Fractional Square Root Divisor Mapping (FSRDM): A Continuous Geometric Heuristic for Semi-Prime Factor Localization and Asymptotic Probability Analysis

This paper introduces the Fractional Square Root Divisor Mapping (FSRDM), a continuous geometric heuristic for semi-prime factor localization. The framework studies the relationship between the fractional component of the square root of a composite number and the localization of its prime divisors. Extensive computational experiments across large semi-prime datasets investigate the stability of the normalized prediction error, convergence behavior, and the asymptotic structure of the resulting error distribution. The results suggest a stable empirical convergence region for binary composite structures. The framework is presented as a heuristic approach and does not claim a deterministic polynomial-time factorization algorithm.