After 15 months of bombardment and suffering, the prospect of a cease-fire and a hostage release deal in Gaza provides Palestinians and Israelis with a glimmer of jubilation, but it’s a view tinged with uncertainty.

For Palestinians, the agreement, if it is finalized, is likely to offer at least several weeks of respite from a devastating Israeli military campaign that has killed more than 45,000 people in Gaza, both civilians and combatants.

For Israelis, it could allow for the release of at least one-third of the remaining hostages held by Hamas and its allies. The captives were taken when Hamas raided Israel on Oct. 7, 2023, the first of 466 days of war.

But the ambiguity of the deal, drafts of which were reviewed by The New York Times, also means lingering unease and the possibility of renewed conflict within weeks. To persuade both sides to sign on, mediators forged an arrangement that is worded so loosely that some of its components remain unresolved, meaning that it could easily collapse.

In the first six weeks of the deal, Hamas is expected to release 33 hostages in exchange for several hundred Palestinian prisoners held by Israel. Israel is also meant to gradually withdraw its troops eastward, allowing for hundreds of thousands of displaced Palestinians to return home.

For the deal to last longer than six weeks, Israel and Hamas still need to resolve certain issues, including the terms by which Hamas will release the approximately 65 other hostages, some of whom are believed to be dead, in its custody. To prolong the truce, both sides would also need to agree to end the war entirely, while Israel would need to withdraw from strategic areas of Gaza — moves that are opposed by key members of Israel’s ruling coalition.

Should those talks break down, the war could continue after a 42-day truce, if not earlier.

That means the coming weeks will remain fraught for the families of the Israeli hostages who will likely not be released in the deal’s first phase. Gazans will live with the possibility that Israel’s strikes could continue.

This precarity also presents potential peril for both Hamas and Benjamin Netanyahu, Israel’s prime minister.

If war resumes, a severely weakened Hamas might finally lose its grip on Gaza. But if the deal becomes permanent, Hamas would have a greater chance of retaining power in the territory — a symbolic victory for a group that at one point seemed close to ceding its 17-year rule.

An outcome that leaves Hamas in control could prove damaging to Mr. Netanyahu, whose far-right coalition partners have threatened to leave his coalition if Hamas survives, a departure that would destabilize and potentially collapse his government.

For months, Mr. Netanyahu has avoided an arrangement that would risk such a threat to his power. The ambiguity of the deal is partly the result of his need to present it as only a temporary arrangement.

The coming weeks could help clarify whether the prime minister feels politically strong enough to face down his coalition partners. Even if he does, other shoals await: The end of the war will likely lead to a national inquiry about Israel’s security failures on Oct. 7, 2023, possibly uncovering revelations that could damage Mr. Netanyahu as well as his security chiefs.

Despite these uncertainties, analysts say, the deal still stands a reasonable chance of becoming permanent. The loose language of the agreement would allow the cease-fire to drag on as long as the two sides remain locked in negotiations, even if those negotiations take longer than six weeks to reach further agreement.

And both sides have reasons to keep extending the negotiations, however fruitless the talks.

Hamas, isolated and weakened, wants to remain dominant in Gaza, and a cease-fire allows it time to recuperate.

Mr. Netanyahu has long hoped to forge landmark diplomatic ties with Saudi Arabia. Negotiations for such a deal, which were derailed by the outbreak of war in 2023, would likely only resume if the truce holds.

A Saudi-Israel deal “can’t happen with an ongoing war in Gaza, with large numbers of Palestinian casualties, Hamas holding Israeli hostages and a worsening humanitarian catastrophe,” said Aaron David Miller, a fellow at the Carnegie Endowment for International Peace, a Washington-based research group.

Similarly, a large protest movement in Israel is pushing Mr. Netanyahu to extend the deal in order to release every hostage; such public pressure could ultimately drown out any backlash he faces for ending the war. The euphoria and celebration that is expected to accompany each hostage release may also accelerate momentum and public support in Israel for a permanent arrangement that leads to freedom for every captive.

The role of the Trump administration will also be crucial. Mr. Trump’s Middle East envoy, Steve Witkoff, played a key role in recent days in pushing Israel toward a deal, officials say, and the administration’s continued interest may decide how long the deal lasts.

