If every part of me changes, am I still the same person? (Ship of Theseus)
Replacing a ship's planks asks what kind of continuity the word same is meant to track. Material identity, functional organization and a continuous history can give different answers without contradiction. OPH approaches a person through an ongoing organization of records, self-reading and causal dependencies. Replacing matter can preserve that organization; keeping the same atoms need not preserve it. Two reconstructed copies could share memories and patterns while becoming distinct continuing episodes. Deciding whether either counts as the original requires an explicit account of personal identity and ownership. The observer framework makes those questions precise, but agreement about a physical description does not by itself prove that a person's first-person perspective survives copying.
See also If I were copied exactly, would the copy be me?, Are you your memories?, Why do many brain processes feel like one experience? (The combination problem)
Also in Chapter 40: Does It Feel Like Anything, and What Is Left to Decide?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 35: What Is Anything Made Of?watch a universe make its own particles