A tied note across the barline keeps its accidental without restating it

A note tied across a barline shows no accidental on the continuation; the pre-barline accidental governs the rest of the new bar as if restated there.

Gould, 'Accidentals' chapter; Read ch.6; Ross ch.5 -- universal agreement.

This rule can be decided from pitches, durations and voices — no layout required. A validator can check it before anything is drawn.