There's a 32 light year volume that encompass my whole history. The universe seems to preserve every point of my life to a resolution. If
https://en.wikipedia.org/wiki/Entropic_gravity turns out correct (or something like it), my life is preserved in perfect resolution across an increasingly large volume of space.
Separately:
There's no point in my life where I'm ever the same person. I've continually evolved.
With human history, the resolution of records continues to expand. Fossils, artifacts, writing, photos, and Google search logs all contain personal information. The resolution of historical information shows a clear trend.
Am I immortal if only a moment of my life is preserved, or am I immortal if all points of my life can be accurately be resimulated?
I would argue there is no difference. In order to resimulate me at any point in time, my context, my surroundings, must be considered. My context exists for historic reasons. In order for my brain to be interpretable its application in real world interactions must be considered the the world can only be understood by knowing its history.
To know me you need to know my life and surroundings at all points in time. Technology is slowing increasing the resolution of human immortality, although the universe seems to have already accomplished this perfectly.