“Trump is going to be the critical variable when it comes to the Israeli side,” said Michael Koplow, an analyst at Israel Policy Forum, a New York-based research group.

“If Trump is happy with having orchestrated the first phase and then moves on to other issues, it will be harder to keep the cease-fire in place,” Mr. Koplow said.

If Mr. Trump retains his focus, “it will be tougher for Netanyahu not to find ways to extend the cease-fire deal and figure out other ways to appease his disgruntled coalition members,” Mr. Koplow added.

Johnatan Reiss contributed reporting from Tel Aviv.

Jair Bolsonaro has had a rough couple of years: election losses, criminal cases, questionable embassy sleepovers. So when he finally received a piece of good news last week — an invitation to President-elect Donald J. Trump’s inauguration — it lifted his spirits.

“I’m feeling like a kid again with Trump’s invite. I’m fired up. I’m not even taking Viagra anymore,” the former Brazilian president said in an interview on Tuesday, employing his trademark sophomoric humor. “Trump’s gesture is something to be proud of, right? Who’s Trump? The most important guy in the world.”

But reality has a way of spoiling plans.

Brazil’s Supreme Court has confiscated Mr. Bolsonaro’s passport as part of an investigation into whether he tried to stage a coup after losing re-election in 2022. To attend Monday’s inauguration, Mr. Bolsonaro has had to request permission from a Supreme Court justice who is also his political nemesis.

On Wednesday, Brazil’s attorney general recommended that his request be rejected. Mr. Bolsonaro admitted he would likely be watching from home.

That likely split screen — Mr. Trump returning to the world’s most powerful job while Mr. Bolsonaro stays home on court orders — would encapsulate the two political doppelgängers’ starkly divergent paths since they were voted out of office and then claimed fraud.

In 2025, Mr. Trump will head to the White House — and Mr. Bolsonaro could be headed to prison.

Three separate criminal investigations are closing in on Mr. Bolsonaro, and there are widespread expectations in Brazil — including from Mr. Bolsonaro himself — that he could soon be at the center of one of the highest-profile trials in Brazil’s history.

“I’m being watched all the time,” Mr. Bolsonaro, 69, said in the lively 90-minute interview, in which he aired grievances, repeated conspiracy theories and confessed his anxiety about his future. “I think the system doesn’t want me locked up; it wants me eliminated.”

But developments in the United States have given Mr. Bolsonaro new hope. Mr. Trump, Elon Musk and Mark Zuckerberg are leading a global push for free speech, he said, and he hopes that could somehow transform the political landscape in Brazil. “Social networks decide elections,” he said.

For years, Mr. Bolsonaro has accused a Brazilian Supreme Court justice, Alexandre de Moraes, of censoring conservative voices and politically persecuting him. Justice Moraes has indeed become one of the most aggressive policemen of the internet in a democracy, ordering social networks to block at least 340 accounts in Brazil since 2020, and often keeping his reasons under seal.

That led to a clash with Mr. Musk last year, resulting in the judge’s ban on Mr. Musk’s social network, X, in Brazil. Mr. Musk eventually backed down. But the dispute drew global attention to Mr. Bolsonaro’s complaints about Brazil’s Supreme Court.

So Mr. Bolsonaro said he was delighted last week when Mr. Zuckerberg said his company would “work with President Trump to push back against” foreign governments that want to “censor more.” One of his main examples were “secret courts” in Latin America “that can order companies to quietly take things down.”

Brazilian officials took that as a shot across the bow. The next day, Justice Moraes warned that social networks could only operate in Brazil if they follow Brazilian law, “regardless of the bravado of big tech executives.”

Mr. Bolsonaro had a different view. “I’m liking Zuckerberg,” he said. “Welcome to the world of good people, of freedom.”

How exactly will Mr. Trump and the tech executives affect his many legal and political challenges? Mr. Bolsonaro was vague. “I’m not going to try to give Trump any tips, ever,” he said. “But I hope his politics really spill over into Brazil.”

Elizabeth Bagley, the outgoing U.S. ambassador to Brazil, said Mr. Bolsonaro’s wish that the United States could come to his rescue is far-fetched. The U.S. government does not interfere with another country’s judicial process, she said.

