The Rule：{{x, y}, {y, z}} -> {{x, z}, {x, w}, {w, z}}
This model investigates the emergence of causal geometry from a minimal graph-rewriting rule.
Unlike standard branching trees, this rule facilitates state merging (interference), mimicking a Dynamic Programming optimization process within the causal graph.
The evolution demonstrates Markovian properties where the spatial structure ('ripple') expands purely based on local connectivity, creating a discrete spacetime fabric that exhibits Causal Invariance. This serves as a computational candidate for interpreting the 'Many-Worlds' path integral as a deterministic graph optimization problem.
Proposed Model Description (Short Explanation)
Nodes represent discrete universe slices (microstates of spacetime).
Each node encodes a complete instantaneous configuration of the universe.
Directed edges represent causal relations between slices.
An edge from node A to node B indicates that B is a possible successor state generated from A.
The network is constructed through a recursive update process combining
(1) a Markov-style probabilistic transition rule, and
(2) a deterministic local causal rule.
Together, these govern how new spacetime slices branch and evolve.
A path from the root to any node corresponds to a possible history of the universe.
Compressing such a path yields the emergent notions of time and macroscopic causality.
The diagrams shown depict the evolving causal structure and the resulting spatial slice (wavefront) produced by these rules.
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