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We approximate intersection numbers ψ d1 1 · · · ψ dn n g,n on Deligne-Mumford's moduli space M g,n of genus g stable complex curves with n marked points by certain closedform expressions in d 1 , . . . , d n . Conjecturally, these approximations become asymptotically exact uniformly in d i when g → ∞ and n remains bounded or grows slowly. In this note we prove a lower bound for the intersection numbers in terms of the above-mentioned approximating expressions multiplied by an explicit factordoi:10.3842/sigma.2020.086 fatcat:bkvse6kgnrc45hqn2g7y2wqonu