Mr. Bolsonaro has bigger problems than censorship. Over the past year, Brazil’s federal police has formally accused him of crimes in three separate cases.

In one, the police said Mr. Bolsonaro took money from the sale of jewelry he received as state gifts, including a diamond Rolex watch from the Saudis that his aide later sold at a Pennsylvania mall. Mr. Bolsonaro blamed the situation on unclear rules around who owned such gifts.

In a second, the police said he participated in a plot to falsify his Covid-19 vaccination records so he could travel to the United States. Mr. Bolsonaro said he did not receive the vaccine, but denied knowing of efforts to fake his records.

And in the most grave accusation, the police said Mr. Bolsonaro “planned, acted in, and had direct and effective control over” a conspiracy to carry out a coup.

The federal police recently released two reports, totaling 1,105 pages, that detailed its accusations, including that he personally edited a decree for a national state of emergency designed to prevent the election’s winner, President Luiz Inácio Lula da Silva, from taking office.

Mr. Bolsonaro abandoned the plan after he pitched three leaders of Brazil’s military and two refused to take part, the police said.

In the interview, Mr. Bolsonaro vehemently denied any coup plot — he handed over power after all, he said — but he did admit having discussed the decree. “I won’t deny it to you,” he said. “But in the second conversation it was given up.”

He said he considered a state of emergency because he believed the election had been stolen, but Justice Moraes had blocked his party’s request to overturn the results. Then his team realized Congress would have to approve the measure, too. “Forget it,” he said. “We lost.”

Yet the police said there was a far darker plan at the center of the conspiracy: assassinating Mr. Lula, his running mate and Justice Moraes. The police have arrested five men whom they accuse of planning to carry out the assassinations, four of them from an elite Brazilian military unit.

The men, the police said, deployed to Justice Moraes’s neighborhood several weeks before Mr. Lula’s inauguration. They were prepared to kidnap the judge but abandoned the plot after Mr. Bolsonaro did not declare the state of emergency, the police said.

The police said Mr. Bolsonaro was aware of the plan. The closest link the police disclosed was that the plan had been printed at the presidential offices and later taken to the presidential residence.

Mr. Bolsonaro denied he knew anything about such a plot. “Whoever made this possible plan should respond,” he said. “On my part, there was no attempt to execute three authorities.”

He then downplayed the accusations. “Even so, I think it was just another fantasy — bravado. Nothing. This plan is unfeasible. Impossible,” he said. He admitted he knew the accused leader of the plot. “Everyone is responsible for their actions,” he said. “Although, as far as I know, he did not take any action.”

Brazil’s attorney general is weighing whether to indict the former president, which would likely lead to a high-profile trial this year and a potential prison sentence.

While maintaining his innocence, Mr. Bolsonaro admitted he worried about his freedom because Justice Moraes could help convict him. “I’m not worried about being judged,” he said. “My worry is who will judge me.” After police confiscated his passport last year, he slept for two nights at the Hungarian embassy in an apparent bid for asylum.

Brazil’s courts have already taken action. Six months after he left office, Brazil’s electoral court, led by Justice Moraes, barred Mr. Bolsonaro from office until 2030 because of his attacks on Brazil’s voting systems.

Mr. Bolsonaro called the ruling “a rape of democracy” and said he was trying to find a way to run in next year’s presidential election. Two Supreme Court justices he nominated will lead the electoral court before the election, he said. Those judges have told him, he said, “that my ineligibility is absurd.”

Polls show Mr. Bolsonaro remains by far Brazil’s most popular conservative candidate, but many on the right are seeking new options. Some have speculated about his sons: One, Flávio, 43, is an experienced senator, while another, Eduardo, 40, is a congressman who speaks English and has built close ties to the MAGA movement.

But Mr. Bolsonaro is not yet ready to hand over the keys to his movement. He said he would only support his sons staying in Congress for now. “For you to be president here and do the right thing, you have to have a certain amount of experience,” he said, as another son, Carlos, 42, looked on with a blank expression.

Should Mr. Bolsonaro stage a political comeback, he said he would focus his administration on deepening ties with the United States and moving away from China.

