Remark: Which elementary errors are being counted

For the explicit ideal construction every error above is zero. For an approximate factorized logical implementation with $O({a_n}^{-1})$ charged elementary steps on a fixed physical journey, a uniform per-step error $o(a_n)$ is sufficient.

This last statement requires the specified logical factorization. It is not a claim that arbitrary errors coupling all registers in all blocks of a large conservative cone have only $O({a_n}^{-1})$ contributions. Such a model needs its own complete finite-channel error ledger.