Resolution of Sylvester's Conjecture on Dispersion Matrices Using

This document presents a detailed resolution of Sylvester’s Conjecture on dispersionmatrices using the tSylvester formula. Through rigorous mathematical derivations and nu-merical evaluations, we demonstrate that the formula accurately identifies the conditionsunder which dispersion matrices exist infinitely. Additionally, we provide explicit proofs,calculations, and interpretations of the results, establishing the sufficiency of tSylvester asa solution framework for this conjecture