The dynamics of binary alternatives for a discrete pregeometry

TL;DR

This paper explores a stochastic model of discrete pregeometry using directed dyadic acyclic graphs, aiming to identify self-organized structures that could represent physical objects.

Contribution

It introduces a binary-alternative-based dynamics for graph growth, linking paths to binary outcomes, and discusses the emergence of self-organized structures.

Findings

Probabilistic growth model for directed dyadic acyclic graphs

Analysis of self-organized structures within the graph

Potential connection to physical objects

Abstract

A particular case of a causal set is considered that is a directed dyadic acyclic graph. This is a model of a discrete pregeometry on a microscopic scale. The dynamics is a stochastic sequential growth of the graph. New vertexes of the graph are added one by one. The probability of each step depends on the structure of existed graph. The particular case of dynamics is based on binary alternatives. Each directed path is considered as a sequence of outcomes of binary alternatives. The probabilities of a stochastic sequential growth are functions of these paths. The goal is to describe physical objects as some self-organized structures of the graph. A problem to find self-organized structures is discussed.