Abstract: The anticocking high torque removal closure assembly comprises a container having a neck, a cap threadingly received on the neck, a first thread on the neck, a second thread in the cap, and a rib in the cap spaced from a revolution of the second thread and having a sharp outer edge. The first thread has an upper surface, a side surface and a lower surface, the second thread has an upper surface, a side surface and a lower surface.A first "allowable cock dimension" (ACD) is defined between a horizontal line through the junction of the side surface and the lower surface of the second thread and a horizontal line through the junction of the neck with the upper surface of the first thread when the cap is received on the neck. A second "minimum cock dimension" (MCD) is defined between a horizontal line through the sharp outer edge of the rib and a horizontal line through the junction between the side surface and the lower surface of the first thread when the cap is received on the neck.