Your Tuesday Briefing

https://www.nytimes.com/2022/10/04/briefing/ukraine-advances-russia-nuclear-weapons.html

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Russian forces in Ukraine were on the run yesterday across a broad swath of the front line, as the Ukrainian military pressed on toward the city of Lysychansk and made gains in the south after its weekend capture of Lyman, a strategic rail hub. Any loss of territory in the Donbas region undermines Russia’s objectives, which focus on seizing and incorporating the region.

The Kremlin reflected the disarray of its forces on the ground, where territory was rapidly changing hands, acknowledging that it did not yet know what new borders Russia would claim in southern Ukraine. In Russia, nationwide turmoil and protests have erupted in response to the military conscription that has brought the war home to many Russians.

Events on the battlefield have threatened to make a mockery of Russia’s proclaimed annexations of four Ukrainian regions, as Ukrainians continued to recapture blasted, largely depopulated cities and towns from the retreating Russians. In the south, Ukrainian forces have pushed deeper into the Kherson region, in what a senior Ukrainian military official described as the beginning of the active phase of a monthslong offensive operation.

Pentagon response: Ukraine’s rapid retaking of territory in the northeast and the progress that its forces are making against Russian forces in the south represent a “stunning success,” a senior official said.

In other updates from the war:

Undersea explosions in the Baltic Sea have brought the war closer to Europeans, raising anxiety levels and threatening to undermine resolve to help Ukraine fight on.

Elon Musk, Tesla’s chief executive, has offered his own proposal for a peace deal to end the war, prompting a swift and dismissive response from Volodymyr Zelensky, the president of Ukraine.

For Vladimir Putin, the Russian president, the small nuclear weapons in Russia’s arsenal have proved better as weapons of terror and intimidation than as weapons of war. Analysts have come to doubt how useful these arms would be in advancing his objectives — especially as rendering parts of Ukraine uninhabitable could risk making Russia an international pariah.

Even a small nuclear explosion could cause thousands of deaths and render a base or a downtown area uninhabitable for years. Then there is the problem of prevailing winds: The radiation released by Russian weapons could easily blow back into Russian territory. And no matter the size of the blast, the radiation effects would be long-lasting.

Great secrecy surrounds Russia’s arsenal of tactical arms, which vary in size and power. The heavy warhead that fits atop an Iskander-M missile could reach cities in Western Europe. Russian figures put the smallest nuclear blast from the Iskander payload at roughly a third of the Hiroshima bomb’s explosive power.

History: In some respects, Putin is following the post-World War II playbook developed by the U.S., as it planned how to defend Germany and the rest of Europe against a large-scale Soviet invasion and the idea was to use the tactical weapons to slow an invasion force.

Britain’s economy faces many challenges: the effects of Brexit on investment and labor access; an overburdened National Heath Service; inflation at a 40-year high. Faced with big problems, Liz Truss, the British prime minister, and Kwasi Kwarteng, the new chancellor of the Exchequer, offered big solutions, with an economic proposal that was heavy on tax cuts and deregulation.

But after a backlash from investors, economists and Conservative Party members, Kwarteng has reversed one of the government’s proposals — abolishing the tax rate of 45 percent on the highest earners. That plan had drawn a lot of criticism, but proposals for other tax cuts worth tens of billions of pounds remain intact, as the government insists it is on the right path.

Many economists condemned the government’s plans as misguided amid high inflation and rising interest rates. In recent days, the opposition Labour Party has pulled far ahead in the polls, putting Truss’s leadership on shaky ground from the outset.

Cause and effect: The plan provoked a severe sell-off in British government bonds and a plunge in the value of the pound. The Bank of England had to step in to bring order to the markets, as the portfolios of pension funds teetered and mortgage lenders withdrew loans from bewildered borrowers.

North Korea fired a ballistic missile over Japan for the first time in five years, prompting the Japanese government to warn residents in two northern prefectures to seek shelter.

An independent commission in Indonesia will investigate the deaths of at least 125 people, including 33 children, at a soccer game on Saturday.

Sacheen Littlefeather, the Apache activist and actress who declined Marlon Brando’s Academy Award on his behalf in 1973, has died at 75.

A yearlong investigation found “systemic” abuse at all levels of American women’s soccer.

France’s justice minister was ordered to stand trial in a conflict-of-interest case, a first for a sitting justice minister.

Oil prices jumped yesterday after news that OPEC Plus might cut production. The move would reverse increases that had pushed prices down.

Svante Pääbo, the Swedish geneticist who sequenced the Neanderthal genome, won the Nobel Prize in Physiology or Medicine.

Kim Kardashian will pay $1.26 million after failing to disclose that she had been paid to promote a crypto product.

A fishing contest in Ohio has been rocked by scandal after contestants were accused of trying to make fish they caught heavier.

With high property prices and a large population, Tokyo has long been known for small accommodations. But the 95-square-foot apartments that have become popular with the city’s young people are pushing the boundaries of normal living.

One benefit of small living, one resident says, is less ice cream. There simply isn’t the space for a working freezer.

Ten months after Paris St. Germain’s Kheira Hamraoui was beaten with an iron bar: There is shock and disgust as Hamraoui’s former P.S.G. teammate Aminata Diallo has been charged, and a police investigation is ongoing. There will surely be more twists in this extraordinary story.

Brazil, France, Argentina favored to win the World Cup: Brazil remains the favorite to win the World Cup, but Argentina is on the rise, while England has dropped in the odds.

What Chelsea would get with Nkunku: Delayed finishes, clever runs and a surprising number of headed goals. Christopher Nkunku is hugely talented, so Chelsea needs to get the most from him. Here’s an inside look at a significant transfer.

Two years after the police killing of George Floyd sparked global protests against police brutality, cop shows seem as popular as ever: In the U.S., 18 crime-related programs are slated for prime-time slots on the major broadcast networks, and three of the five most-viewed scripted network shows last season featured law enforcement.

But beneath the surface, there are signs that the genre has been evolving. A new wave of crime shows aims to explore the world of law enforcement in a more nuanced way, attempting to answer calls for reform — of both policing and television’s depictions of it — without losing the viewers that have kept them so popular, Marc Tracy writes for The Times.

“They do address these things now,” said George Pelecanos, the detective novelist who has written for HBO crime shows, including “The Wire” and “We Own This City.” “But it’s all in the context of episodic television: We have a cop who plants evidence or is abusive, but by the end of the hour that guy’s going to get kicked off the force. It was one bad apple.”

For more: On the 20th anniversary of “The Wire,” why the celebrated crime drama series stands alone.

These meatless polpette pair perfectly with pasta.

A new Anthony Bourdain biography is light on subtlety and heavy on grit.

Bjork’s 10th studio album can be heavy going. But it’s well worth an effort, our critic writes.

Here’s today’s Mini Crossword, and a clue: Damage (four letters).

And here are today’s Wordle and the Spelling Bee.

You can find all our puzzles here.

That’s it for today’s briefing. Thanks for joining me. — Natasha

P.S. The Times won five News and Documentary Emmys this week, for work across News and Opinion.

The latest episode of “The Daily” is on Latino voters in the U.S.

You can reach Natasha and the team at briefing@nytimes.com.