structure EquivalenceStatement (J : ℕ) (F : AggFun J) where
/-- (i) → (ii): Fixed point implies power mean -/
fp_implies_pm : IsAggFixedPoint J F → IsPowerMean J F
/-- (ii) → (i): Power mean implies fixed point -/
pm_implies_fp : IsPowerMean J F → IsAggFixedPoint J FEmergence results from Paper 1, Sections 3-5: