riot-gear-clad teddy bear, a pair of zip ties strapped to its chest ($62); key chains engraved with crowd-control phrases like “Disperse or we fire” and “Warning: Tear smoke” ($4 each); and a set of 18 three-inch figurines, clutching rifles and shields and bearing police warning flags about illegal assembly (“festive special offer”: $114).

It seemed unlikely that any sort of protest would break out in such a heavily fortified location. Still, officials seemed eager to forestall even a hint of the so-called soft resistance Mr. Luo had singled out in his speech. As journalists waited to enter the open house, security officers asked some who were wearing yellow or black face masks — colors associated with the pro-democracy movement — to swap them for blue ones the authorities provided.

four pro-democracy activists tried to march through parts of downtown, bearing a poster that said “Without democracy and human rights, there is no national security.” They were followed by dozens of police officers.

In other parts of the city, schoolchildren — including those in kindergarten — were enlisted in the promotion of national security. Education has been a particular focus for the authorities, who have blamed what they call biased curriculums for turning Hong Kong’s youth against the government.

On Thursday morning, many schools hosted ceremonies to raise China’s national flag and sing the national anthem (which the Hong Kong government last year made a crime to disrespect).

At the Wong Cho Bau middle school, which is run by a pro-Beijing teachers’ union, the principal told students during a morning assembly that national security should be incorporated into every part of their curriculum, including geography and biology classes, as well as weekly flag-raising ceremonies.

“These daily accumulations can help us construct our own national concept and identity, so as to achieve prosperity and glory for the country,” said the principal, Hui Chun-lung. “So everybody should study hard. If the youth are strong, then China is strong.”

Afterward, school officials showed off colorful slips of paper that students had filled out and pasted onto a “community mosaic wall.” “Please express your opinion toward the idea of ‘Support national security, guard our home,’” the prompt said.

In response, the students expressed their gratitude to the government and their relief that the pro-democracy protests had subsided. “Those people who protest everywhere are intolerable, destroying public places and hurting our home,” one student wrote.

Other students’ responses were even more effusive.

“I think the idea of supporting national security and guarding our home is extremely without problems! Support! Support! Extremely support!” one student wrote. “Whatever the national security law says, goes! I very much have no opinion!”

Joy Dong contributed research.

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John Naisbitt, Business Guru and Author of ‘Megatrends,’ Dies at 92

His marriage to Ms. Senior ended in divorce, as did his second, to Patricia Aburdene. Along with his daughter, he is survived by his third wife, Doris (Dinklage) Naisbitt; his sons James, David and John; another daughter, Nana Naisbitt; a stepdaughter, Nora Rosenblatt; 11 grandchildren and two step-grandchildren.

Mr. Naisbitt ran out of money after only two semesters, and with his first child on the way he dropped out of college to take a job writing speeches for executives at Eastman Kodak, in Rochester, N.Y.

He and his family moved to Chicago in 1957, where he worked in public relations jobs. He worked in Washington between 1963 and 1966, first as an assistant to the director of the National Education Commission, then as an assistant to the secretary of health, education and welfare.

It was during an assignment to assess the impact of various Great Society programs under President Lyndon B. Johnson, he said, that he first developed his method of trend analysis. A fan of American history, he had been reading books about the Civil War by Bruce Catton, who had relied heavily on contemporary newspapers to get a sense of the country’s mood during the war.

“I went out to a newsstand and I bought about 50 out-of-town newspapers,” he told The Christian Science Monitor in 1982. “And I was absolutely stunned what I learned in three hours about what was going on in America.”

He called it “content analysis,” and after he returned to Chicago, he put it into practice with his first firm, the Urban Research Corporation. Long before computers made such work nearly instantaneous, Mr. Naisbitt employed a small army of analysts to read through scores of newspapers a day, clipping stories about urban protests, crime and campus unrest, which he drew on to write reports for nonprofit and corporate clients.

