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Donald Trump has announced a 10-day ceasefire in Lebanon, to be followed by a meeting between Israeli and Lebanese leaders next week, a deal that it is hoped will bring progress toward a parallel peace agreement between the US and Iran.

The ceasefire took effect at midnight local time in Lebanon, where Israel had been conducting devastating airstrikes aimed at wiping out the Iranian-backed Hezbollah militia.

Trump said on social media that the truce was agreed after he held separate “excellent conversations” with Lebanon’s president, Joseph Aoun, and the Israeli prime minister, Benjamin Netanyahu, yesterday.

Netanyahu said the ceasefire offered an opportunity for a “historic peace agreement” but insisted that the disarmament of Hezbollah remained a precondition.

• What has Lebanon said? The Lebanese army warned people displaced from southern Lebanon about returning home because of intermittent shelling that was reported after the ceasefire came into effect.

• This is a developing story. Follow the liveblog here.

Newly unsealed records reveal Amazon’s price-fixing tactics, California attorney general claims

Hundreds of previously redacted records reveal how Amazon has put pressure on independent sellers on its platform to raise their prices on the sites of competitors such as Walmart and Target so that Amazon can appear to have lower prices, California authorities allege.

Amazon became concerned if a competitor was selling an item for even a penny less, according to one segment of the newly unredacted evidence.

The documents, which have never previously been reported on, include internal emails, deposition testimony and confidential corporate presentations that the California attorney general, Rob Bonta, obtained as part of a civil case his office launched in 2022 accusing Amazon of large-scale price fixing.

• What has Amazon said? It has called the claims in the lawsuit “entirely false and misguided”. The company said in a statement: “Amazon is consistently identified as America’s lowest-priced online retailer, and it is ironic that the attorney general seeks to have us feature higher prices in ways that would harm consumers and competition.”

D4vd arrested on suspicion of killing teen girl whose body was found in his Tesla

The R&B singer D4vd has been arrested in connection with the killing of a teenage girl whose severely decomposed body was found in his Tesla, Los Angeles police said on Thursday.

The 21-year-old musician, who was born David Anthony Burke, is being held without bail, according to city authorities.

In September, LAPD detectives were called to a tow yard in Hollywood after receiving reports of a foul odor emitting from an impounded car that was registered to Burke. The car had been towed from the Hollywood Hills after appearing to be abandoned.

Authorities found a dismembered body that was later identified as 14-year-old Celeste Rivas Hernandez. She had been reported missing in 2024 and had last been seen in Lake Elsinore, approximately 60 miles south-east of downtown Los Angeles.

• What has D4vd said? In a statement, the singer’s legal team maintained his innocence. “There has been no indictment returned by any grand jury in this case and no criminal complaint filed. David has only been detained under suspicion,” the lawyers said. “The actual evidence in this case will show that David Burke did not murder Celeste Rivas Hernandez and he was not the cause of her death.”

In other news …

• Donald Trump has selected Erica Schwartz to lead the Centers for Disease Control and Prevention (CDC), bringing to an end a months-long search for a permanent head of the troubled public health agency.

• Todd Lyons, the acting director of US Immigration and Customs Enforcement (ICE), is stepping down after a turbulent year carrying out Trump’s immigration agenda.

• The Democrat Analilia Mejia won a New Jersey special election for the US House yesterday, defeating the Republican Joe Hathaway on a message of standing up to Trump.

Stat of the day: 42% of young men say religion is very important to them – compared with 30% of women

Young men are now more likely than young women in the US to say religion plays a major role in their lives, according to findings from Gallup. Data covering 2024-25 indicates that 42% of men aged 18 to 29 describe religion as very important to them, a significant rise from 28% in 2022-23. Young women’s responses have remained largely unchanged over the same period, holding at roughly 30%.

Culture pick: Why do we love to believe cinema’s best lines were improvised?

From The Godfather to Saltburn, the internet is awash with claims that actors are ditching the script and making it up as they go along. What’s behind our desire to invest in these behind-the-scenes “secrets”?

Don’t miss this: Pop star boyfriend posting from Coachella, celebrity statesman, global brand – Justin Trudeau’s offbeat political afterlife

Justin Trudeau’s post-political life has taken an unusually high-profile turn, with the former Canadian prime minister recently commenting on Hungary’s election while attending Coachella with his girlfriend, Katy Perry. The tonal contrast hinted at the challenge facing Trudeau: how to shape a political legacy and decide the extent to which he wants to remain public spectacle.

Climate check: Colombia convenes climate ‘coalition of the willing’ to break global fossil fuel deadlock

Everybody knows fossil fuels drive climate breakdown, yet until recently they were largely absent from UN climate summit outcomes. Frustrated by this, Colombia has teamed up with the Netherlands to host a conference to begin a “transition away from fossil fuels” – a move that looks increasingly prescient amid rising fuel prices linked to global conflict.

Last Thing: Hegseth channels his inner Tarantino with fake Bible verse from Pulp Fiction

This week Pete Hegseth, the US defense secretary, recited what he said was a Bible passage at a Pentagon prayer session. But film buffs quickly noted it closely resembled a monologue from a Quentin Tarantino film. Delivering a prayer for search-and-rescue crews that he said was based on Ezekiel 25:17, Hegseth used wording far closer to Samuel L Jackson’s speech in Pulp Fiction.

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