But first, he just wants to go to Washington this weekend. “I ask God for the chance to shake his hand,” Mr. Bolsonaro said of Mr. Trump. “I don’t even need a photo, just to shake his hand.”

The Chinese government is stepping up measures to root out potential troublemakers and suppress social discontent, after a spate of mass killings has shaken the country and stirred fears about public safety.

Armed police have been stationed outside of schools, with bollards erected nearby to prevent cars from ramming into people. Police officers have increased patrols in supermarkets, tourist attractions and other crowded places, and pledged to better regulate knives and other weapons. Officials have also promised to help the unemployed and distribute holiday subsidies to the needy.

The security push, which the authorities in some places have labeled “Operation Winter,” follows a string of recent attacks that put a renewed spotlight on China’s struggling economy. In November, a driver plowed into a crowd outside a sports center in the city of Zhuhai, killing at least 35 people in China’s deadliest attack in a decade. A stabbing that killed eight people, and another car ramming outside a school, followed barely a week afterward. In all three cases, officials said the perpetrators were venting financial dissatisfactions.

After the Zhuhai attack, China’s leader, Xi Jinping, ordered officials to “strictly prevent extreme cases.” The authorities at all levels have raced to comply.

The drivers in the two car attacks were sentenced to death late last month, in unusually speedy trials that showed the government’s determination to crack down on possible copycats.

Projecting stability and control has long been one of the ruling Chinese Communist Party’s biggest preoccupations, its implicit justification for limiting citizens’ civil liberties. But that preoccupation has become even more central as high youth unemployment, soaring foreclosures and deteriorating international relations have fueled widespread anxiety about China’s future. Some government workers have gone unpaid, as local governments’ finances stagnate.

Public protests, mostly related to economic issues such as investment losses or unpaid wages, grew by 18 percent in the first 11 months of 2024, compared to the year before, according to a tracker by Freedom House, a Washington-based advocacy group.

But Beijing has remained reluctant to strengthen the country’s social safety net or offer substantial direct relief to consumers. Instead, it has leaned on more heavy-handed tactics to root out those with grievances.

The central government urged officials to ensure social stability during the holiday season, saying in a Dec. 27 notice that they should “conduct dragnet investigations for all kinds of conflicts and hidden risks and dangers.”

In Yinchuan, a city in northwestern China, police officers investigated whether there were any incidents of bullying or disputes between faculty or students, according to a news release.

In Yancheng, in eastern China, the police have checked karaoke bars, rental housing and hotels for potential layabouts.

At a recent meeting of villagers and local party officials in central Henan Province, the police “encouraged everyone to actively report on any conflicts and disputes that have occurred in the village recently.” Under Mr. Xi, the Chinese government has renewed calls for ordinary residents to keep an eye on one another.

The central government routinely issues guidance about ensuring a safe holiday season. But this year, the instructions on social stability were more detailed. They singled out venues to keep an eye on — including campuses and sports venues — and called on officials to monitor public opinion and provide “positive guidance.”

Discussion about the attacks, and about economic discontent in general, has been heavily censored. Relatives of the victims have also been prevented from speaking with journalists.

Economists and public commentators have suggested that the government should focus more on boosting consumer confidence, and offering stronger protections for ordinary people against financial hardships. The authorities have at times acknowledged those demands, such as in their promises to combat wage arrears for migrant workers, or provide holiday handouts to homeless people or people with disabilities.

This month, many civil servants across the country discovered that they had been given a surprise pay raise, according to discussion on social media, though the government did not issue any formal announcement.

Yet many calls for more substantive reforms have been censored, themselves deemed threats to social stability.

“They should have been looking for what forces turned these people into beasts, but instead they ran off to investigate the ‘five types of losers,’” Li Chengpeng, a former prominent Chinese journalist now living overseas, wrote on social media. He was referring to local government notices that circulated online directing officials to surveil people who had suffered losses, such as of jobs or investments.

Still, the same economic downturn that may be fueling some people’s grievances may also make it difficult to sustain the heightened security measures.

Many local governments are already swimming in debt. They are under intense pressure now to answer Mr. Xi’s call to prevent mass incidents, but their money and manpower will soon come under strain, said Hongshen Zhu, an assistant professor at Lingnan University in Hong Kong who studies Chinese governance.