With his first marriage ending and his company losing money, he moved back to Washington in the mid-1970s and opened another, similar firm. It also failed, leading him to file for personal bankruptcy in 1977.

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Her Boss Sent Harassing Texts. So She Beat Him With a Mop.

HONG KONG — It was a thrashing to behold.

A government worker in northeastern China who complained of harassing text messages from her boss was captured on video beating him with the business end of a mop, spurring debate about the persistence of workplace harassment and turning her into an internet sensation.

In the 14-minute video, the woman, later identified by her last name, Zhou, can be seen throwing books at the face of her boss, identified as Wang, and dousing him with water, in addition to hitting him with the mop. He is seen hiding his face behind his fingers, attempting to apologize and saying that he had been joking when he sent the messages.

It is unclear exactly when the incident took place, but local news outlets said the woman filed a police report last week accusing her boss of harassment, and the video began circulating widely online this week. It has been viewed millions of times, with many social media users relishing what they saw as an uncommon display of resistance against an authority figure in a country with limited workplace protections against sexual harassment. Many users sided with the woman, lauding her for flipping the balance of power and calling her a defender of justice and a martial arts warrior.

Lu Pin, a prominent Chinese feminist activist, said that many people viewed the video as an outlet for pent-up anger over the general absence of accountability for harassers and of available recourse from courts or the police. Many victims of harassment feel powerless to report it and worry that they will be disbelieved or retaliated against if they do.

become the targets of lawsuits themselves. In 2019, after a woman in the Chinese city of Chengdu filed a police report saying she had been harassed by a colleague, the colleague sued. Though the lawsuit was largely dismissed, the woman was ordered to make a court-reviewed apology in a work chat group where she had discussed the harassment, so as to undo the “adverse effects” to her colleague.

In the video footage of the mop episode, Ms. Zhou says that Mr. Wang sent her unwanted text messages on three occasions and that others in the office had received similar unwelcome attention. She can be seen and heard making a call and accusing her boss of assault.

While on the phone, she says that she has already reported his actions to the police. According to local news outlets, the police said that they registered her report against her boss last week and were investigating her claims. Government offices in the city of Suihua and the district of Beilin, as well as the Beilin district police, did not respond to requests for comment.

Activists called for more protections from the system for such cases.

“How can more victims who have not attracted public attention be supported?” Ms. Lu said. “These questions have only been raised, and there are no answers.”

Ms. Zhou’s case is helped by the fact that she has a recording of her boss’s admissions, Mr. Longarino said.

In many situations, he said, “there is no viral video.”

Claire Fu contributed research from Beijing.

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Some Pubs and Shops Reopen in England, Raising Hopes for Economic Recovery

For the past year, the British economy has yo-yoed with the government’s pandemic restrictions. On Monday, the next bounce began as shops, outdoor dining, gyms and hairdressers reopened across England for the first time in months.

In London, friends gathered at tables outside a pub at one minute after midnight to toast the reopening. Others queued in light flurries at 7 in the morning for shops to open their doors. Barbers and beauty salons had long queues, and by lunchtime the outside tables at restaurants had filled up.

But the pandemic has left Britain with deep economic wounds that have shattered historical records: the worst recession in three centuries and record levels of government borrowing outside wartime.

Topshop on Oxford Street, one of Europe’s busiest shopping streets. Many neighborhood restaurants are now darkened, empty shells.

Eat Out to Help Out.”

Beginning in the fall, a second wave of the pandemic stalled the recovery, though the economic impact wasn’t as severe as it had been last spring. Still, the government is spending about 344 billion pounds, or $471 billion, on its pandemic response. To pay for it, it has borrowed a record sum and is planning the first increase in corporate taxes since 1974 to help rebalance its budget.

Andy Haldane, the central bank’s chief economist, said in February. “As its energies are released, the recovery should be one to remember after a year to forget.”

Even though a lot of retail spending has shifted online, reopening shop doors will make a huge difference to many businesses. Foot traffic across Britain’s shopping locations on Monday was more than double what it was last week, according to data from Springboard.

