Explore the decidability bounds of Presburger arithmetic extended by sine in this 46-minute seminar talk by Eion Blanchard from the University of Illinois at Urbana-Champaign. Delve into the Model Theory Seminar series, examining previous results and extensions of Presburger arithmetic. Gain insights into the methodology, including visualization techniques and fine mesh analysis. Discover the encoding process, theorem formulation, and decidability implications. Investigate the Channels conjecture with practical examples and explore Boolean combinations. Conclude with a discussion on proxy solutions and their relevance to the extended arithmetic system.