2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74047The Shapiro conjecture in the real Schubert calculus fails to hold for flag manifolds, but in a very interesting way. In this extended abstract, we give a refinement of that conjecture for the flag manifold and present massive experimentation (over 12 GigaHertz-Years) that supports our refined conjecture. We also establish relationships between different cases of the conjecture and describe some new phenomena uncovered in this experimentation.Extended abstract, 12 pages, 4 .eps figuresAlgebraic Geometry14N15, 14P99, 14Q99text