This paper presents a new visual framework for understanding the reduction and elimination steps used to solve Catalan's Conjecture, famously known as Mihailescu's Theorem. Rather than relying solely on separate algebraic equations, this approach maps the exponents of the Diophantine equation onto a two-dimensional coordinate grid. By applying established historical milestones as structural filters, we show how the vast majority of the infinite solution space can be systematically scrubbed.First, we utilize Chao Ko's and Lebesgue's proofs to eliminate all even powers from the grid space. Second, we apply the prime power reduction rule to remove composite odd powers, simplifying the problem to unique odd prime exponents. Prime exponents are all that remain. Finally, we demonstrate a domino effect where the systematic removal of a baseline prime automatically filters out all future higher-power multiples.The resulting grid view does not replace the algebraic proofs, but instead organizes them into a cohesive, scannable architecture. This visual model bridges the gap between raw algebra and structural geometry, offering a valuable utility for educational demonstrations and algorithmic filtering tools in number theory.