The Isoradion Operation Method: Integerizing Irrationality through Orthogonal Axis Displacement and Positional Capture

Description This preprint introduces the Isoradion Operation Method, a revolutionary computational framework designed to eliminate irrational number errors in high-precision digital systems. Core Concepts: Positional Capture: Instead of calculating infinite decimal values, the system shifts the vertical and horizontal axes to intercept irrational coordinates. Origin Integerization: By defining the captured position as a new integer starting point (0,0), all subsequent operations are performed through error-free integer arithmetic. Irrational Orthogonality: Utilizing the movement of orthogonal axes to 'trap' irrational points within an existence-based grid system. This method provides a fundamental solution for semiconductor lithography, AI matrix optimization, and the 13 major scientific challenges by replacing traditional floating-point calculation with spatial displacement logic.