{"paper":{"title":"North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Satisfiability solvers classify all north-east lattice paths avoiding up to six collinear points and find a 327-step example for seven.","cross_cats":["cs.DM","cs.LO"],"primary_cat":"math.CO","authors_text":"Aaron Barnoff, Curtis Bright","submitted_at":"2025-11-28T14:34:26Z","abstract_excerpt":"We investigate the Gerver-Ramsey collinearity problem of determining the maximum number of points in a north-east lattice path without $k$ collinear points. Using a satisfiability solver, up to isomorphism we enumerate all north-east lattice paths avoiding $k$ collinear points for $k \\leq 6$. We also find a north-east lattice path avoiding $k = 7$ collinear points with 327 steps, improving on the previous best length of 260 steps found by Shallit."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We also find a north-east lattice path avoiding k = 7 collinear points with 327 steps, improving on the previous best length of 260 steps found by Shallit.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The SAT encoding correctly captures the collinearity-avoidance condition and the solver's search is exhaustive up to isomorphism for k≤6 and finds a valid 327-step example for k=7.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"SAT solvers enumerate all north-east lattice paths avoiding k collinear points for k≤6 and produce a 327-step path for k=7, improving the prior record of 260 steps.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Satisfiability solvers classify all north-east lattice paths avoiding up to six collinear points and find a 327-step example for seven.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"42600e5692e5a3000c7b1a7baa69ea8654e568e2d2cd4542109b7706a5b9de3a"},"source":{"id":"2511.23226","kind":"arxiv","version":2},"verdict":{"id":"91b87144-e3b3-4533-965d-d4f6075a3bc7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T03:53:49.565526Z","strongest_claim":"We also find a north-east lattice path avoiding k = 7 collinear points with 327 steps, improving on the previous best length of 260 steps found by Shallit.","one_line_summary":"SAT solvers enumerate all north-east lattice paths avoiding k collinear points for k≤6 and produce a 327-step path for k=7, improving the prior record of 260 steps.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The SAT encoding correctly captures the collinearity-avoidance condition and the solver's search is exhaustive up to isomorphism for k≤6 and finds a valid 327-step example for k=7.","pith_extraction_headline":"Satisfiability solvers classify all north-east lattice paths avoiding up to six collinear points and find a 327-step example for seven."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.23226/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"}