2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220080This note is a follow up of math.AG/0612267v2 and it is largely inspired by a beautiful description of Baker-Norine of non-effective degree (g-1) divisors via chip-firing game. We consider the set of all theta characteristics on a tropical curve and identify the Riemann constant as a unique non-effective one among them.4 pages, still an addendum to math.AG/0612267v2, exposition improved, description of positive theta addedAlgebraic GeometryCombinatoricstext