So Dr. Hayworth urged Dr. Fahy to find some way for his work to be better validated. “We have to be able to see it to believe it,” he said.

In fact, there was one way Dr. Fahy had considered. He could fix the brain’s structure in place with chemicals first, just as Dr. Mikula was doing, buying time to perfuse the cryoprotectant more slowly to avoid dehydration. But he lacked the funds, he said, for a project that would have no practical business application for organ banking. Also, his company’s focus is on what he calls “reversible” cryopreservation, whereas fixing the brain’s structure in place with chemicals, as is done in chemopreservation, would place biological revival, the goal of many Alcor members, even farther out of reach.

Kim’s talk was well-received. Josh, watching from the audience, felt warmed by the applause that broke out several times during her short presentation. Yet he noticed her losing her train of thought more than once.

Inevitable Complications

In early November, Kim assigned her power of attorney to Josh. She understood, Josh later realized, better than he had, how little time she had left.

“I know that, Mom and Dad, you probably would respect my last wishes,” she said to her phone camera. “But Josh knows me best.”

Josh, who one year granted Kim’s birthday wish to dress her, now dressed her every day.

They had decided that Kim would die in the hospice Alcor had suggested near its headquarters in Scottsdale, one that would allow the cryonics team to be on hand with all its equipment so the preservation procedure could begin immediately. And after a sharp exchange, in which her father threatened to take Kim home with him to Florida, Mr. Suozzi backed down.

“Josh and I have only one thing in common,” Mr. Suozzi said with a certain reluctant admiration. “And that is our love for Kim.”