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A simple device that speeds up a semiautomatic weapon’s rate of fire is at the center of a case that could cast a shadow over a government agency’s ability to regulate firearms.

For Michael Cargill, a fierce defender of gun rights who sells firearms in Austin, the accessory, a bump stock, was until 2017 a niche item on the shelves of his store, Central Texas Gun Works. It mainly appealed to people who were injured or disabled, like veterans who needed support firing a gun or by “people who just wanted to have fun,” he said.

But that year, a high-stakes gambler stationed on the 32nd floor of a Las Vegas hotel opened fire on a country music festival, killing 60 people and injuring hundreds. In his arsenal were a dozen AR-15-style rifles outfitted with the device.

Government officials swiftly called for a ban, eliciting alarm among gun store owners like Mr. Cargill, 54, a gregarious Army veteran who said that the mugging and assault of his grandmother had shaped his views on gun control.

“I was one of the only people who said, hold on, wait a minute,” said Mr. Cargill, who has challenged the ban and is represented by the New Civil Liberties Alliance, a legal advocacy group that primarily challenges what it views as unlawful uses of administrative power. “This is insane that anyone would go along with this. We need to stop this now.”

On Wednesday, the Supreme Court will consider whether the Trump administration acted lawfully in enacting a ban that makes it illegal to buy or possess the part. It is not a case that turns on the Second Amendment. Rather, it is one of a number of challenges aimed at limiting the reach of administrative agencies — in this instance, the Bureau of Alcohol, Tobacco, Firearms and Explosives.

“During the Trump administration, the bump stock ban cropped up as a rather glaring example of unlawful administrative power,” Philip Hamburger, a founder of the New Civil Liberties Alliance, said in an email. “This rule turned half a million people into felons overnight. That’s not a power that the Constitution gives to administrative agencies — so it deserved a lawsuit.”

In a brief to the court, the solicitor general, Elizabeth B. Prelogar, arguing for the government, said that reversing the ban “threatens significant harm to public safety.”

“Bump stocks are machine guns because they allow a shooter to fire ‘automatically more than one shot by a single function of the trigger,’” Ms. Prelogar wrote.

The case hinges on whether bump stocks convert semiautomatic rifles into machine guns.

The device hooks onto a rifle’s stock, the part of the gun that is held against the shoulder, and harnesses the energy from the gun’s kickback to bump the stock back and forth, allowing the weapon to fire faster.

The bureau enacted the ban in 2018 by clarifying its interpretation of the National Firearms Act of 1934, which makes it a crime to make or own a machine gun, saying it extended to bump stocks. Under federal law, a machine gun is defined as “any weapon which shoots, is designed to shoot, or can be readily restored to shoot, automatically more than one shot, without manual reloading, by a single function of the trigger.”

At issue is whether the A.T.F. overstepped its bounds in enacting a ban without congressional action. A ruling against the agency could undermine its authority to regulate firearms and accessories.

The day before the ban went into effect, Mr. Cargill strolled into the A.T.F. office in Austin, handed over two bump stocks and announced his lawsuit.

Mr. Cargill said he hoped gun owners would pay close attention, even though the case does not center on the Second Amendment.

“It doesn’t matter if you’re pro-gun or anti-gun,” he said. “An agency can’t do this.”

The president of the New Civil Liberties Alliance, Mark Chenoweth, said the case fit in with other legal challenges by the group.

“A.T.F. is completely misinterpreting existing law to reach this far-fetched result,” Mr. Chenoweth said in an email, “and it flip-flopped from the interpretation it maintained for over a decade — including during the entirety of the Obama administration.”

Mr. Chenoweth declined to discuss the organization’s donors, but he said that group receives support from “a wide variety of donors.”

“N.C.L.A. is completely independent and not part of any other organization, umbrella group or donor entity,” Mr. Chenoweth wrote.

Federal tax documents show the group has received at least $1 million from the conservative Charles Koch Foundation. Mr. Chenoweth previously served as counsel for legal reform for Koch Industries.

The lead lawyer in the case is Jonathan F. Mitchell, best known for drafting anti-abortion laws that ultimately led the Supreme Court to abolish the constitutional right to the procedure. Mr. Mitchell, who declined to comment, also recently argued on behalf of former President Donald J. Trump to challenge the Colorado Supreme Court’s decision to remove him from the state’s primary ballot.

