Explore the concept of explicit near-fully X-Ramanujan graphs in this 22-minute IEEE conference talk by Ryan O'Donnell and Xinyu Wu from Carnegie Mellon University. Delve into the fascinating world of finite graphs that resemble infinite graphs, and discover how random finite graphs can exhibit similar properties. Examine the concept of d-regular trees and learn about graphs that spectrally resemble infinite structures. Investigate the role of adjacency matrices and formal polynomials in graph theory. Gain insights into the approach using finite permutations and matrix-weighted polynomials. Conclude with a discussion of the presenters' results and potential open problems in this field of study.