Positive Jacobi realizations for complete-bipartite symmetric edge polytopes

This preprint constructs explicit positive Jacobi realizations for the centered Ehrhart polynomials of type-A symmetric edge polytopes of K(4,n) and K(5,n). Together with the known smaller families and symmetry, it proves the canonical-line property whenever min(m,n) is at most 5. It also proves positivity of the first two inverse tail coefficients for every integer pair 3 <= m <= n, using exact symbolic positive-coefficient certificates for the second coefficient. The remaining tail coefficients and the full complete-bipartite canonical-line conjecture are not settled. Status: internally reviewed preprint; external mathematical review and formal peer review are pending.