2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166198The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.24 pages, version for publicationQuantum AlgebraMathematical Physicstext