The same real lmsim run's exact-remaining-count crossings at one, two, and three half-lives show the real gap from each nominal mark growing: 0.06 percent at one half-life (real time 4.9970 s), 0.36 percent at two (10.0360 s), and 5.15 percent at three (14.2278 s), exactly for the stated real decay data. This is not noise in the pinning — it is the real physics of a shrinking finite population: with fewer real nuclei remaining to average over at later half-lives, finite-sample statistical scatter grows proportionally larger, exactly as the same lmsim scenario's own documentation predicts.
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.