The lethal potential of a bump stock, which retailed for less than $200 when it first went on the market in 2010, came into startling view in October 2017.

That month, Stephen Paddock, 64, took aim at thousands of concertgoers, firing more than 1,000 rounds of ammunition over about 11 minutes. It remains the deadliest mass shooting in modern U.S. history. Investigators found about a dozen rifles modified with bump stocks in his hotel suite.

The day after, Mr. Cargill’s store sold out of bump stocks.

“Whenever something happens like a shooting incident or something like that and people think the government is going to ban a particular part, people then want to purchase them,” Mr. Cargill said.

Unusual alliances emerged to back a ban on bump stocks, but there were signs from the start that the politically divisive move could be open to challenges.

Lawmakers, including several leading Republicans, signaled openness to prohibiting the device. Even the National Rifle Association endorsed tighter restrictions.

Spurred in part by the mounting political pressure, Mr. Trump, a vocal supporter of the Second Amendment, vowed to enact a ban.

In response, the Justice Department promised to review the legality of bump stocks, but A.T.F. officials had privately indicated that any ban would likely require action by Congress, where bipartisan action has often stalled.

The A.T.F.’s decision to ban the device amounted to an about-face, raising questions about the extent of its authority to regulate the accessory.

Mr. Cargill was among those outraged by the ban, saying it would open the door to more gun control.

“You give the A.T.F. an inch, they will take a mile,” Mr. Cargill said. “I was shocked that no one was putting up a fight. I said, something has got to be done. You can’t just walk into people’s homes and take something that they legally purchased.”

Federal courts wrestled with the legality of the ban, issuing conflicting rulings. The divisions increased the likelihood that the Supreme Court would weigh in.

After a federal trial judge in Texas sided with the government in Mr. Cargill’s case, he appealed to the U.S. Court of Appeals for the Fifth Circuit. Eventually, the full court agreed with Mr. Cargill by vote of 13 to 3, split along ideological lines.

“A plain reading of the statutory language, paired with close consideration of the mechanics of a semiautomatic firearm, reveals that a bump stock is excluded from the technical definition of ‘machine gun’ set forth in the Gun Control Act and National Firearms Act,” Judge Jennifer Walker Elrod wrote.

Addressing concerns that “bump stocks contribute to firearm deaths,” she added that “it is not our job to determine our nation’s public policy.”

The three dissenting judges, all Democratic appointees, argued that the majority’s reasoning served to “legalize an instrument of mass murder.”

In Tuesday night’s results in Michigan, around one in eight Democrats voted “uncommitted” in the Democratic primary — a protest of the Biden administration’s policies toward Israel and the war in Gaza.

In some predominantly Arab American precincts in Dearborn, around three in four Democrats cast a protest vote for uncommitted.

Having one in eight Democrats vote uncommitted in an uncontested primary is not wholly unusual. As recently as the last time a Democratic president sought re-election, in 2012, 11 percent of Michigan Democratic caucusgoers voted for “uncommitted” instead of for Barack Obama.

Having three in four Democratic primary voters in Arab American communities do it, on the other hand, is an eye-popping figure. It goes well beyond the norm, and it’s a powerful indication that the war in Gaza poses serious political risks to President Biden.

What does it mean for the general election? That’s not an easy question to answer, but here are four things to consider.

1. A protest vote is hard to interpret

A vote for “uncommitted” was a serious form of protest against Mr. Biden, but it’s just not the same as voting for Donald J. Trump in the general election. That simple fact limits how much we can read into the results for November, especially as there was no exit poll to offer insight into the attitudes of protest voters.

At the same time, it’s also possible that Mr. Biden’s problems go well beyond those who voted uncommitted in a primary. The typical Democratic primary voter is disproportionately old, white and loyal to Democrats. Mr. Biden might be faring even worse among the kinds of Democratic-leaning voters who stayed home.

2. Protest votes have a history

Even though it may be hard to interpret a protest vote in a primary, the risk of defection from this group of voters should be taken seriously. This issue is very personal for them. There are also signs of defection in the polling, including in the last Times/Siena poll in Michigan. And their arguments for defection — complicity in genocide — are plainly enough to switch a vote if taken at face value.

