2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17070The well known string solution to Bethe ansatz equations is shown to be inconsistent in its widely accepted form. A valid refinement demanding higher order corrections in subsequent roots is identified. A new alternative string solution is proposed for finite long chains, consistent with the non-Bethe strings observed earlier.Revtex, 5 pages, no figureCondensed MatterHigh Energy Physics - TheoryMathematical PhysicsExactly Solvable and Integrable SystemsQuantum Physicstext