Graph model overview, events scales structure and chains of events

TL;DR

This paper introduces a background independent graph model for spacetime emergence, emphasizing the role of colored combinatorial graphs, conformal expansion, and self-similarity across scales, with potential links to string theory.

Contribution

It presents a novel graph-based framework for modeling spacetime emergence using colored, conformally expanding graphs with hierarchical levels and connections to Clifford statistics.

Findings

Graph coloring determines cluster structures and loop types.

Conformal expansion preserves probability and induces self-similarity.

Emerging structures relate to strings and Clifford algebra concepts.

Abstract

We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on vertexes, endowed with a classical distribution of colors probability on the graph vertexes. The graph coloring determines the graph structure in clusters of graph vertices (events) that can be monochromatic (homogeneous loops) or polychromatic (inhomogeneous loops). The probability is conserved after the graph conformal expansion from an initial seed graph state to higher (conformally expanded) graph states. The emerging structure has self-similar characteristics on different scales (states). From the coloring, different levels of vertices and thus graph levels arise as new aggregates of colored vertices. In this second (derived) graphs level, the derived graph vertices correspond to the polychromatic edges (with differently colored vertices) of the initial graph. Vertex aggregates are related, as some levels (graph states) to plexors and twistors (involving Clifford statistics). Two metric levels are defined on the colored graph, the first level is a natural metric defined on the graph, the second level emerges from the first and related, due to symmetries. Metric structure reflects the graph colored structure under conformal transformations evolving with its states under conformal expansion. In some special cases vertices/events chains could be related to strings generalizations.