There’s another reason it should be taken seriously: history. Major foreign policy conflicts have often reshaped the electoral map, especially among immigrant communities whose identity have remained tied to their home countries.

• The Cold War. Even today, Cuban Americans tend to vote Republican, as many fled the Communist Castro regime and supported the more fervently anti-Communist Republican Party. There’s a plausible case that the Elian González controversy in Florida was sufficient to decide the 2000 election.

  A similar anti-Communist story helps explain why Vietnamese Americans typically vote Republican, even as other Asian Americans tend to vote Democratic.

• World War II. The outbreak of war in Europe turned the American electoral map into an Axis vs. Allies game board. German, Italian and Irish Americans swung Republican in the 1940 election to oppose the Franklin D. Roosevelt administration’s opposition to the Axis powers and support for Britain. There were many German Catholic counties in the Midwest that routinely voted Democratic up until the war, and essentially never did so again.

  Mr. Roosevelt, meanwhile, won overwhelming support from Jewish and Polish voters. And he surged nearly 30 points to almost win Maine, one of the two states he lost in 1936 and home to many voters of English and French Canadian ancestry.

• The Arab-Israeli War. In 1948, a sizable share of Jewish voters defected to the third-party candidate Henry Wallace over President Truman’s tepid support for the newly created state of Israel. Many Jewish neighborhoods in New York City gave Mr. Wallace more than 20 percent of the vote. It was enough to cost Mr. Truman the state of New York.

• The War on Terror. Arab and Muslim Americans swung toward Democrats in the wake of 9/11, the war on terror and the Bush administration’s decision to invade Iraq. That was even true in Michigan, where Dearborn voted for George W. Bush in 2000 before voting for John Kerry by a 19-point margin in 2004. Sound familiar?

The relatively recent history of Arab American and Muslim voters being more favorable toward Republican candidates makes it even easier to envision a shift back to Republicans today. This isn’t a liberal voting group.

3. The effect is small

With that history, one could imagine Arab American and Muslim voters lurching decidedly toward Mr. Trump. That would obviously be bad news for Mr. Biden, but there’s one consolation for Democrats: These voters are a small share of the electorate, and it’s hard to see even a huge swing being decisive.

Imagine, for a moment, that in the last election Mr. Biden had lost every single voter in Dearborn, Hamtramck and Dearborn Heights — the three Michigan townships where Arab Americans make up at least 30 percent of the population. He still would have won Michigan — and still would have won it by more than he did Wisconsin, Arizona or Georgia.

For that same reason, Mr. Biden’s deficit in the polling of Michigan can’t mostly be attributed to his weakness among Arab American and Muslim voters. Overall, Arab Americans make up 2 percent of the state’s population and probably an even smaller share of the electorate. There are non-Arab Muslim voters, of course, adding another percentage point or more. In the end, 3 percent of the electorate can only do so much.

4. Still, anything could be decisive

Because the country is so narrowly divided, every vote counts, and right now Mr. Biden appears to need every vote he can get. If Arab American and Muslim voters swing by 30 points toward Mr. Trump, as suggested by our Times/Siena poll in Michigan, that could cost Mr. Biden a percentage point in a critical battleground state where he’s already trailing in the polls. If the race were close enough, it’s possible these voters could decide the 2024 election.

For decades, privacy experts have been wary of snooping from space. They feared satellites powerful enough to zoom in on individuals, capturing close-ups that might differentiate adults from children or suited sunbathers from those in a state of nature.

Now, quite suddenly, analysts say, a startup is building a new class of satellite whose cameras would, for the first time, do just that.

“We’re acutely aware of the privacy implications,” Topher Haddad, head of Albedo Space, the company making the new satellites, said in an interview. His company’s technology will image people but not be able to identify them, he said. Albedo, Mr. Haddad added, was nonetheless taking administrative steps to address a wide range of privacy concerns.

Anyone living in the modern world has grown familiar with diminishing privacy amid a surge security cameras, trackers built into smartphones, facial recognition systems, drones and other forms of digital monitoring. But what makes the overhead surveillance potentially scary, experts say, is its ability to invade areas once seen as intrinsically off limits.