“As long as no new incidents occur, the priority of public safety will drop for local governments until the next public outcry happens,” he said.

It was a tense conversation between two authoritarian leaders accustomed to getting their way.

President Vladimir V. Putin of Russia was offering explanations for the Azerbaijan Airlines plane crash that had killed 38 people days earlier. Perhaps it was a flock of birds, Mr. Putin said, or an exploding gas canister. Maybe a Ukrainian drone.

But President Ilham Aliyev of Azerbaijan was not buying it, according to two people familiar with that late December phone call. It had become clear within hours of the crash that the plane had been shot down by Russian air defenses in what appeared to be a lethal mistake. It left shrapnel lodged in the leg of one passenger and riddled the fuselage with holes.

On Dec. 29, Mr. Aliyev went public with his anger without mentioning the Russian president by name. “Attempts to deny obvious facts,” he said, “are both nonsensical and absurd.”

The people who described the phone call insisted on anonymity to discuss sensitive diplomatic communications. The Kremlin did not respond to a request for comment.

The furor over the plane crash — and Mr. Aliyev’s willingness to challenge Mr. Putin in public — has revealed a remarkable breach between two post-Soviet rulers who had become close over more than two decades in power. Mr. Putin tried to enlist Mr. Aliyev in an apparent effort to keep quiet the cause of the crash; Mr. Aliyev, emboldened by Russia’s weakened influence in lands it once dominated, insisted that Russia publicly recognize its guilt.

Interviews last week with Azerbaijani officials and people close to the government showed how the Dec. 25 crash of an Embraer 190, with 67 people aboard, has become a geopolitical milestone for the former Soviet Union. Rather than allowing Mr. Putin to dictate his response to the tragedy, Mr. Aliyev has repeatedly lashed out at Russia over its failure to accept responsibility.

Rasim Musabekov, a member of the Azerbaijani Parliament’s foreign affairs committee, described Russia’s response to the crash as “an absurd attitude.”

“Azerbaijan will not accept such a chauvinist attitude,” he added.

Behind the scenes, the interviews showed, those tensions flared directly between Mr. Aliyev and Mr. Putin, even though the two autocrats have often found common ground. In the call on Dec. 28 and another the next day, the people familiar with the calls said, Mr. Putin urged Mr. Aliyev to agree to have a Moscow-based aviation body investigate the crash. Mr. Aliyev refused, insisting that the plane’s black boxes be decoded in Brazil, where the jet was made, a striking display of mistrust of the Russian leader.

Officials in Azerbaijan’s capital, Baku, arranged interviews for The New York Times with three survivors, who said it became clear to some passengers that they were under attack immediately after at least two explosions rocked the plane in midair.

After the second blast, a girl started screaming. Leyla Omarova, 28, looked across the aisle from her window seat and saw the girl’s tights stained with blood.

Three rows behind them, Nurullah Sirajov, 71, had been trying to comfort his wife. The first bang must have been the landing gear, he’d told her. They had never flown before.

Then came the second explosion, a rush of wind from the back of the plane and yells, he said, from other passengers: “They hit us.”

As the jet jerked up and down, coming within 100 feet of the Caspian Sea, Mr. Sirajov thought that at least his and his wife’s marital squabbles over who would die first would finally be resolved: They would die together. But after the front part of the plane disintegrated on impact, the tail section broke off, turned over and slid hundreds of yards through the sandy soil.

“Anyone alive?” Mr. Sirajov remembers yelling in the sudden silence as he dangled upside-down from his seatbelt.

Because Europe closed its airspace to Russia after Mr. Putin’s invasion of Ukraine, many Russians flying westward now connect in Azerbaijan, an oil-and-gas-rich former Soviet republic of 10 million sandwiched between Russia and Iran. Russia also sees Azerbaijan as a key link in an expanded trade route south to Iran, India and the Persian Gulf.

Its role as a transit point for a Russia beset by sanctions is just one way that Azerbaijan has seen its leverage rise against its far larger northern neighbor. Mr. Aliyev has also taken advantage of the Russian military’s distraction in Ukraine to push Russian peacekeeping troops out of Nagorno-Karabakh, the Armenian-controlled enclave that Azerbaijan recaptured in 2023.

