How does the universe stay consistent everywhere if each part only checks its neighbors?
Each part fixes disagreements with its neighbors, and the result is consistent everywhere exactly when the records around every closed loop cancel, which no single pair can check. Three people in separate rooms each hold a coin. Each pair meets and records only same or different, and all three pairs record different. Any two records fit together. All three cannot, because counting different as 1, with one plus one making zero, the loop totals 1 where it needs 0. Wire twelve observers as the corners of a twenty-sided solid and repair brings all 2,048 starting states to the one consistent state. Flip one record and repair converges anyway, leaving exactly one unit of disagreement that can be moved and never removed. That stubborn leftover is what a particle turns out to be.
Also in Chapter 36: Why These Laws and Not Others?.
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 6: Why Isn't Agreeing With Your Neighbors Enough?watch a universe make its own particles