“This is a giant camera in the sky for any government to use at any time without our knowledge,” said Jennifer Lynch, general counsel of the Electronic Frontier Foundation, who in 2019 urged civil satellite regulators to address this issue. “We should definitely be worried.”

Against that concern, Mr. Haddad and other supporters of Albedo’s technology say real benefits must be weighed, especially when it comes to fighting disasters and saving lives.

“You’ll know which house is on fire and where the people are fleeing,” said D. James Baker, a former head of the National Oceanic and Atmospheric Administration, which licenses the nation’s civilian imaging satellites.

Based in the Denver area, Albedo Space has 50 employees and has raised roughly $100 million. It plans to launch its first satellite in early 2025, Mr. Haddad said. Ultimately, he foresees a fleet of 24 spacecraft.

Investors in Albedo include Breakthrough Energy Ventures, the investment firm of Bill Gates. Albedo’s strategic advisory board includes former directors of the C.I.A. and the National Geospatial-Intelligence Agency, an arm of the Pentagon.

The company’s website makes no mention of imaging people, or the privacy issues. Even so, reconnaissance experts say regulators should wake up before its spacecraft start taking their first close-ups.

“It’s a big deal,” said Linda Zall, a former C.I.A. official whose decades-long career involved some of the nation’s most powerful spy satellites. The capabilities will hit home, she predicted, when people realize that things they’re trying to hide in their backyards can now be observed with new clarity. “Privacy is a real issue,” Dr. Zall said.

“It’s taking us one step closer to a Big-Brother-is-watching kind of world,” added Jonathan C. McDowell, a Harvard astrophysicist who publishes a monthly report on civilian and military space developments.

While spacecraft in orbit have long studied the planet, the potential for civilian life to be surveilled by satellites was driven home by the Chernobyl nuclear disaster. Moscow had denied any serious trouble. But a nonmilitary American satellite took a picture on April 29, 1986, showing that the reactor’s core had ruptured in a fiery breach that was spewing deadly radioactive debris into the atmosphere.

The American news media released the image. It confirmed a disaster, helped start the field of satellite journalism and — almost immediately — stoked fears of snooping from space.

“The quality of the pictures is expected to improve rapidly,” Privacy Journal, a monthly newsletter published in Washington, warned shortly after the atomic disaster. Television news directors, it said, were now seeking to gain unfettered access to space images that could ultimately track everything from troop movements to backyard Jacuzzis.

The visual power of a space camera is usually expressed as the length, in meters, of the smallest feature it can resolve. The figure for early cameras was meters. Now it’s centimeters. Overall, experts say, that improvement makes the new images hundreds of times more detailed and revealing.

The satellite that imaged Chernobyl in 1986 was known as Landsat. NASA built it to monitor crops, forests and other resources on the ground. The craft’s orbit was roughly 400 miles up, and its camera could make out ground objects as small as 30 meters. In contrast, the Chernobyl complex was nearly a kilometer in length. So analysts could easily see it and the exploded reactor.

After the Cold War, in 1994, the Clinton administration approved the commercial use of American spy technology. By 1999, Space Imaging, a subsidiary of Raytheon and Lockheed Martin, launched its first satellite. It had a resolving power of one meter. The New York Times displayed the satellite’s first image atop its front page. The Washington Monument stood out clearly, its shadow long in the morning light.

As predicted, pictures from orbit have continually improved in quality, aiding news reporting on wars, refugees, secret bases, human rights abuses, environmental destruction, natural disasters and military buildups.

In 2016, The Associated Press won a Pulitzer Prize for uncovering labor abuses in the seafood industry that amounted to slavery. Its journalists used satellite images to track industry ships. Many news organizations, including The Times, now employ specialists skilled in the analysis of satellite imagery.

Mark Brender, a satellite journalism pioneer, noted that reporters on the ground can be harassed and blocked. “But cameras in space are safe from those kinds of pressures,” he said. “They’ve become as indispensable to a free society as a hand-held camera or a printing press.”

Today, the most powerful civilian imaging satellites can differentiate objects on the ground as small as 30 centimeters, or about a foot in diameter. The images let analysts discern road markings and even aircraft tail numbers.

