{"paper":{"title":"Witness-split + window-cardinality refinement for $r_3(N)$: Architecture, empirical results, and a structural hard pocket","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Mehmet Ergezer","submitted_at":"2026-05-31T17:48:17Z","abstract_excerpt":"We describe a reproducible computational framework for upper-bound searches on r_3(N), the maximum size of a 3-term-arithmetic-progression-free subset of [1,N]. The framework combines a verified lower-bound witness, endpoint forcing, depth-d witness-variable splitting, OEIS A003002 window-cardinality pruning, and recursive refinement of timed-out subproblems. Applied to the frontier case N = 212, K = 44, it found no feasible 44-set across millions of CP-SAT subproblems, supporting but not proving the conjectural value r_3(212) = 43. A 300-second recap leaves 45 resistant chunks; one-hour HiGHS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04016","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04016/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}