2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166922We prove the vanishing of the space of 3-loop Jacobi diagrams of odd degree. This implies that no 3-loop finite-type invariant can distinguish between a knot and its inverse.13 pages. Section on the even degree case expanded. Various minor correctionsGeometric TopologyCombinatorics57M27, 05C10Vanishing of 3-Loop Jacobi Diagrams of Odd Degreetext