Albedo aims to leap ahead by imaging objects as small as 10 centimeters, or four inches. That became possible because the Trump administration in 2018 took steps to relax the regulations that govern civil satellite resolution. “Soon,” Technology Review, an M.I.T. magazine, warned in 2019, “satellites will be able to watch you everywhere all the time.”

What inspired Albedo’s sharp clarity goals, Mr. Haddad said, was Mr. Trump’s sharing an American spy image from his Twitter account that showed a heavily damaged launchpad in Iran. The image’s resolution was judged to be roughly 10 centimeters, and that led to wide discussion of the commercial possibilities.

Mr. Haddad grew up in Houston and studied engineering at Johns Hopkins University and the University of Texas. He then worked for Lockheed Martin in Sunnyvale, Calif. — which has long built spy satellites. Some can rival or exceed a school bus in size and typically cost billions of dollars.

Mr. Haddad founded Albedo with Winston Tri, a former Facebook software engineer, and AyJay Lasater, a former Lockheed Martin satellite engineer. They saw a commercial market for 10-centimeter imagery, but not if the costs were astronomical. Their solution was to place satellites in very low orbits that were comparatively close to their earthly subjects. That would let the satellite fleet use smaller cameras and telescopes, slashing costs.

Landsat was orbiting more than 400 miles up when it imaged Chernobyl. In contrast, Albedo’s founders planned orbits as low as 100 miles At low elevations, spacecraft cut through the planet’s thin outer atmosphere, which can slow them down and shorten their orbital life. The Albedo craft, slightly larger than a full-size refrigerator, will use booster jets to counteract the atmospheric drag.

To charge batteries, satellites often have large arrays of solar panels that spread out like wings. Not Albedo. To reduce the drag, the founders planned a cylindrical spacecraft covered with solar cells.

Albedo was founded in 2020, and Mr. Haddad was confronted with privacy concerns at the outset. Addressing them in a discussion on an online tech forum, he wrote, “We realize we have to properly address privacy and misuse prevention.”

To lower the risks, Mr. Haddad added, the company would approve new customers on a case-by-case basis, develop ways to identify bad actors and make sure its contract terms and conditions spelled out punitive measures for violations of company policy.

In December 2021, Albedo won regulatory approval to loft an imaging satellite with 10-centimeter resolution. Its technology quickly caught the attention of the military and the nation’s intelligence agencies.

In 2022, Albedo received a $1.25 million contract with the Air Force to see if the company’s gear could meet a standard rating scale that measures image interpretability. The tests included identifying hardware on electronics vans, fairings on fighter jets and missile tubes on warships.

In April 2023, the company received another $1.25 million contract — this time with the National Air and Space Intelligence Center, which assesses foreign threats. Late last year, it also signed a contract to have its technology assessed by the National Reconnaissance Office, which runs the nation’s spy satellites.

Albedo’s website says its imagery can help governments “monitor hotspots, eliminate uncertainty, and mobilize with speed.” The company, in listing its core values, says it supports “data-driven investigative journalism” among other activities that “ensure we improve the world we live in.”

Illustrating the fleet’s observational powers, Mr. Tri, the Albedo co-founder, said the space cameras could detect such vehicle details as sunroofs, racing stripes and items in a flatbed truck. “In some cases,” he said, “we may even be able to identify particular vehicles, which hasn’t been possible up to this point.”

The company expects civilian customers to include city planners looking for potholes on roads, conservation groups tracking wildlife, insurance companies surveying roof damage and power line companies seeking to prevent wildfires.

John E. Pike, director of Global Security.org, a nonprofit research group based in Alexandria, Va., said Albedo was downplaying what could become significant.

“You’re going to start seeing people,” he said. “You’re going to see more than dots.” Satellite images of Palestinians fleeing fighting in the Gaza Strip, Mr. Pike noted, illustrate the current observational limits. The images show either dense crowds in which no individuals can be discerned or — in the case of smaller groups of people on roads — tiny flecks and dark spots.

Mr. Pike echoed Mr. Haddad in saying the new technology would be unable to identify particular individuals. However, he said the space cameras would most likely be able to distinguish children from adults as well as sunbathers in swimsuits from those in further states of undress.

“This is the archetypal, first-order privacy concern — that somebody would see you sunbathing,” Mr. Pike said.

Legal experts note that drones are highly regulated by federal, state and local laws that make them subject to claims of trespass and privacy violation. No-fly zones include not only airports, military bases and sporting events but individuals. California law bars drone operators, unless they have permission, from taking pictures of people engaged in private, personal or family activities.

Ms. Lynch of the Electronic Frontier Foundation said her discouraging experience with satellite regulators a half decade ago suggested to her that little would be done to mandate a protection of privacy from the eyes in the sky.

Albedo and its backers, she added, are “operating with blinders on and not seeing the ramifications” for human rights.

February is usually frigid perfection for the ice rink at Millennium Park in downtown Chicago, a favorite winter stop for tourists and local families that stands in the shadow of the reflective sculpture known as the Bean.

On Tuesday morning, the rink was melting.

Under an intense sun and 70-degree air temperatures, water slowly trickled out of the empty rink, flooding the surrounding concrete. Baby birds splashed happily in the pools of water. The ticket counter was abandoned, apparently closed for the day.

Winter in Chicago — or the lack of it — reached an unnerving peak on Tuesday, when the city came close to breaking a 48-year-old high-temperature record.

But forecasters said that the balmy spell was not going to last. They pointed out that the mild conditions in Chicago and around the Midwest this week were extreme, not just for the warmth but also for what would follow.

That was likely to include plunging temperatures dropping into the 20s, blustery northwest winds gusting up to 40 miles an hour and potentially dangerous storms, including tornadoes.

Still, for most of Tuesday, Chicago looked and felt like summer: Apartment windows were pushed open to catch the warm breeze. Restaurants set up tables and chairs on sidewalks for al fresco lunch service, a rare sight in a Chicago February.

The lakefront was teeming with runners, cyclists and couples strolling hand in hand.

“We expected it would be very cold,” said Ana Marchal, 41, a doctor from Cádiz, Spain, who arrived in Chicago on Monday for a vacation with her husband, Rolf Hartmann.

They had figured on spending their holiday indoors, by shopping, visiting museums or attending Blackhawks and Bulls games.

Instead, they found themselves walking on the beach, looking delighted and a little perplexed. They stopped to take a selfie by Lake Michigan, which is usually icy and forbidding this time of year.

“How beautiful,” Mr. Hartmann said. “It looks like the sea.”

“It’s colder in Spain than here,” Dr. Marchal said.

Others found the weather ominous.

Shailaja Chandrashekararao, a social worker who moved from India to Chicago last year, had just finished a 10-kilometer jog downtown. She said she would have liked to keep running.

“It was too hot,” Ms. Chandrashekararao said, tugging at the sleeve of her neon-orange workout top.

Climate change has made summers in India unbearably, dangerously brutal, she said, making Chicago something of a weather haven. But the city’s mild winter, on the heels of the warmest year on record in 2023, felt eerie and unpredictable.

“I’m not enjoying this,” she said. “It’s quite crazy, actually.”

Temperatures are also rising across the Midwest, in part because of human-caused climate change, according to the 2023 National Climate Assessment, the government’s premier compilation of scientific knowledge on the effect of human-caused warming. The report also noted that the warming posed significant economic risk to the region.

The June-like temperatures will be one factor in producing severe thunderstorms in the Chicago area Tuesday evening and overnight. Some of the storms could spawn tornadoes, forecasters said, with the most likely area stretching from Missouri across southern Illinois and northern Indiana to Michigan. Tornadoes that occur after dark can be more dangerous because so many people are asleep.

The main threat from the storm system, though, will be hail, possibly including hailstones as large or larger than hen’s eggs.

Unseasonably high temperatures across the Great Plains, along with high winds, were propelling wildfires in Nebraska and Kansas, which were still a threat on Tuesday after forcing evacuations this week. Wildfires were also raging across the Texas Panhandle.

And from Tuesday to Wednesday in Chicago, the temperature could drop by nearly 60 degrees, according to David King, a meteorologist for the National Weather Service.

“It’s remarkable,” he said, noting that the last time the city saw such a rapid temperature drop was in the 1990s. “It’s just a wild time for weather here in Chicago.”

