The same real lmsim run's exact-count crossings at one, two, and three half-lives, showing the real gap from the nominal mark growing as fewer real nuclei remain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The relative gap is small at the first two half-lives

The real remaining-count crossings at one and two half-lives land at t=4.9970 and t=10.0360 seconds, within a real 0.0600 and 0.3600 percent of their nominal marks.

0.0600<0.36000.0600<0.3600
Real crossing gap across further half-livesEach real crossing sits near its own nominal half-life multiple; the gap grows.n=1: real=4.9970 s, gap=0.0600%n=2: real=10.0360 s, gap=0.3600%

The gap widens further at the third half-life

The real crossing at three half-lives lands at t=14.2278 seconds, a real 5.1480 percent gap from its nominal mark — the largest of the three, because fewer real nuclei remain to average over.

0.3600<5.14800.3600<5.1480
Real crossing gap across further half-livesEach real crossing sits near its own nominal half-life multiple; the gap grows.n=1: real=4.9970 s, gap=0.0600%n=2: real=10.0360 s, gap=0.3600%n=3: real=14.2278 s, gap=5.1480%