Ledecky, who came up maddeningly short in her world-record bid in the 400 freestyle Sunday, offered another explanation: numerology. She informed Gemmell afterward that she won the 800 freestyle at the London Olympics on Aug. 3, 2012, and set her first world record in the 800 at the 2013 world championships on Aug. 3. Monday was another Aug. 3 — and she was in the third heat to boot.

Ledecky’s world record was the first of three set on the second day of the meet. In the evening session, Sarah Sjostrom of Sweden lowered her day-old mark in the 100 butterfly by a hundredth of a second, winning in 55.64 seconds. Katinka Hosszu of Hungary broke the longest-standing individual women’s world record with a 2:06.12 in the 200 individual medley. She surpassed the American Ariana Kukors’s 2:06.15, recorded in 2009 in a suit that has since been outlawed.

The women’s 1,500 final is Tuesday, and Ledecky hopes it will serve as a similarly sublime warm-up for the 200-meter freestyle semifinals that will follow roughly 20 minutes later. The 200 freestyle has a marquee field that includes the defending champion — and Ledecky’s teammate — Missy Franklin.

Franklin, who left the pool before Ledecky’s race to rest for her 100-meter backstroke semifinal, was eating lunch when she heard about the record. “Katie’s so special in that some people might almost get used to breaking a world record every time they swim,” Franklin said. “But I feel like she really, really appreciates it, but she also doesn’t do it for the world record. She’s just going out there and trying to be her best, and that just happens to be a world record.”

It must be a sinking feeling for Ledecky’s rivals, many of whom are accustomed to setting the pace and swimming from ahead, to be falling farther and farther behind. How do they relax and be their best when they are getting lapped on a world stage? Before she was done, Ledecky had lapped the swimmers in Lanes 1, 8 and 9. The competitor in Lane 1 happened to be her teammate Katy Campbell, a U.C.L.A. standout who won the national title in the 1,500 free last summer after Ledecky scratched.

Campbell, who finished 1 minute 12 seconds behind Ledecky, said, “I mean, it’s tough racing her, but you know you’re racing the best, and you know that if you can get close to her, you are probably one of the best, too.”