The nonintegrality conjecture for diminished Sombor energy

Let $G$ be a graph, and let its diminished Sombor energy be the sum of the absolute values of the eigenvalues of its diminished Sombor matrix. Nonintegrality conjecture. There does not exist a graph whose diminished Sombor energy is an integer value. This conjecture proposes that diminished Sombor energy is never integral, extending the paper's study of spectral properties and bounds for the diminished Sombor matrix; its resolution is not established in the supplied text.