# A prime system with many self-joinings

## TL;DR

This paper constructs a unique example of a prime dynamical system with specific rigidity and rank properties, whose self-joinings form a Paulsen simplex, highlighting a novel structure in ergodic theory.

## Contribution

It presents the first known example of a prime system with self-joinings forming a Paulsen simplex, expanding understanding of self-joining structures in ergodic systems.

## Key findings

- Constructed a rigid, rank 1, prime transformation
- Demonstrated the self-joinings form a Paulsen simplex
- First example of such a prime system with this property

## Abstract

We construct a rigid, rank 1, prime transformation that is not quasi-simple and whose self-joinings form a Paulsen simplex. This seems to be the first example of a prime system whose self-joinings form a Paulsen simplex.