Daunt Books, a small chain of independent bookstores, had been busy preparing to reopen for the past week. Throughout the lockdown, a skeleton crew “worked harder than they’ve ever worked before, just to keep a trickle” of revenue coming in from online and telephone orders, said Brett Wolstencroft, the bookseller’s manager.

“The worst moment for us was December,” Mr. Wolstencroft said, when shops were shut in large parts of the country beginning on Dec. 20. One day’s worth of revenue in the run-up to Christmas is similar to a week’s worth during the rest of the year. “Realizing you’re losing your last bit of Christmas is exceptionally tough.”

pubs, hairdressers, cinemas and hotels shut for months on end, Brits are expected to build up £180 billion in excess savings by June, according to estimates by the Office for Budget Responsibility. That money, once people can get out more, is expected to be the engine of the recovery — even though economists are debating how much of it will end up in the tills of businesses. Some forecast just 5 percent, saying that medium- and high-income households are more likely to keep hold of their savings.

one phase of the reopening. Pubs can serve customers only in outdoor seating areas, and less than half have such facilities. Hotels will also remain closed for at least another month, alongside indoor dining, museums and theaters. The next reopening phase is scheduled for May 17.

Over all, two-fifths of hospitality businesses have outside space, said Kate Nicholls, the chief executive of U.K. Hospitality, a trade group.

“Monday is a really positive start,” she said. “It helps us to get businesses gradually back open, get staff gradually back off furlough and build up toward the real reopening of hospitality that will be May 17.”

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England’s Lockdown Eases, but Economic Toll Persists

For the past year, the British economy has yo-yoed with the government’s pandemic restrictions. On Monday, the next bounce began as shops, outdoor dining, gyms and hairdressers reopened across England for the first time in months.

In London, friends gathered at tables outside a pub at one minute after midnight to toast the reopening. Others queued in light flurries at 7 in the morning for shops to open their doors. Barbers and beauty salons had long queues, and by lunchtime the outside tables at restaurants had filled up.

But the pandemic has left Britain with deep economic wounds that have shattered historical records: the worst recession in three centuries and record levels of government borrowing outside wartime.

Topshop on Oxford Street, one of Europe’s busiest shopping streets. Many neighborhood restaurants are now darkened, empty shells.

Eat Out to Help Out.”

Beginning in the fall, a second wave of the pandemic stalled the recovery, though the economic impact wasn’t as severe as it had been last spring. Still, the government is spending about 344 billion pounds, or $471 billion, on its pandemic response. To pay for it, it has borrowed a record sum and is planning the first increase in corporate taxes since 1974 to help rebalance its budget.

Andy Haldane, the central bank’s chief economist said in February. “As its energies are released, the recovery should be one to remember after a year to forget.”

Even though a lot of retail spending has shifted online, reopening shop doors will make a huge difference to many businesses. Foot traffic across Britain’s shopping locations on Monday was more than double what it was last week, according to data from Springboard.

Daunt Books, a small chain of independent bookstores, had been busy preparing to reopen for the past week. Throughout the lockdown, a skeleton crew “worked harder than they’ve ever worked before, just to keep a trickle” of revenue coming in from online and telephone orders, said Brett Wolstencroft, the bookseller’s manager.

“The worst moment for us was December,” Mr. Wolstencroft said, when shops were shut in large parts of the country beginning on Dec. 20. One day’s worth of revenue in the run-up to Christmas is similar to a week’s worth during the rest of the year. “Realizing you’re losing your last bit of Christmas is exceptionally tough.”

pubs, hairdressers, cinemas and hotels shut for months on end, Brits are expected to build up £180 billion in excess savings by June, according to estimates by the Office for Budget Responsibility. That money, once people can get out more, is expected to be the engine of the recovery — even though economists are debating how much of it will end up in the tills of businesses. Some forecast just 5 percent, saying that medium- and high-income households are more likely to keep hold of their savings.

one phase of the reopening. Pubs can serve customers only in outdoor seating areas, and less than half have such facilities. Hotels will also remain closed for at least another month, alongside indoor dining, museums and theaters. The next reopening phase is scheduled for May 17.

