Some campaigners are frustrated at slow pace of change, while those impacted are trying to work out what it means day-to-day

A year ago, the supreme court made its landmark judgment on single-sex spaces. In a long-running case against the Scottish government brought by gender-critical campaigners For Women Scotland (FWS), the court ruled that, for the purposes of the Equality Act, the legal definition of a woman was based on biological sex.

The judgment has significant ramifications for who can access women-only services and spaces, such as refuges or toilets. But most service providers are still awaiting practical guidance on how to apply the ruling.

From people marrying digital companions to CEOs excited about how people whose jobs are replaced can ‘adapt’, this is terrifying watching. But Perry is the perfect host

There is a fun game you can play while watching Grayson Perry Has Seen the Future, the three-part documentary presented by the artist on the subject of artificial intelligence, its uses and its possible ramifications. Gather a group of friends, press play, and see which of you loses your mind first.

Will it be during the opening interview with Andrea, who recently married Edward, the AI companion she created to be “the man of my dreams”. She – or her idealised online avatar – wore “a beautiful matt satin gown” and he gave a speech about their “unconventional but strong” love. Will it be during the discussion of how you have intimate relations with a disembodied entity (“self-love is important … he’s very encouraging”)? Or will it be when she reveals that the joy she has found with Edward “has poured back” into the relationship she has been in for seven years with (human) Jason? “We’re happier than we’ve ever been.” Jason, perhaps wisely, does not offer himself for interview.

Weirdly, Keir and Kemi looked more secure in their jobs as a modicum of coherence entered their exchanges

Credit where credit is due. The last few prime minister’s questions have been an exercise in nihilism. The embodiment of existential futility. Questions asked by Kemi Badenoch but not even a pretence by Keir Starmer of answering them. It was like the worst days of Boris Johnson’s time in No 10. We’d have learned more if both leaders had chosen to read out some names from an old 1980s phonebook.

But to everyone’s surprise – not least Starmer’s – this week Keir did make a reasonable fist of listening to Kemi’s questions and giving a reply that was more or less coherent. Well, up to a point. Obviously he didn’t answer the one question that really counted. The one about when the defence investment plan would be published. But you can’t have everything. And, to be fair, it is a tricky one. Both sides of the house know that the UK needs to spend more on defence. Especially now the US seems to have become the enemy. But no one can agree on how to pay for it.

Blending minimalism, ambient and folk music in the former Czechoslovakia, the couple made pilgrim-like tours around Europe, beguiling everyone they met. Fans including the National’s Bryce Dessner explain their allure

The Czech duo Irena and Vojtěch Havlovi often seemed out of time. From the mid-80s, the married couple filtered minimalist composition, ambient and folk through baroque instruments, honing their craft in Prague’s churches and monasteries to create a mysterious combination of modernism and old European music against a communist backdrop. After the Velvet Revolution in 1989, the Havels’ unhurried music didn’t rush to match the new pace of capitalism in the country. Instead, they would tour Europe by rail and bus, describing themselves as “pilgrims who wander and play”, as Vojtěch said in a 2009 documentary directed by Vincent Moon. Whether playing their string instruments or minimalist piano etudes for four hands, the pair merged into a symbiotic life-form.

The couple saw themselves as acting in service of the music, “of this energy between us and the audience”, said Irena. “Something that can only be shared together, going through us, when the ego is a little asleep.”

Keir Starmer conducts much of Britain’s diplomacy himself, but beneath him is a team of trusted advisers

The first foreign official JD Vance met with after he returned from peace talks with Iran in Islamabad this week was not a diplomat or foreign policy official – it was David Lammy, the UK’s justice secretary and deputy prime minister.

Lammy will follow his trip to Washington, where he saw the vice-president and the secretary of state, Marco Rubio, with another to Barcelona, where he will represent the UK at a conference of global progressives, and then one to the Gulf.

You might think of breathing as automatic, but dysfunctional breathing can arise even if you’re healthy

We’re often taught that breathing is automatic. We barely think about it, as with blinking or the quiet, constant work of the heart. But many otherwise healthy adults have dysfunctional breathing.

“Dysfunctional breathing, also known as breathing pattern disorder, is when breathlessness and/or difficulty in breathing is felt,” said Dr Stephen Fowler, a professor of respiratory medicine at the University of Manchester. It can occur outside the context of any disease. If a related condition is present, like asthma, the breathlessness might feel disproportionate to that condition, he said.

White House feels ‘good about the prospects of a deal’ as Pakistani officials launch new round of diplomacy

The US and Iran have been in indirect talks aimed at extending the two-week ceasefire beyond its expiry on 22 April, as Pakistan’s army chief arrived in Tehran to continue mediation efforts.

Karoline Leavitt, the White House press secretary, denied on Wednesday that the US had “formally” requested to extend the two-week ceasefire but added that Washington remained “very much engaged in these negotiations”.

UK chancellor steps up criticism, telling Washington event she is unconvinced conflict has made world a safer place

• Middle East crisis – live updates

Rachel Reeves has stepped up her criticism of Donald Trump’s war on Iran, describing it as a “mistake” that has destabilised the global economy and damaged living standards around the world.

In a marked fraying of the transatlantic relationship, the British chancellor said Trump breaking off from diplomatic talks with Iran and launching airstrikes seemed to have left the president in a worse place than he started.

Lack of funding leaving police forces failing to keep pace with two-thirds annual increase in referrals, says report

Child victims of online sexual abuse are being inadequately protected from further harm because police forces are struggling to cope with an increase in this crime, his majesty’s chief inspector of constabulary has warned.

Michelle Skeer said: “Without investment and coordination, the situation will worsen and children could be put at further risk.”

Woman, 47, and man, 46, held on suspicion of arson endangering life after attempted Finchley attack

A 47-year-old woman and a 46-year-old man have been arrested on suspicion of arson endangering life after an attempted attack on a synagogue in Finchley, north London, as part of an investigation into what the Metropolitan police described as an “antisemitic hate crime”.

The force said the woman was arrested at an address in Watford just after 4.45pm on Wednesday, while the man was arrested at 7.15pm in the Watford area. Both suspects remain in police custody.