On the entropy bound of three dimensional simplicial gravity

TL;DR

This paper proves an exponential upper bound for the partition function in 3D simplicial gravity under a weaker assumption about sphere construction, advancing theoretical understanding of quantum gravity models.

Contribution

It establishes a new, weaker assumption for bounding the partition function of 3D simplicial gravity, improving theoretical insights into the model's behavior.

Findings

Partition function has an exponential upper bound.

The assumption on sphere construction is weaker than previous models.

Provides theoretical foundation for 3D quantum gravity analysis.

Abstract

It is proven that the partition function of 3-dimensional simplicial gravity has an exponential upper bound with the following assumption: any three dimensional sphere $S^3$ is constructed by repeated identification of neighboring links and neighboring triangles in the boundary of a simplicial 3-ball. This assumption is weaker than the one proposed by other authors.