Over all, two-fifths of hospitality businesses have outside space, said Kate Nicholls, the chief executive of U.K. Hospitality, a trade group.

“Monday is a really positive start,” she said. “It helps us to get businesses gradually back open, get staff gradually back off furlough and build up toward the real reopening of hospitality that will be May 17.”

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A Clash of Wills Keeps a Leonardo Masterpiece Hidden

French curators had worked for a decade to prepare a major exhibition marking the 500th anniversary of the death of Leonardo da Vinci. When it opened, though, the most talked-about painting they had planned to show — “Salvator Mundi,” the most expensive work ever sold at auction — was nowhere to be seen.

Plucked from shabby obscurity at a New Orleans estate sale, the painting had been sold in 2017 as a rediscovered “lost” Leonardo and fetched more than $450 million from an anonymous bidder who kept it hidden from view. The chance to see it at the Louvre museum’s anniversary show two years later had created a sensation in the international art world, and its absence whipped up a storm of new questions.

Had the Louvre concluded that the painting was not actually the work of Leonardo, as a vocal handful of scholars had insisted? Had the buyer — reported to be Saudi Arabia’s Crown Prince Mohammed bin Salman, though he had never acknowledged it — declined to include it in the show for fear of public scrutiny? The tantalizing notion that the brash Saudi prince might have gambled a fortune on a fraud had already inspired a cottage industry of books, documentaries, art world gossip columns, and even a proposed Broadway musical.

None of that was true.

In fact, the crown prince had secretly shipped the “Salvator Mundi” to the Louvre more than a year earlier, in 2018, according to several French officials and a confidential French report on its authenticity that was obtained by The New York Times. The report also states that the painting belongs to the Saudi Culture Ministry — something the Saudis have never acknowledged.

a 2011 Leonardo exhibition at the National Gallery in London that included the “Salvator Mundi.”

If the only painting were displayed, he explained, “people could decide for themselves by experiencing the picture.”

Believed to have been painted around 1500, “Salvator Mundi” was one of two similar works listed in an inventory of the collection of King Charles I of England after his execution in 1649. But the historical record of its ownership ends in the late 18th century.

the anonymous buyer was a surrogate for the Crown Prince of Saudi Arabia.

Now the controversy has made headlines again with the release of a new French documentary this past week claiming that the Louvre had concluded that Leonardo had “merely contributed” to the “Salvator Mundi.” Set to air on French television on Tuesday, the documentary features two disguised figures, identified as French government officials, asserting that Crown Prince Mohammed would not loan the painting to the anniversary exhibition because the Louvre refused to attribute the work fully to Leonardo.

by Alison Cole of The Art Newspaper. Scanned copies of the confidential report became prized possessions among prominent Leonardo experts across the world, and The New York Times obtained multiple copies.

Experts at the Center for Research and Restoration of the Museums of France, an independent culture ministry institute, used fluorescent X-rays, infrared scans and digital cameras aimed through high-powered microscopes to match signature details of the materials and artistic techniques in the “Salvator Mundi” with the Louvre’s other Leonardo masterpieces.

The thin plank of wood on which the “Salvator Mundi” was painted was the same type of walnut from Lombardy that Leonardo used in other works. The artist had mixed fine powdered glass in the paint, as Leonardo did in his later years.

Traces of hidden painting under the visible layers, details in the locks of Christ’s hair, and the shade of bright vermilion used in the shadows all pointed to the hand of Leonardo, the report concluded.

“All these arguments tend to favor the idea of an entirely ‘autographed’ work,” Vincent Delieuvin, one of two curators of the anniversary exhibition, wrote in a lengthy essay describing the examination, noting that the painting had been “unfortunately damaged by bad conservation” and by “old, unquestionably too brutal restorations.”

