A Reconstruction of Fermat's Marvelous Proof: Structural Mismatch on Integer Lattices

This paper provides a revolutionary reconstruction of Fermat's Last Theorem (FLT) by returning to the fundamental principles of arithmetic available during the 17th century. Departing from the complex machinery of modern elliptic curves and modular forms, the author, JUNE WOO KOO, proposes that the impossibility of integer solutions for $n \ge 3$ is a direct consequence of the "Collapse of Integer Order." The core argument establishes that while $n=2$ (Pythagorean triples) maintains a perfect resonance with the discrete integer lattice, higher-degree energy states ($n \ge 3$) create a structural mismatch. By decomposing the equation into its cyclotomic fragments, it is shown that these pieces cannot be simultaneously contained within the integer domain without "leaking" into irrationality. This mismatch triggers a mandatory Infinite Descent, leading to the logical extermination of any assumed solution. This work suggests that the integrity of the integer grid itself serves as a universal filter against high-degree instability.