Mr. Aliyev has solidified his country’s alliance with Turkey and armed Azerbaijan with high-tech weapons purchased from Israel. He has waged a fierce crackdown against activists and independent journalists, but has maintained a relationship with Europe, which sees Azerbaijan as a key alternative to Russian oil and gas.

Farhad Mammadov, a political analyst in Baku, said that Russia’s political and economic “levers of pressure” on Azerbaijan had been reduced to “practically none.” Aykhan Hajizada, the spokesman for Azerbaijan’s Foreign Ministry, was blunt in arguing that his country had leverage over Russia: “They don’t want to lose Azerbaijan as well,” he said.

The uproar over the plane crash has emerged as a test case. A senior American diplomat, speaking on condition of anonymity because he was not authorized to comment publicly, described the fallout from the crash as “a proof of concept” for Azerbaijan’s ability to stick up for itself. Other post-Soviet countries that have also sought a more arm’s-length relationship with Russia, like Kazakhstan, are watching closely.

“If this is how you behave in this incident with Azerbaijan, then what will the Uzbeks, the Kazakhs and the other remaining partners of Russia think of you?” Mr. Musabekov, the member of Parliament, asked. “It’s that Russia, as a state, is a very, very toxic partner that you need to minimize relations with.”

Mr. Aliyev, who studied in Moscow and took over as Azerbaijan’s ruler from his father in 2003, learned about the crash while en route to a summit of post-Soviet leaders in St. Petersburg. He called Mr. Putin from the plane to tell him he was not coming.

Hours later, Azerbaijani officials landed in Aktau, Kazakhstan, the airport where the Embraer 190 had tried to make an emergency landing. At the crash site nearby, the officials immediately realized that the theories of a bird strike or exploded oxygen canister that they had been hearing from Russia were wrong.

“When I saw the aircraft, it was riddled with holes,” Rinat Huseynov, the safety director for Azerbaijan Airlines, said in an interview. “We didn’t imagine that this was possible at all.”

Mr. Aliyev and Mr. Putin spoke again twice in the days after the crash. Mr. Putin apologized for the “tragic incident” happening in Russian airspace but did not acknowledge that Russia had shot down the plane. The day after the apology, on Dec. 29, Mr. Aliyev went public to accuse Russia of a cover-up.

“Unfortunately, for the first three days, we heard nothing from Russia except for some absurd theories,” Mr. Aliyev said.

Officials said they expected preliminary findings from the investigation by the end of January. Mr. Aliyev reiterated last week that Russia needed to accept responsibility and pay compensation, while the Kremlin said it was cooperating with the probe.

“We are interested in an absolutely objective and unbiased investigation,” Dmitri S. Peskov, Mr. Putin’s spokesman, told reporters last week.

The Azerbaijanis’ working theory is that the shrapnel from exploding missiles of a Russian Pantsir air-defense system damaged the plane. Metal fragments as large as four inches long were found at the crash site.

The flight data and cockpit voice recorders, officials said, could help explain why the pilots chose to cross the Caspian Sea to land in Kazakhstan rather than at a closer airport in Russia; Mr. Huseynov, the airline safety director, said the decision appeared logical given the cloudy conditions in southern Russia at the time.

Inside the passenger cabin, the flight attendants were trying to calm the panic. Ms. Omarova, en route to see family in Russia, said she lost consciousness. Mr. Sirajov, who had packed New Year’s presents for grandchildren in Grozny, said all he could think about was comforting his wife.

Flight data shows that after crossing the Caspian Sea, more than an hour after the pilots reported what they thought was a bird strike, the plane crashed on a second attempt to land at Aktau airport. All of the survivors were sitting in roughly the rear third of the plane, according to a person close to the investigation.

After the tail section came to a stop, Mr. Sirajov fumbled in the darkness to open his seatbelt, unable to tell what had happened to his wife. Only later did he learn that she had also survived.

Finally, Mr. Sirajov yanked his belt open and tumbled onto the cabin’s ceiling. “Go that way, go that way,” he recalls hearing as someone pushed him toward a sliver of light.