group is higher priority than the ethynyl group because "something" should beat "nothing. If I go in the "losing direction" on the ring, then the alkyne would be higher priority. I don't know the logic of which direction I should be going.