  We prove essentially optimal fine-grained lower bounds on the gap between a
data structure and a partially retroactive version of the same data structure.
Precisely, assuming any one of three standard conjectures, we describe a
problem that has a data structure where operations run in $O(T(n,m))$ time per
operation, but any partially retroactive version of that data structure
requires $T(n,m) \cdot m^{1-o(1)}$ worst-case time per operation, where $n$ is
the size of the data structure at any time and $m$ is the number of operations.
Any data structure with operations running in $O(T(n,m))$ time per operation
can be converted (via the "rollback method") into a partially retroactive data
structure running in $O(T(n,m) \cdot m)$ time per operation, so our lower bound
is tight up to an $m^{o(1)}$ factor common in fine-grained complexity.
