I use Spider Project which have some functionality to work for Fragments and Reference Books that P6 does not so I will limit my suggestion to what I believe you can mimic in P6.

To apply this procedure you must estimate first and last controlling activity dates of your fragment within the update period and use the factors to do the math for approximate durations that will make some sense. If your fragment started you need that date, if finished or still in progress you need the information regarding the completed or partially completed activity(es).

For each short duration schedule fragment:

1. Create a separate small schedule,
2. set the fragment start equal to actual activity start,
3. using formulas or the P6 equivalent - global changes adjust the activities duration in small increments so that the same formula can be used in sequential,
4. run the adjustments until target date for your controlling activity is matched,
5. use the dates before DD of the segment to update your schedule. If you have intermediate date actual you can update and apply the scaling to intermediate updates depending on how much granularity you want.
6. For partially completed fragments you can estimate remaining duration of activities by updating the adjusted fragnet as planned to update DD.
7. About lag you can figure it out if you want to apply a factor to time lags.

We have, with fragments, that we can define some activities to be scalable and other that have  fixed duration for example concrete curing is not scalable, but this you can consider with the use of filters. The following is an example of how it might be implemented within P6.

I am using finish date of activity 5 as my target date of controlling activity but if not finished it could be - Fit to start date.

As you can deduct the scale factor came out to be 1.34 = 4.03/3 = 5.38/4.00.

You can optionally create a user defined field to record which dates are real actual dates and which dates are approximate, making the update transparent to others for their understanding.

For shorter activity durations you might need to display dates with seconds.

This is an idea on the works as I have never been in such need.

Best regards,

Rafael