Certified first-excess census for three-term arithmetic progressions on intervals, 3 <= N <= 55

Reproducibility dataset for the manuscript First-excess supersaturation and extremal extensions for three-term arithmetic progressions. For each 3 ≤ N ≤ 55, the archive determines the global first-excess value q_N = M_3(r_3(N)+1,N) and the minimum one-point extremal-extension cost mu_N. The certified classification is q_N < mu_N exactly for N = 37 and N = 55, with q_N = 2 and mu_N = 3 in both cases. The census contains 122 Boolean decision instances: 55 satisfiable thresholds with explicit models checked as arithmetic witnesses, and 67 unsatisfiable thresholds with plain DRAT proofs independently verified by DRAT-trim. The archive includes exact CSV/JSON results, source code, DIMACS instances, proof traces, logs, software versions, and SHA-256 manifests.