A normal daytime high in Chicago at this time of year is about 40 degrees. According to the National Oceanic and Atmospheric Administration, only 4.3 percent of the Great Lakes’ surface is ice-covered, well below the average.

The unseasonably warm and dry winter has affected tourism in the region, especially in Michigan, Wisconsin and Minnesota, where industries that depend on snow have suffered. Gov. Tony Evers of Wisconsin announced last week that many businesses in northern Wisconsin — ski slopes, restaurants and snowmobiling tours, for example — may be eligible for a federal disaster loan program if they have incurred losses from the mild winter.

The mild day on Tuesday was already feeling familiar, said Charles Jones, who manages maintenance work for a residential building in downtown Chicago.

Mr. Jones spent his break standing outside in short sleeves, as people walked their dogs in the sunshine. He has lived in Chicago his whole life, he said, and was used to the harsh winters that the city is known for. But it was hard to remember the last winter where the cold had felt truly brutal — “a few years ago, maybe,” he shrugged.

This winter has been a lot like the one before, Mr. Jones said, without very much snow or many cold, icy days. In the last few months, he said, he has only had to salt the sidewalk twice.

“I don’t trust this weather, though,” he said. “You know we’re going to get a little snow before winter is done. It’s Chicago. It can be 70 and then jump down to 30.”

Judson Jones contributed reporting.

Since Sam Bankman-Fried was convicted of fraud last year, he has hired a new lawyer known for courtroom showmanship. A group of sympathetic law professors has pushed for a reappraisal of his actions. And his parents have turned for help to former employees of FTX, the collapsed cryptocurrency exchange he founded.

From a federal detention center in Brooklyn, Mr. Bankman-Fried, 31, has continued to fight his case behind the scenes, as he aims for a lenient sentence and prepares to appeal his conviction. On Tuesday, his lawyers filed a legal memo in U.S. District Court in Manhattan, arguing that he should receive a prison sentence of between five and a quarter and six and a half years.

Mr. Bankman-Fried is “deeply, deeply sorry” for “the pain he caused over the last two years,” the memo said. “His sole focus after the collapse of FTX was making customers whole.”

The filing was a crucial step before Mr. Bankman-Fried’s sentencing on March 28, when the federal judge overseeing his case, Lewis A. Kaplan, will decide how long to imprison the onetime billionaire on charges that carry a maximum sentence of 110 years. But it was only one prong of a long-shot strategy orchestrated by Mr. Bankman-Fried’s family and friends to reverse his conviction and engineer a public reappraisal of his leadership at FTX.

Since last year’s trial, Mr. Bankman-Fried has hired Marc Mukasey, who once represented former President Donald J. Trump, to oversee his sentencing, as well as a separate lawyer at the law firm Shapiro Arato Bach to handle the appeal. His parents, the Stanford University law professors Joe Bankman and Barbara Fried, have also been involved in the defense, helping line up people to write letters vouching for their son’s character that were included in the sentencing memo.

In an interview, Natalie Tien, a former assistant to Mr. Bankman-Fried at FTX, said she had written a letter for the memo after exchanging emails with Mr. Bankman and Ms. Fried.

“I don’t have grudges over him, and I do feel bad for his parents,” Ms. Tien said.

A spokesman for Mr. Bankman-Fried declined to comment. Representatives for Mr. Bankman and Ms. Fried did not respond to requests for comment.

Federal prosecutors are set to outline their own sentencing recommendation in a filing due March 15. But according to Mr. Bankman-Fried’s memo, a probation officer has already recommended a 100-year sentence, a punishment his lawyers called “barbaric.”

Even if Judge Kaplan decides not to impose the maximum sentence, Mr. Bankman-Fried could face decades behind bars.

The judge “could still give a very serious sentence given how young Mr. Bankman-Fried is — say, a 30- or 35-year sentence,” said Miriam Baer, vice dean at Brooklyn Law School.

A spokesman for Damian Williams, the U.S. attorney for the Southern District of New York, declined to comment.

Before FTX collapsed in November 2022, Mr. Bankman-Fried was one of the most prominent figures in the renegade crypto industry, a widely celebrated billionaire whose face was splashed across billboards and magazine covers.

