LONDON — Sprinting across the finish line in the women’s 4 x 100-meter relay, Carmelita Jeter extended her left arm and pointed toward the clock. The time was almost unfathomable. The accomplishment was almost entirely unexpected: 40.82 seconds. World record. The US women earned redemption, then history with its gold-medal performance in the relay.

The US shattered East Germany’s nearly 27-year-old record (41.37), a mark once thought untouchable. It was set during years of systematic doping by East German athletes. The US also rewrote the East German’s Olympic record (41.60) set at the 1980 Moscow Games.