{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RXTMQ56LAH6YOOI2EL5LVRGFB5","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":"3cbdfee6b6b8e229eccd0cd513ad283950c363639a913a865f6cfa23349ac31a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T15:45:26Z","title_canon_sha256":"4003d505cd2e704b8b6b5a7f0dc7eef40d269dbe84fdfa8af467298dc77e339e"},"schema_version":"1.0","source":{"id":"1806.05119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05119","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05119v1","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05119","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"RXTMQ56LAH6Y","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RXTMQ56LAH6YOOI2","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RXTMQ56L","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:671fe6f65086aaed367f34b424fb09d5b72348b556be9b0cc002231a548457d3","target":"graph","created_at":"2026-05-18T00:13:20Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Gy\\'arf\\'as and Lehel and independently Faudree and Schelp proved that in any 2-coloring of the edges of $K_{n,n}$ there exists a monochromatic path on at least $2\\lceil n/2\\rceil$ vertices, and this is tight. We prove a stability version of this result which holds even if the host graph is not complete; that is, if $G$ is a balanced bipartite graph on $2n$ vertices with minimum degree at least $(3/4+o(1))n$, then in every 2-coloring of the edges of $G$, either there exists a monochromatic cycle on at least $(1+o(1))n$ vertices, or the coloring of $G$ is close to an extremal coloring -- in whi","authors_text":"Louis DeBiasio, Robert A. Krueger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T15:45:26Z","title":"Long monochromatic paths and cycles in 2-colored bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05119","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:285326e56a7b70f45bda9aa9a614fd94596fbb17aec2e6065fe3812026111f0a","target":"record","created_at":"2026-05-18T00:13:20Z","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":"3cbdfee6b6b8e229eccd0cd513ad283950c363639a913a865f6cfa23349ac31a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-13T15:45:26Z","title_canon_sha256":"4003d505cd2e704b8b6b5a7f0dc7eef40d269dbe84fdfa8af467298dc77e339e"},"schema_version":"1.0","source":{"id":"1806.05119","kind":"arxiv","version":1}},"canonical_sha256":"8de6c877cb01fd87391a22fabac4c50f4d09750a83a77f0e54e0b174cb1d6a37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8de6c877cb01fd87391a22fabac4c50f4d09750a83a77f0e54e0b174cb1d6a37","first_computed_at":"2026-05-18T00:13:20.086642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:20.086642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7QQhcpf2N3HjZdF6bilvId6Z3Uxo36MnoBDlUDMCoYkWtyVxWtPsgw0H89fhdl52vVhItIHlSiusyzjIWE/OBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:20.087296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:285326e56a7b70f45bda9aa9a614fd94596fbb17aec2e6065fe3812026111f0a","sha256:671fe6f65086aaed367f34b424fb09d5b72348b556be9b0cc002231a548457d3"],"state_sha256":"3b0e91762c9f489d0792e469d08fc096af8f9d05012be304564e9d78c6b0c6dd"}