I guess the best conversion of cosine similiarity to distance would of course be d(A,B) = arcCos(Cosine_similiarity(A,B)), i.e. the angle between the 2 directio

I guess the best conversion of cosine similiarity to distance would of course be d(A,B) = arcCos(Cosine_similiarity(A,B)), i.e. the angle between the 2 directions, which would have the property that subdividing a geodesic arc and calculating the sum of distances along the subdivision results in the same distance as the start and end point.