An end member for a container having a circumferential sidewall, the end member having a peripheral seaming edge adapted to be integrally connected to the sidewall, and having a central panel wall with a means for opening a frangible panel segment of the panel wall is claimed. The end member comprises a deboss panel recessed in the central panel. The deboss panel has first and second spaced apart end portions joined by first and second sidewalls. The first spaced apart end portion has an apex and first and second arcuate portions. A distance between the first and second arcuate portions is defined by a plurality of progressively increasing secant lengths located in spaced relation from the apex. A score groove is located within the deboss panel defining an outer perimeter of the frangible panel segment. The score groove has a first end and a second end joined to the first end by a curvilinear segment. The first end and the second end are separated by a generally linear hinge segment of the central panel wall. The curvilinear segment includes first and second curved segments joined by a transition point located adjacent the apex of the deboss panel. The generally arcuate transition region is defined by a plurality of progressively increasing chordal lengths located in spaced relation from the apex of the deboss panel. A ratio of the plurality of progressively increasing secant lengths to the progressively increasing chordal lengths increases along respective lengths of the first and second arcuate portions of the deboss panel.