theorem bhattacharyya_uniform_self {J : ℕ} (hJ : 0 < J) :
bhattacharyyaCoeff (symmetricShare J) (symmetricShare J) = 1 :=
fisherRaoDistance_self (symmetricShare J)
(fun _ => by simp [symmetricShare])
(symmetricShare_sum hJ)Information Geometry of CES: