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.

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.”

Leaders of Poland and Germany hail Péter Magyar’s majority as a turning of the tide – but analysts say there were other reasons for defeat of prime minister

For Poland’s Donald Tusk, the crushing defeat of Hungary’s illiberal prime minister, Viktor Orbán, after 16 years in office was evidence that the world was no longer “condemned to authoritarian and corrupt governments”.

Germany’s chancellor, Friedrich Merz, also believes the two-thirds majority secured by Orbán’s centre-right challenger, Péter Magyar, in Sunday’s elections was “a clear signal against rightwing populism” that showed “the pendulum is swinging back”.

The president’s attack on the head of the Catholic church and the AI depiction of himself as a Christ-like figure have not gone down well with one of the largest groups of swing voters in the US

Poor persecuted Donald Trump has frequently portrayed himself as a modern messiah. Some of his supporters, meanwhile, have compared him directly to Jesus. And, to be fair, while the son of God didn’t eat Big Macs on a private jet and encourage his followers to buy AI stocks, there are similarities between the two figures. Namely the miracle-working. The US president may not be able to turn water into wine, but he’s turned public office into a personal goldmine. This week, Trump also managed to transform a staunch atheist (me) into a defender of the Catholic church.

I’m not defending everything, mind you, just Pope Leo XIV’s recent condemnations of war. “God does not bless any conflict,” the pope wrote on X on Friday. “Anyone who is a disciple of Christ, the Prince of Peace, is never on the side of those who … drop bombs.” During Saturday prayers, the pope also called out the “delusion of omnipotence”. While Leo didn’t name names, his statements were widely interpreted as a rebuke of the Trump administration, which has repeatedly framed its warmongering in religious terms.

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.

Exclusive: Climate action blockers including Saudi Arabia, Russia and major fossil fuel firms set to make extra $234bn by end of 2026

• Middle East crisis – live updates

The world’s top 100 oil and gas companies banked more than $30m every hour in unearned profit in the first month of the US-Israeli war in Iran, according to exclusive analysis for the Guardian. Saudi Aramco, Gazprom and ExxonMobil are among the biggest beneficiaries of the bonanza, meaning key opponents of climate action continue to prosper.

The conflict pushed the price of oil to an average of $100 (£74) a barrel in March, leading to estimated windfall war profits for the month of $23bn for the companies. Oil and gas supplies will take months to return to pre-war levels and the companies will make $234bn by the end of the year if the oil price continues to average $100. The analysis uses data from a leading intelligence provider, Rystad Energy, analysed by Global Witness.

Scientists say finding is ‘very concerning’ as collapse would be catastrophic for Europe, Africa and the Americas

The critical Atlantic current system appears significantly more likely to collapse than previously thought after new research found that climate models predicting the biggest slowdown are the most realistic. Scientists called the new finding “very concerning” as a collapse would have catastrophic consequences for Europe, Africa and the Americas.

The Atlantic meridional overturning circulation (Amoc) is a major part of the global climate system and was already known to be at its weakest for 1,600 years as a result of the climate crisis. Scientists spotted warning signs of a tipping point in 2021 and know that the Amoc has collapsed in the Earth’s past.

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.

‘Palestine’s Mandela’ suffers three recent attacks including assault where prison guards set a dog on him, lawyer says

The jailed Palestinian leader Marwan Barghouti is at immediate risk in Israeli jails, where he has been attacked three times in as many weeks, including in one assault last month where prison guards set a dog on the 66-year-old, his lawyer has said.

Barghouti is often called Palestine’s Nelson Mandela. He is respected across otherwise feuding Palestinian factions, has broad popular support across occupied Palestine, repeatedly engaged with Israeli officials before his detention and long backed a two-state solution.