Shortly after Mr. Ulbricht was sentenced, he received a letter from a French tech worker in Los Angeles, Caroline Debrion. She told him that she had followed the trial and thought he could use support. They exchanged letters almost every day.

“I dated so many jerks in L.A., and Ross was just very real and just super kind,” she said in 2021, according to a recording of a conversation with an associate obtained by The Times. “Ross is very, very romantic.”

Their relationship caused friction in the family. Ms. Ulbricht and Ms. Debrion sometimes butted heads, two people familiar with the women said. Against the wishes of Ms. Ulbricht, who had shielded her son from the media, Ms. Debrion helped persuade Mr. Ulbricht to participate in a Silk Road documentary, a last-ditch effort to sway public opinion.

Caroline, a volunteer and project manager for the FreeRoss website, clarified the case: "Ross has never been prosecuted for injury or death, or for endangering another person."

The design of FrontierMath differs from many existing AI benchmarks because the problem set remains private and unpublished to prevent data contamination

Problems in [the International Mathematical Olympiad] typically require creative insight while avoiding complex implementation and specialized knowledge [but for FrontierMath] they keep the first requirement, but outright invert the second and third requirement