Jean-Luc Martinez, the Louvre president, was even more definitive. “The results of the historical and scientific study presented in this publication allow us to confirm the attribution of the work to Leonardo da Vinci,” he wrote in the preface. (His current term is set to end this month, and President Emmanuel Macron of France is overdue to announce whether he will extend Mr. Martinez’s tenure or appoint a new leader.)

The Louvre was so eager to include the “Salvator Mundi” in its anniversary exhibition that the curators planned to use an image of the painting for the front of its catalog, officials said.

But the Saudis’ insistence that the “Salvator Mundi” also be twinned with the “Mona Lisa” was asking too much, the French officials said.

Extraordinary security measures surrounding the “Mona Lisa” make the painting exceptionally difficult to move from its place on a special partition in the center of the Salle des États, a vast upstairs gallery. Placing a painting next to it would be impossible, the French officials argued.

Franck Riester, the French culture minister at the time, tried for weeks to mediate, proposing that as a compromise the “Salvator Mundi” could move close to the “Mona Lisa” after a period in the anniversary show, the French officials said. .

And even after the exhibition opened without the “Salvator Mundi,” in October 2019, French officials kept trying.

Prince Bader bin Farhan al-Saud, an old friend of Crown Prince Mohammed who had acted as his surrogate bidder for the “Salvator Mundi,” had later been named Saudi Arabia’s minister of culture. When he happened to visit to Paris, the French culture minister and Louvre president led him on a private tour of the museum and exhibition to try to persuade him to lend the painting, the French officials said.

A spokesman for the Saudi Embassy in Washington declined to comment.

A planned section of the catalog detailing the authentication was removed before publication, and the museum ordered that all copies of the report be locked away in storage.

Sophie Grange, a Louvre spokeswoman, said museum officials would be forbidden to discuss any such document because French rules prohibited disclosing any evaluation or authentication of works not shown in the museum.

Corinne Hershkovitch, a leading French art lawyer, said these “long-held traditions” had been “formalized by law in 2013, in a decree establishing the status of heritage conservators.”

But with the French refusing to talk about the painting and the Saudis refusing to show it, the proliferating questions about the painting have taken a toll, said Robert Simon, a New York art dealer involved in the rediscovery of the “Salvator Mundi.”

“It is soiled in a way,” he said, “because of all this unwarranted speculation.”

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Why We’re Freaking Out About Substack

Isaac Saul, who told me his nonpartisan political newsletter Tangle brought in $190,000 in its first year, wrote recently that he came to Substack “specifically to avoid being associated with anyone else” after being frustrated by readers’ assumptions about his biases when he worked for HuffPost.

One of the writers who left Substack over transgender issues, Jude Doyle, argued that its system of advances amounted to a kind of editorial policy. But the analogy to a media company isn’t clear. Grace Lavery said she wanted Substack to broaden its definition of harassment, but said she didn’t think threats to boycott the email service over writers she disagrees with made political sense. She has had bitter public disputes with other Substack writers, including the journalist Jesse Singal, over their writing on gender policy. “Boycotting Substack because of Jesse Singal would be like boycotting a paper company” over a writer who has books printed on their paper, she said.

Mr. Singal compared Substack with the unregulated, decentralized internet of a decade ago. “In the golden age of blogging, writers hated each other but they went back and forth over each other’s ideas. Now, people call the manager all the time,” he said.

So the biggest threat to Substack is unlikely to be the Twitter-centric political battles among some of its writers. The real threat is competing platforms with a different model. The most technically powerful of those is probably Ghost, which allows writers to send and charge for newsletters, with monthly fees starting at $9. While Substack is backed by the venture capital firm Andreessen Horowitz, Ghost has Wikipedia vibes: It is open-source software developed by a nonprofit.

One of Substack’s biggest newsletters, The Browser, with 11,000 paid subscribers, left for Ghost last August. Nathan Tankus, an economics writer who is leaving Substack over trans issues, has also moved to Ghost. David Sirota, who runs the left-leaning investigative site The Daily Poster, said he was considering leaving for Outpost, a system built on Ghost, because “we want our operation and our brand to stand on its own.”

