This week has seen renewed hope for ending the war in Iran, 10 weeks since it started, with four weeks of stalemate, a ceasefire and skirmishes over the blockade of the Strait of Hormuz. Intermittent peace talks have boiled down to a 14-point, one-page "memorandum of understanding", crafted by Steve Witkoff and Jared Kushner, which has been sent to Pakistani mediators and is being reviewed by Tehran.

If agreed, the conflict would be declared over, with a 30-day window for talks on core issues, namely Iran's nuclear programme, the Strait of Hormuz and sanctions relief for the regime.

It's been a week of headline hell for Britain's Prime Minister Keir Starmer. Having survived recurring controversies including the Mandelson affair, but headed into UK local elections with his approval ratings in nosedive, he's picking up nicknames faster than his beloved Arsenal are points. "Captain Hindsight", "Sir Flip Flop", say the opposition. And while Arsenal enjoy their place at the top of the table – set to win the Premier League for the first time in two decades – Starmer's popularity ratings are in the relegation zone. After a dismal election performance and the success of the populist Reform UK party, there's talk of a Labour plot to oust him before the next elections.

Finally, it's been the second week of the OpenAI trial: a case brought by Elon Musk claiming OpenAI breached its founding principles. This week, the mother of four of Musk's children, Shivon Zilis, took the stand – both about what was going on at OpenAI, but also about her and Musk's personal relationship. 

Produced by Gavin Lee, Théo Vareille, Daniel Whittington, Alessandro Xenos.