Exact Escape Times of Langton's Ant in Four Rows

Exact first-exit maxima over all initial colorings and internal poses: S(4,n)=34n-150 for every n>=13, with every smaller value determined. Etse supplied the matching lower family for n>=14 and finite computations. A complete persistent-response classification and an all-width integer induction establish the exact upper bound and resolve his four-row linear-bound conjecture. Exact finite implementations verify the certificates and attainment constructions.