And it’s easy to leave. Unlike on Facebook or Twitter, Substack writers can simply take their email lists and direct connections to their readers with them.

Substack’s model of taking 10 percent of its writers’ subscriptions is “too greedy of a slice to take of anyone’s business with very little in return,” said Ghost’s founder and chief executive, John O’Nolan, a tattooed, nomadic Irishman who is bivouacked in Hollywood, Fla. He said he believed subscription newsletter publishing was “destined to be commoditized.”

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A Soviet ‘Lord of the Rings’ Is Unearthed, Epic in Its Own Way

Arseny Bulakov, the chairman of the St. Petersburg Tolkien Society, called the production “a very revealing artifact” of its era: “filmed in destitute times, without stage settings, with costumes gathered from acquaintances — and at the same time with great respect for Tolkien and love for his world.”

Mr. Bulakov said it reminded him “of the early years of Tolkienists” in Russia. “Not getting paid for half a year, dressed in old sweaters, they nevertheless got together to talk about hobbits and elves, to rewrite elvish poems by hand, to try to invent what was impossible to truly know about the world.”

Tolkien’s books were hard to find for decades in the Soviet Union, with no official translation of “The Hobbit” until 1976 — “with a few ideological adaptations,” according to Mark Hooker, the author of “Tolkien Through Russian Eyes.” But the “Rings” trilogy was “essentially banned” for decades, he said, perhaps because of its religious themes or the depiction of disparate Western allies uniting against a sinister power from the East.

In 1982, an authorized and abridged translation of “Fellowship” became a best seller, Mr. Hooker said. Translators started making unofficial, samizdat versions in the years that followed — translating and typing out the entire text on their own.

“Khraniteli” was broadcast at a moment of “great systemic turmoil” as the Soviet Union was dismantled, and part of “the flood of ideas that rushed in to fill the vacuum,” Mr. Hooker said. “For the average Russian, the world had turned upside-down.”

Irina Nazarova, an artist who saw the original broadcast in 1991, told the BBC that in retrospect, the “absurd costumes, a film devoid of direction or editing, woeful makeup and acting — it all screams of a country in collapse.”

Mr. Hooker compared the production itself to a samizdat translation, “with all the rough edges.” Among them are wobbling cameras, as though the hobbits were filming their journey with a camcorder, and sudden cuts to a narrator who, smoking a pipe or smiling silently, sometimes seems content to leave his audience in the dark.

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Has the Era of Overzealous Cleaning Finally Come to an End?

When the coronavirus began to spread in the United States last spring, many experts warned of the danger posed by surfaces. Researchers reported that the virus could survive for days on plastic or stainless steel, and the Centers for Disease Control and Prevention advised that if someone touched one of these contaminated surfaces — and then touched their eyes, nose or mouth — they could become infected.

Americans responded in kind, wiping down groceries, quarantining mail and clearing drugstore shelves of Clorox wipes. Facebook closed two of its offices for a “deep cleaning.” New York’s Metropolitan Transportation Authority began disinfecting subway cars every night.

But the era of “hygiene theater” may have come to an unofficial end this week, when the C.D.C. updated its surface cleaning guidelines and noted that the risk of contracting the virus from touching a contaminated surface was less than 1 in 10,000.

“People can be affected with the virus that causes Covid-19 through contact with contaminated surfaces and objects,” Dr. Rochelle Walensky, the director of the C.D.C., said at a White House briefing on Monday. “However, evidence has demonstrated that the risk by this route of infection of transmission is actually low.”

primarily through the air — in both large and small droplets, which can remain aloft longer — and that scouring door handles and subway seats does little to keep people safe.

who wrote last summer that the risk of surface transmission had been overblown. “This is a virus you get by breathing. It’s not a virus you get by touching.”

