Recorded pipe-poiseuille-nk-three-grid-2026-10-10: the Newton-Krylov solver reproduces Hagen-Poiseuille flow at second order on the swept circle with 9, 17 and 33 cells across. It is the solver's first analytical evidence and also backs the sweep generator and the circle cross-section. The dual-time solver did not converge on the 33-cell grid at the same time step, which page 24 now states.