As world leaders feted Qatar for brokering a truce between Israel and Hamas last week, its negotiators doubled down on their mediation efforts, fearful the ceasefire was about to collapse before it started. The tiny Gulf state's negotiators knew Israel and Hamas had yet to agree on when, or how, the ceasefire and the swap would begin, according to sources in Qatar, the Palestinian Territories and Egypt familiar with the high-stakes talks. It was necessary to clarify all the points in the agreement and make sure they meant the same thing to Israel and Hamas, a source briefed on the negotiations said.