Three Versions of Schrödinger's Cat: Are Atoms of the Same Element Identical?

This preprint advances the claim that atoms of the same isotope are not strictly identical: differences in nuclear microstructure and history make their decay behavior discretely individual. I revisit Schrödinger’s tiny-sample setup, Einstein’s framing, and the popular single-atom retelling. The first two can be viewed as ensembles—multiples of the third—and the single-atom lens makes the initial-time issue explicit: starting today versus starting tomorrow selects different points along an ongoing, irreversible process; swapping in and out of a box does not reset the process. Hence, the familiar “50% in one hour” probability is personal (i.e., time-dependent)—a modeling choice tied to the chosen t0, not a physically grounded restart condition. I develop a discrete, AI-inspired logic to formalize these points and discuss implications for interpretation, measurement, and practical heuristics (e.g., fusion).