Large-scale AI/ML training systems depend on two assumptions that are rarely examined: (1) that checkpoints represent atomic snapshots of global training state, and (2) that infrastructure updates can be applied without inducing mixed-protocol cluster states. Both assumptions are instances of a deeper structural error: the Forward-In-Time-Only (FITO) category mistake, which confuses protocol convergence properties with temporal predicates. We formalize this confusion as a type error: the identification of a temporal snapshot $\mathsf{Snap}(t)$ with a convergence property $\mathsf{Conv}(\mathcal{P},e)$. We model checkpoint execution in a process-algebraic framework and prove that under asynchronous composition with crash-recovery failures, no temporal instant can serve as an atomicity boundary. We reformulate checkpoint inconsistency on an epoch lattice and show that atomicity is a measure-zero event whose complement grows exponentially with the number of independent persistence domains. We formalize mixed-epoch recovery as a type violation in the optimization algebra and show that the resulting update is not a valid step of any standard optimizer. For firmware fleet updates, we strengthen the known consensus-hardness result: atomic deployment requires not merely agreement but common knowledge of the epoch transition, which is strictly unattainable in asynchronous systems with unreliable communication. We conclude by sketching a bilateral convergence protocol, inspired by Open Atomic Ethernet, that achieves $\mathsf{Conv}(\mathcal{P},e)$ without requiring $\mathsf{Snap}(t)$ -- replacing the FITO assumption with constraint semantics.