Introduction
This semester, the Ping Pong Group finished its work from the previous two semesters of TXGL. We finalized an algorithm which worked with a generalized version of the Ping Pong Lemma to find intervals of \(\mathbb{RP}^1\) meeting certain containment conditions which guarantee the faithfulness of a particular group representation in \(\text{SL}(2, \mathbb{R})\). To showcase our work, we create a new visualization tool in the GitHub repository along with a web-based demo of a few valid intervals we found for a cyclic free product, triangle group, and surface group.