The C.D.C. has previously acknowledged that surfaces are not the primary way that the virus spreads. But the agency’s statements this week went further.

“The most important part of this update is that they’re clearly communicating to the public the correct, low risk from surfaces, which is not a message that has been clearly communicated for the past year,” said Joseph Allen, a building safety expert at the Harvard T.H. Chan School of Public Health.

Catching the virus from surfaces remains theoretically possible, he noted. But it requires many things to go wrong: a lot of fresh, infectious viral particles to be deposited on a surface, and then for a relatively large quantity of them to be quickly transferred to someone’s hand and then to their face. “Presence on a surface does not equal risk,” Dr. Allen said.

In most cases, cleaning with simple soap and water — in addition to hand-washing and mask-wearing — is enough to keep the odds of surface transmission low, the C.D.C.’s updated cleaning guidelines say. In most everyday scenarios and environments, people do not need to use chemical disinfectants, the agency notes.

“What this does very usefully, I think, is tell us what we don’t need to do,” said Donald Milton, an aerosol scientist at the University of Maryland. “Doing a lot of spraying and misting of chemicals isn’t helpful.”

Still, the guidelines do suggest that if someone who has Covid-19 has been in a particular space within the last day, the area should be both cleaned and disinfected.

“Disinfection is only recommended in indoor settings — schools and homes — where there has been a suspected or confirmed case of Covid-19 within the last 24 hours,” Dr. Walensky said during the White House briefing. “Also, in most cases, fogging, fumigation and wide-area or electrostatic spraying is not recommended as a primary method of disinfection and has several safety risks to consider.”

And the new cleaning guidelines do not apply to health care facilities, which may require more intensive cleaning and disinfection.

Saskia Popescu, an infectious disease epidemiologist at George Mason University, said that she was happy to see the new guidance, which “reflects our evolving data on transmission throughout the pandemic.”

But she noted that it remained important to continue doing some regular cleaning — and maintaining good hand-washing practices — to reduce the risk of contracting not just the coronavirus but any other pathogens that might be lingering on a particular surface.

Dr. Allen said that the school and business officials he has spoken with this week expressed relief over the updated guidelines, which will allow them to pull back on some of their intensive cleaning regimens. “This frees up a lot of organizations to spend that money better,” he said.

Schools, businesses and other institutions that want to keep people safe should shift their attention from surfaces to air quality, he said, and invest in improved ventilation and filtration.

“This should be the end of deep cleaning,” Dr. Allen said, noting that the misplaced focus on surfaces has had real costs. “It has led to closed playgrounds, it has led to taking nets off basketball courts, it has led to quarantining books in the library. It has led to entire missed school days for deep cleaning. It has led to not being able to share a pencil. So that’s all that hygiene theater, and it’s a direct result of not properly classifying surface transmission as low risk.”

Roni Caryn Rabin contributed reporting

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Biden’s Tax Plan Aims to Raise $2.5 Trillion and End Profit-Shifting

WASHINGTON — Large companies like Apple and Bristol Myers Squibb have long employed complicated maneuvers to reduce or eliminate their tax bills by shifting income on paper between countries. The strategy has enriched accountants and shareholders, while driving down corporate tax receipts for the federal government.

President Biden sees ending that practice as central to his $2 trillion infrastructure package, pushing changes to the tax code that his administration says will ensure American companies are contributing tax dollars to help invest in the country’s roads, bridges, water pipes and other parts of his economic agenda.

On Wednesday, the Treasury Department released the details of Mr. Biden’s tax plan, which aims to raise as much as $2.5 trillion over 15 years to help finance the infrastructure proposal. That includes bumping the corporate tax rate to 28 percent from 21 percent, imposing a strict new minimum tax on global profits and levying harsh penalties on companies that try to move profits offshore.

The plan also aims to stop big companies that are profitable but have no federal income tax liability from paying no taxes to the Treasury Department by imposing a 15 percent tax on the profits they report to investors. Such a change would affect about 45 corporations, according to the Biden administration’s estimates, because it would be limited to companies earning $2 billion or more per year.

