Six years ago, she was diagnosed with Alzheimer’s disease. The illness is particularly common among African Americans, and it struck B. Smith at her prime; it ravaged her brain, jumbling her memories, turning her sentences into alphabet soup.

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Not long after, B.’s restaurants shuttered. Her appearances dried up. With Dan Gasby, her husband and business partner of more than two decades, she turned her efforts to speaking about Alzheimer’s and advocating for research. Then, she didn’t do much talking at all.

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But Dan turned to social media. He took over their Facebook page, sending near-daily missives to their 30,000 followers on the realities of caring for a spouse who was rapidly forgetting him — the fear she’d developed, her anger and frustration, his own.

Then, in December, Dan posted a Facebook photo of himself with a woman with a thick blond mane and delicate features. They are beaming, a dapper couple out to dinner. But the caption referenced, of all things, an old rap song by 50 Cent and the Game. “Hate it or love it,” it read. “You can debate, but for me, I’m feelin’ great.” He even used a hashtag: #whylie.

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Dan had never been the type to bite his tongue, never bothered with niceties.

At 64, he had a wife, and he had a girlfriend named Alex Lerner. He was happy and in love.

And, well, why lie?

In sickness and in health. Every day, people say the words. But what could they possibly mean to you, until you've experienced sickness? B. and Dan and Alex are reckoning with it still.

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A few days after Christmas, they were together under one roof. B. was munching on pretzels as she circled the living room. One of their five hulking Italian mastiffs was snoring contentedly on the floor.

“Hellllllo!” B. said as she shuffled over to Alex, whom she has come to know only as her friend.

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“How are you?” Alex, 53, asked warmly. She has a room in this house, where she stays when she makes the roughly two-hour drive from her Manhattan home.

“Wait, wait, wait, lemme, Barbara,” B. said, wrapping Alex in a hug. “I was talking over there, with the baby . . . that was caught late . . . she’s a little, you know. We were there, we played candy, we do it all the time.”

Alex smiled and nodded, though she knew there was no baby. B. is still a charmer, quick to join conversations, full of laughter. But her sentences are often just words, incongruously strung together.

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They settled onto a leopard-print sofa, where Dan was describing his family’s new dynamic: “If ‘This Is Us’ and ‘Modern Family’ came together, it would be us,” he said.

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But it’s almost impossible to know what B. would have to say about it. Dan has told her that Alex is his girlfriend, and he said it doesn’t seem to register. And so a sea of Internet critics has taken up her cause.

“You don’t bring your mistress in the house where your WIFE lives. She’s not dead,” one wrote on Facebook this month.

“She’s having her lifestyle funded by a black woman, and this white woman didn’t have to build a thing with you,” a YouTube vlogger inveighed in one video that has racked up more than 100,000 views and thousands of unsympathetic comments.

They’ve called for court intervention, a petition or anything that might save B. Smith from what, to them, looks at best like cruelty and at worst, predation.

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It riles Dan to hear how many of them assume he’s some kind of Svengali, manipulating B., living off his wife’s success, when he’d helped make it reality.

So, on social media, he pokes back. “Especially the ones who have a direct line with The Almighty I need your heavenly insights!” he wrote sarcastically in one recent Facebook post.

Dan’s overshare-y online behavior exasperates Dana, 32, his daughter from a previous marriage. “I tell him all the time to be careful with what he posts,” she said, shrugging. “I say: ‘Look, you’re going to make people mad. You either have to be okay with that, or you have to change.’ ”

Dan believes that his critics are racists who have targeted him because he happens to love a white woman, suggesting “that I’m flaunting her,” he said, looking at Alex.

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“I have been married to a black woman for 26 years,” he said. “I have a PhD in black love.”

Alex reached over and touched B.’s hand, and then got up to pour her some ginger ale.

Barbara Elaine Smith met Dan Gasby in the dining room of her first B. Smith's restaurant, not far from Times Square.

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A girl from rural Pennsylvania, B. worked as a babysitter, a governess and a lounge singer till she got her big break in modeling: In 1976, she became the second black woman to snag the cover of Mademoiselle. The work dispatched her to France and Italy, where she lived for a time, learning to love food, drink and beautiful things. At what seemed like the height of her career, she seemed to simply sashay into the restaurant business.

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Dan was a tall TV executive who had been executive producer of the Essence Awards. When he first saw B., glamorous and poised, so good at making others feel good, he thought, “I wish I had someone in my family like her.”

They’d both been married before. But this coupling was synergistic.

At their 1992 wedding, Dan didn’t use flowery prose to describe their relationship. He used sports terminology. He and B. were each other’s cutmen, he told the models and city officials and celebrities who attended. “A cutman,” Dan explained, “is the guy in the corner of the boxing ring who cleans up fighters and sends them back to battle.”

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“We’ll always be in each other’s corner,” he concluded.

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They managed 18 happy years before B. got sick. She scored a television show, “B. Smith With Style,” and a regular stint on the “Today” show; launched a magazine; and opened three successful restaurants. (At Washington’s Union Station for nearly 20 years, B. and Dan ran what one critic called “the grandest dining room on the Hill and maybe in the city.”) She still has home goods for sale at Bed Bath & Beyond.

She parented his daughter, Dana, teaching her a love for cooking. Their house bustled with famous friends, Dana recalled, such as Aretha Franklin and Maya Angelou. Dan was by B.’s side for all it.

He was there when B., whom Dan teasingly called “one-take Barbie,” was explaining her chicken wings recipe to Savannah Guthrie on a “Today” show cooking demo and went completely blank.

