A sequential growth dynamics for a directed acyclic dyadic graph

TL;DR

This paper introduces a stochastic sequential growth model for a directed acyclic dyadic graph, representing a discrete spacetime framework where particles emerge as symmetrical structures without relying on continuous spacetime concepts.

Contribution

It proposes a novel Markovian growth dynamics for a causal set-based discrete spacetime model, emphasizing self-organization and symmetry in particle-like structures.

Findings

Growth process is Markovian and causality-driven

Particles modeled as symmetrical self-organized structures

Framework avoids reliance on continuous spacetime

Abstract

A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical self-organized structures of the graph without any reference to continuous spacetime. The dynamics of the model is considered. This dynamics is stochastic sequential additions of new vertexes. Growth of the graph is a Markovian process. This dynamics is a consequence of a causality principle.