Diplomats from three continents say they've solved the five-month conundrum that has maintained the Middle East on a war footing. What they lack is an endorsement from the one whose voice really counts the green light: the one man.

Over the past few days, mediators from Pakistan, Egypt and Qatar have been hopping around the world, carrying a compromise proposal that would resolve a single issue that has kept a US-backed ceasefire deal from fully taking effect with Iran: the control of traffic in the Strait of Hormuz. Last month's memorandum of understanding has given Tehran a veto over the movement of ships through the waterway. Washington thinks in a different way than the document reads. That technical void, as it sounds, is why it was a deal that was signed with a lot of fanfare, and by mid-July, bombs were beginning to fly once again.

The two governments that do sit on the strait, Iran and Oman, have now signed the language that's supposed to fill that chasm. Donald Trump is sitting with the document in his hand. He is keeping it there intentionally, the sources say, until following his meet with Prime Minister Benjamin Netanyahu in his Oval Office, the first such face-to-face meeting between the two leaders since before the war started.

That sequence speaks for itself. Trump would not be in a position to give Netanyahu a done deal to respond to; he wants to listen to Netanyahu and then make a decision. It's a small courtesy, a sign of a greater and ever-growing reality both men acknowledge: they don't want the same Iran.

The conflict that broke out Feb 28 was supposed to result in the obliteration of Iran's nuclear and missile programmes. Rather, after 13 days of American strikes on Iranian assets in July alone, US Central Command (CENTCOM) quietly ended the bombing campaign last Friday not because Iran had capitulated, but because, as reported widely, the Pentagon had depleted its inventory of strike targets near Hormuz and become concerned about its dwindling supply of missile interceptors. Iran, in turn, has been silent as well, expressly on the agreement that Washington be silent as well. It is not a peace, but an exhaustion.

Netanyahu is coming to Washington with a different message. He is planning to present to Trump new intelligence that proves Iran's military and nuclear program is already regenerating under the new supreme leader, Mojtaba Khamenei, Israeli officials said. The unstated request is for the U.S. to get back on board and start fighting again. But Trump's own advisors have advised him to do the exact opposite, urging him not to strike further because doing that will drive Gulf allies away, run down his munitions reserves even more and, not least, cost Americans their money, in the form of energy prices, four months before the US midterms.

The last of that is where the diplomacy and the economics of this story just get tangled up. The Strait of Hormuz is the route for about a fifth of the world's seaborne oil trade and each major escalation this year has almost immediately appeared on the pump. The spring closing of the strait by Iran pushed Brent crude to over $114 a barrel and for a few weeks left United States gasoline markets in a frenzy. Crude rallied by about 8% in one week in a row during a resumption of fighting in mid-July while CENTCOM repeatedly stated the waterway was open under American protection. As word spread on Monday that Tehran was directly trying to ease tensions in the strait with Saudi Arabia and Oman, Brent edged back toward the $85 a barrel mark and West Texas intermediate had dropped below $82 a small but significant step that traders are taking as an early indicator that markets believe a deal is in the works, rather than a fourth round of war. Goldman Sachs has advised clients that if the Hormuz port is completely reopened for normal shipping operations, the price for Brent will probably finish in the vicinity of $80 by year's end, but flagged that attacks and strikes on Saudi infrastructure in the Red Sea remain a “wild card” that could push prices in the opposite direction.

There is also a broader regional context, one which has subtly shifted since the beginning of the war. Bahrain and Kuwait have also been conducting their own counter-strikes in recent days against targets that they consider to be Iranian-backed. Saudi Arabia, which has long shied at linking up with Israel too closely, now has interests toying with Jerusalem's on virtually every front: Iran, the Houthis in Yemen, Hezbollah in Lebanon. The newly inked civilian nuclear cooperation agreement between Washington and Riyadh, which Trump has now stated requires the kingdom to be a part of the Abraham Accords at some point, is also in play, right behind Tuesday's meeting, and is wrapped up in Netanyahu's efforts to salvage a normalization victory he so desperately sought before heading into an October election.

All this does not ensure that Tuesday will bring the breakthrough that the mediators see as attainable. Analysts who follow the talks point out the memorandum was not meant to settle the heart of the issue about Hormuz but only to give time for a more comprehensive negotiation, and the 60-day period in the memorandum will expire next month regardless of Trump's action this week. Last week a tanker was hit as recently as last week off the coast of Oman. Commercial traffic through the strait, which had started to pick up again after June's signing, continues to be far short of pre-war levels.

It's obvious that the balance has shifted in the room. It's Trump who's making the call on whether to approve a deal Iran and Oman already accept; it's Netanyahu who's trying to dissuade Trump. In July, that's a much tougher sell for an Israeli prime minister who was trying to convince an American president to go to war in February.