In October, a federal jury convicted him of stealing $8 billion from FTX’s customers to finance political contributions, investments in other companies and lavish real estate purchases.

Mr. Bankman-Fried has maintained he is innocent and pledged to appeal. This month, he replaced his trial lawyers, Mark Cohen and Christian Everdell, with Mr. Mukasey, who is representing another fallen crypto mogul in a separate case and has a reputation for forceful courtroom presentations.

Last year, Mr. Mukasey scored a victory in his defense of Trevor Milton, the founder of the electric truck manufacturer Nikola, who was convicted in 2022 of defrauding investors. A federal judge sentenced Mr. Milton in December to four years in prison, far less than the 11 years that prosecutors had requested.

Working in parallel to Mr. Mukasey is an appellate lawyer and former prosecutor, Alexandra Shapiro, who is a partner at Shapiro Arato Bach. She is expected to file Mr. Bankman-Fried’s appeal after the sentencing.

Mr. Bankman and Ms. Fried have also played a role behind the scenes. Last month, Ms. Tien said, she received a text from one of Mr. Bankman-Fried’s supporters, asking whether she would help with the memo. Then she got a follow-up email from the FTX founder’s parents explaining the sentencing process and urging her to write “from the heart” about their son.

They were “kind of like testing the waters,” Ms. Tien said in an interview. “I pretty much just said ‘yes’ right away.”

Ms. Tien was one of 29 people who wrote letters for the memo, including Mr. Bankman-Fried’s parents, his younger brother and several former colleagues. She called him kind and empathetic and said he had “never acted out of greed or self-interest.”

In the filing, Mr. Mukasey cited the letters to paint Mr. Bankman-Fried as a hard-working, altruistic billionaire who eschewed the trappings of fame and wealth. He also argued that some oddities in the mogul’s behavior could be explained by “neurodiversity.”

Mr. Bankman-Fried has “outward characteristics typical of neurodiversity, such as inconsistent eye contact,” the memo said. “He can be perceived as abrupt, dismissive, evasive, detached or uncaring.”

Outside the formal court process, law professors who know Mr. Bankman-Fried’s parents have also pressed his case.

In January, two close family friends, the Yale Law professor Ian Ayres and the Stanford Law professor John Donohue, wrote an essay for the website Project Syndicate, arguing that “all along” FTX had enough assets to make its customers whole — a point that Mr. Mukasey echoed in the memo.

“Whatever else might be said about Bankman-Fried, he was a brilliant businessman,” Mr. Ayres and Mr. Donohue wrote.

Another law professor, Jonathan Lipson at Temple University, said in an interview that he was working with David Skeel of the University of Pennsylvania law school on an academic paper criticizing Sullivan & Cromwell, the law firm overseeing FTX’s bankruptcy.

In September, Mr. Lipson co-wrote a brief in the bankruptcy case arguing for the appointment of an independent examiner to review Sullivan & Cromwell’s actions, including its close collaboration with federal prosecutors. He said that he had spoken with Mr. Bankman-Fried and his mother last year after another Stanford law professor reached out about the case and offered to put them in contact.

In their article, Mr. Lipson and Mr. Skeel argue that Sullivan & Cromwell “may have distorted the criminal justice process” by giving prosecutors wide-ranging access to FTX’s resources and data, according to an unpublished draft shared with The New York Times.

A Sullivan & Cromwell spokesman declined to comment. In court filings, prosecutors have described the information sharing as “routine practices by companies cooperating in an investigation.”

Mr. Bankman-Fried faces long odds. Criminal convictions are rarely overturned on appeal.

Since last summer, he has been housed at the Metropolitan Detention Center in Brooklyn, where he has spent much of his time working on the case, a person with knowledge of the matter said. Mr. Bankman-Fried has also shared crypto market tips with the guards, the person said, recommending investments in the digital coin Solana.

This month, Mr. Bankman-Fried left the detention center for his first public court appearance since the trial, a hearing to authorize his new legal representation. In a Manhattan courtroom, he appeared clean-shaven and wore a loosefitting brown prison uniform. At times, he turned around and smiled at the reporters sitting in the gallery.

J. Edward Moreno contributed reporting.