President Donald J. Trump’s 2017 tax cuts. Biden administration officials say that law increased the incentives for companies to shift profits to lower-tax countries, while reducing corporate tax receipts in the United States to match their lowest levels as a share of the economy since World War II.

Treasury Secretary Janet L. Yellen, in rolling out the plan, said it would end a global “race to the bottom” of corporate taxation that has been destructive for the American economy and its workers.

“Our tax revenues are already at their lowest level in generations,” Ms. Yellen said. “If they continue to drop lower, we will have less money to invest in roads, bridges, broadband and R&D.”

The plan, while ambitious, will not be easy to enact.

Some of the proposals, like certain changes to how a global minimum tax is applied to corporate income, could possibly be put in place by the Treasury Department via regulation. But most will need the approval of Congress, including increasing the corporate tax rate. Given Democrats’ narrow majority in both the Senate and the House, that proposed rate could drop. Already, Senator Joe Manchin III of West Virginia, a crucial swing vote, has said he would prefer a 25 percent corporate rate.

search of the lowest possible tax bill.

Companies also shift jobs and investments between countries, but often for different reasons. In many cases, they are following lower labor costs or seeking customers in new markets to expand their businesses. The Biden plan would create new tax incentives for companies to invest in production and research in the United States.

weakened by subsequent regulations issued by Mr. Trump’s Treasury Department.

Conservative tax experts, including several involved in writing the 2017 law, say they have seen no evidence of the law enticing companies to move jobs overseas. Mr. Biden has assembled a team of tax officials who contend the provisions have given companies new incentives to move investment and profits offshore.

Mr. Biden’s plan would raise the rate of Mr. Trump’s minimum tax and apply it more broadly to income that American companies earn overseas. Those efforts would try to make it less appealing for companies to book profits in lower-tax companies.

The S.H.I.E.L.D. proposal is an attempt to discourage American companies from moving their headquarters abroad for tax purposes, particularly through the practice known as “inversions,” where companies from different countries merge, creating a new foreign-located firm.

Under current law, companies with headquarters in Ireland can “strip” some of their profits earned by subsidiaries in the United States and send them back to the Ireland company as payments for things like the use of intellectual property, then deduct those payments from their American income taxes. The S.H.I.E.L.D. plan would disallow those deductions for companies based in low-tax countries.

Tax professionals say Mr. Biden’s proposed changes to that law could be difficult to administer. Business groups say they could hamper American companies as they compete on a global scale.

Republicans denounced the plan as bad for the United States economy, with lawmakers on the House Ways and Means Committee saying that “their massive tax hikes will be shouldered by American workers and small businesses.”

coupled with an effort through the Organization for Economic Cooperation and Development to broker a global agreement on minimum corporate taxation, will start a worldwide revolution in how and where companies are taxed. That is in part because the Biden plans include measures meant to force other countries to go along with a new global minimum tax that Ms. Yellen announced support for on Monday.

Treasury Department officials estimate in their report that the proposed changes to the minimum tax, and the implementation of the S.H.I.E.L.D. plan, would raise an estimated $700 billion over 10 years on their own.

Business groups warn the administration’s efforts will hamstring American companies, and they have urged Mr. Biden to wait for the international negotiations to play out before following through with any changes.

Members of the Business Roundtable, which represents corporate chief executives in Washington, said this week that Mr. Biden’s minimum tax “threatens to subject the U.S. to a major competitive disadvantage.” They urged the administration to first secure a global agreement, adding that “any U.S. minimum tax should be aligned with that agreed upon global level.”

However, some companies expressed an openness on Wednesday to some of the changes.

John Zimmer, the president and a founder of Lyft, told CNN that he supported Mr. Biden’s proposed 28 percent corporate tax rate.

“I think it’s important to make investments again in the country and the economy,” Mr. Zimmer said. “And as the economy grows, so too does jobs and so too does people’s needs to get around.”

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