The present invention relates to a tube closure assembly. The assembly includes a tube head that includes a neck and a closure liner sealing said neck, and a cap that includes a punch provided with at least one tooth. The one or more teeth are configured to peripherally cut said closure liner. The cap is configured to transition from an open flush position, in which the one or more teeth are flush with said closure liner, to a perforation position, in which the one or more teeth perforate the closure liner, then from the perforation position to an end-of-travel position allowing partial cutting of the closure liner, the transition from the perforation position to the end-of-travel position being carried out with an angular rotational range below 360°.