The Proof of the ABC Conjecture and the Completion of Its Historical Role — A Shift in Perspective through Fixing the Evaluation Order of Primes—

Abstract / Description This paper presents a proof of the ABC conjecture based on a structural reinterpretation of integer generation. Rather than approaching the conjecture through increasingly refined inequality techniques, this work identifies a prior structural issue: the ambiguity of evaluation order in the decomposition of integers into prime factors. By fixing the evaluation order through the CN2 interference structure and visualizing integer generation using the TK wave-integer diagram, the additive relation a + b = c is reinterpreted as a generative configuration rather than a purely arithmetic coincidence. Within this framework, the relationship expressed by the ABC conjecture emerges as a necessary consequence of the generation structure of integers. The inequality traditionally associated with the conjecture therefore reflects an underlying structural constraint rather than an isolated numerical phenomenon. In this sense, the ABC conjecture is resolved not merely by analytical estimation, but by recognizing the structural mechanism that produces the phenomenon itself. The argument presented here establishes that the evaluation relation required by the ABC conjecture follows inevitably from the generative structure of integers. Beyond the proof itself, the paper also clarifies the historical role of the ABC conjecture. For decades the conjecture acted as a focal point that drove major developments across number theory, arithmetic geometry, and Diophantine analysis. By revealing the structural origin of the phenomenon it describes, this work proposes that the historical function of the conjecture—as a guiding problem that shaped modern number theory—has now reached its natural completion. If the Zenodo preview does not load properly,the paper can also be previewed here: Google Drive preview:https://drive.google.com/file/d/1UmQXYiHnH-GrmXPEmDe3F85GutZNvxZL/view?usp=sharing