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“This is what I do,” she began. “I marinate it in reduced . . . ummm . . .” Guthrie tried to help, to fill in the blanks like a game of Mad Libs, but B. could not remember the name of the liquid in the bowl right in front of her. Her diagnosis came not long after.

There had been signs. Dana saw them in 2008, when she was away attending American University. “We would have the same conversation three times in one day,” she recalled. B. also told her she felt a tingling in her face. “I WebMD’d it, and I said, ‘Oh, she has Alzheimer’s.’ ”

B. and Dan brushed her off.

“You know how, if you didn’t know a hurricane was coming,” Dan explained all these years later, “you would think it was only raining?”

For most of their marriage, B. and Dan split their time between a swanky Manhattan flat and a home on the water in Sag Harbor, a historic beachfront refuge for New York's African American elites. As her Alzheimer's progressed, B. began walking out the door, only to turn up later somewhere on the beach, located by neighbors.

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All the while, she continued to make appearances. “She was quite brilliant in making you feel that she was fine; she could carry it off if she just talked in short sentences and let Dan pick up the slack,” said Michael Schnayerson, a journalist who co-wrote the couple’s 2015 book on Alzheimer’s, “Before I Forget.”

But B. could not hide it forever. She made the newspapers in 2014 when, on her way to Sag Harbor from the city, she hopped off her bus and somehow ended up back in New York alone. She walked to Harlem and ferried to Staten Island and bused back to Manhattan before finally being recognized in a cafe in Midtown the next day, Dan revealed on Facebook later, adding, oddly, “So there are no rumors.”

Soon after, they moved to this East Hampton house, a sleek white box with a tennis court and a pool, in a clearing on 10 otherwise wild acres. But its primary draw was its gate, so B. could no longer wander away.

The reviews and interviews, the glossy ads in which she sold Vaseline lotion or sportswear have been tucked into a room devoted to B.’s achievements, few of which she can remember. As Dana pored over them that day in December, B. walked over to look, fixating on a photo she had taken with Dan years ago. “He’s handsome,” she said. She didn’t know who the woman in the photo was.

Dana moved back home to help in the caregiving. “B. is my mom,” she said. But even B.’s smile, Dana said, has changed somehow. So much has.

Dan and Alex had long been in each other's orbit, two minor planets in Hamptons society.

Dan has a confidence — money, we are certain — that makes strangers wonder aloud whether he is Morgan Freeman or Denzel Washington. (“I’m Denzel Freeman,” he likes to tell them.) Alex, who was born in Germany, nervously tugs at her expensive sweaters, drives a Porsche and casually corrects his pronunciation of “Balazs,” as in Andre, the famed hotelier.

Both were posted up at the same bar one night in summer 2017, when Alex, a few stools over, happened to overhear Dan talking with a friend. She recognized something in him, the same feeling the mother of three had during her divorce: A despairing grief, so thick it enveloped him. A loneliness bubble.

Before she left, she leaned in and told Dan, “If you ever want to talk . . .” She left her number.

So he met her for coffee. Eventually, she told Dan that he ought to visit Le Bilboquet, the new Hamptons boîte that was all the rage. “You know I work there, right?” she asked him. “Aren’t you curious what it looks like?”

Le Bilboquet was the new tenant in the old B. Smith’s.

“Ron owes me an invitation,” he sniffed, meaning Ron Perelman, the billionaire, who was one of its owners. A couple of days later, Dan came strolling in.

For one Hamptons summer, it went on like this — chance encounters, innocent texts.

In their book, Dan admitted that he could be a bon vivant, that he enjoyed flirting. But, he wrote, he had never cheated on B.

So it all moved much more slowly than Tinder speed. “We were friends,” Alex said. “I didn’t want to go out with a married man.” Plus, she’d socialized with B. at charity events. But when Dan invited her to breakfast at a popular hotel with B., she accepted.

Finally, she saw. “This is not a man cheating on his wife,” she told herself. In the middle of breakfast, Alex helped B. to the bathroom.

Alex had a nurturing spirit. And she saw the same in him. “What I admire about him,” she said, “is that he takes care of her.”

Soon after, they started dating, with Dana's blessing. "When he told me," Dana said, "I was like, 'Thank God. I'm happy.' "

Despite the online response, those who know Dan and B. defend the relationship. “Anybody that would judge Dan knows nothing about the disease and the toll it takes” on a marriage, Schnayerson said. “If you can find a companion who can help you get through that, all power to you.”

Dana also pointed out that her father has not abandoned B. by any measure. “She’s in this house. She’s here every day,” she said.

And, on many days, so is Alex. “If I can be compassionate to her,” Alex said, her voice breaking, “if I can do anything for her, it makes me feel good. If it is giving her something to drink or making her something to eat — she loves to eat — I feel good.”

When B. was lucid, she and Dan sometimes clashed over his flirtations. Now, in photos and videos Dan posts on social media, his wife and his girlfriend seem like friends. But are they?

As they talked, B. was in the background, chatty. “Boop-boop-boop,” she said, interrupting. “This looks like a . . . no, I’m not going to say that. I’m not going to say that. I’m not going to say it. Over there. He’s not in there. He’s not in there,” she said. “The guy.”

“What’s his name? What’s her name?” Dan asked, gesturing at Alex.

B. didn’t answer.

“You okay?” Dan asked, softening a bit.

B. looked over at her husband.

“Mmm-hmm.”