An Exact Arithmetic Invariant Linking the Kaprekar Constants 495 and 6174

This note presents an exact arithmetic invariant linking the Kaprekar constants 495 and 6174 through factorization and ratio analysis. The result reveals a rigid structural relation between the unique fixed points of the 3-digit and 4-digit Kaprekar routines, independent of the classical iterative process. To the best of the author's knowledge, this invariant relation does not appear in the existing literature. The work highlights a direct arithmetic correspondence that may contribute to the structural understanding of Kaprekar constants in recreational number theory.