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How can I determine the time value where a history curve takes a specific value?

Using Lookup, LookupMin and LookupMax

The Lookup function allows finding the value of t for a specified value of f(t) = F, where f(t) is a previously defined history. If such a value cannot be found, the largest value (within the specified bounds) of t in the history is returned. The LookupMin and LookupMax functions return the value of t at the minimum or maximum, respectively.

There is GUI support for the Lookup functions in the Function interface in the Stage dialog Responses panel.