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<0.3600
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.