Counting Defects: Semilinear Reachability and Resource Bounds for Langton's Ant

Complete-field realization and a complete bounded-defect schema cover yield effective all-coordinate semilinear synthesis for Langton's ant. Established Presburger counting and flat-run methods support exact initial-supply and defect spectra, a supply dichotomy, a sharp three-parameter fold-consumer classification, small positive witnesses and unary-budget NP membership. A restricted polynomial-size quantifier-free backend encodes physical read/write parity and shared factor counts; an FP^NP minimum-cost upper bound complements the general semilinear compiler.