{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SC7OWC3MX433OR2EZXRODMAANI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4b45024312406ceb27607ba42d3457058853b5e83107d6b51d58902dd6201896","cross_cats_sorted":["cs.DM","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-28T14:34:26Z","title_canon_sha256":"80483a16a9d4dff14d7fce707ada7d433e486e1c256d15ec5ab1f92a663c772d"},"schema_version":"1.0","source":{"id":"2511.23226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.23226","created_at":"2026-05-20T00:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"2511.23226v2","created_at":"2026-05-20T00:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.23226","created_at":"2026-05-20T00:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"SC7OWC3MX433","created_at":"2026-05-20T00:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"SC7OWC3MX433OR2E","created_at":"2026-05-20T00:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"SC7OWC3M","created_at":"2026-05-20T00:02:59Z"}],"graph_snapshots":[{"event_id":"sha256:b758e74b88aa94d94cbac03a206a8e52b75652964267b6a9d721a675a9bdf0f9","target":"graph","created_at":"2026-05-20T00:02:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Satisfiability solvers classify all north-east lattice paths avoiding up to six collinear points and find a 327-step example for seven."}],"snapshot_sha256":"42600e5692e5a3000c7b1a7baa69ea8654e568e2d2cd4542109b7706a5b9de3a"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.23226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Aaron Barnoff, Curtis Bright","cross_cats":["cs.DM","cs.LO"],"headline":"Satisfiability solvers classify all north-east lattice paths avoiding up to six collinear points and find a 327-step example for seven.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-28T14:34:26Z","title":"North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.23226","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-17T03:53:49.565526Z","id":"91b87144-e3b3-4533-965d-d4f6075a3bc7","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"91b87144-e3b3-4533-965d-d4f6075a3bc7"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6cc0bd201eaf924ba4dbc9356ee0bb7e8e837f1ae75d7c0a6e7a46270b693387","target":"record","created_at":"2026-05-20T00:02:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4b45024312406ceb27607ba42d3457058853b5e83107d6b51d58902dd6201896","cross_cats_sorted":["cs.DM","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-11-28T14:34:26Z","title_canon_sha256":"80483a16a9d4dff14d7fce707ada7d433e486e1c256d15ec5ab1f92a663c772d"},"schema_version":"1.0","source":{"id":"2511.23226","kind":"arxiv","version":2}},"canonical_sha256":"90beeb0b6cbf37b74744cde2e1b0006a2894edfcda4a8b222e2e4bbe672635a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90beeb0b6cbf37b74744cde2e1b0006a2894edfcda4a8b222e2e4bbe672635a5","first_computed_at":"2026-05-20T00:02:59.585505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:59.585505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6/3t8jX0WGyBBEKnOTjKw2yg9pD/rJ9FVFOePdF8xfPdDqXbMj6piCocJEPMOxMucE4glg4xCS4cCbUA3EgrDg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:59.586412Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.23226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cc0bd201eaf924ba4dbc9356ee0bb7e8e837f1ae75d7c0a6e7a46270b693387","sha256:b758e74b88aa94d94cbac03a206a8e52b75652964267b6a9d721a675a9bdf0f9"],"state_sha256":"0d98f7a2ada008ac0f6d9a273f2c335de71e40b52c3923f8be77ce349801f33d"}