Local Factor Rigidity and Mass–Defect Bounds for Langton's Ant

A ten-turn window is legal when it occurs cyclically in the standard 104-turn highway word. If every future window is legal and the initial field has m black cells, the ant reaches the standard highway within 12m+212 updates, with optimal coefficient 12. For arbitrary finite-support trajectories, 3(t-s)-26(|B_t|-|B_s|) <= 351*N10(s,t)+322, where N10 counts forbidden windows wholly contained in the interval. The additive constant and asymptotic mass-growth slope are sharp. Separate finite-graph arguments establish attraction and the finite-word mass bound. Exact next-violation algorithms retain the complete output field; endpoint-strip and finite-horizon supply theorems describe legal intervals. Nine is the least factor length supporting a uniform legal-word mass-deficit bound.