Remark: Why the distinction is necessary

A coherent history with several supported readings cannot make the single classical number $T(e_{\mathrm{r}})$ equal several distinct $t_k$. Calling $t_k$ a geometric label is legitimate after $\kappa$ is supplied. Calling every such outcome the actual time of one fixed event would be false. Random classical selection among different reading events is another valid construction, but the event selection must then be included as classical input data.