An Israeli tank brigade has seized control of the Gaza Strip side of the Rafah border crossing with Egypt, authorities say, moving forward with an offensive in the southern city even as cease-fire negotiations with Hamas remain on a knife’s edge. Israel, meanwhile, insisted the deal did not meet its core demands. The high-stakes diplomatic moves and military brinkmanship left a glimmer of hope alive — but only barely — for an accord that could bring at least a pause in the 7-month-old war that has devastated the Gaza Strip.