{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LIONSX2K7H7BJ2WZ2TUJW2K4X4","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":"db62ed27d840e6a0232b3102d0de3c84ae45ad9f78d5a6ab1b1314b4255b3373","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-31T13:09:24Z","title_canon_sha256":"4e9661b69c42d124d196b77ebf03d0b8da0e7fe00552d9a31df136b76fc74da2"},"schema_version":"1.0","source":{"id":"1901.11339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.11339","created_at":"2026-05-17T23:55:02Z"},{"alias_kind":"arxiv_version","alias_value":"1901.11339v1","created_at":"2026-05-17T23:55:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.11339","created_at":"2026-05-17T23:55:02Z"},{"alias_kind":"pith_short_12","alias_value":"LIONSX2K7H7B","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LIONSX2K7H7BJ2WZ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LIONSX2K","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:9690d5126b1fb89705769ba5733e38c3d92ac758b7319d798788a6643bb79081","target":"graph","created_at":"2026-05-17T23:55:02Z","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":"Thomassen formulated the following conjecture: Every $3$-connected cubic graph has a red-blue vertex coloring such that the blue subgraph has maximum degree $1$ (that is, it consists of a matching and some isolated vertices) and the red subgraph has minimum degree at least $1$ and contains no $3$-edge path. We prove the conjecture for Generalized Petersen graphs.\n  We indicate that a coloring with the same properties might exist for any subcubic graph. We confirm this statement for all subcubic trees.","authors_text":"J\\'anos Bar\\'at","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-31T13:09:24Z","title":"Decomposition of cubic graphs related to Wegner's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11339","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:ee982aa15d0ca06a6245d9ac7199129a55d7a0afe3b8756842bec87f13d9ace1","target":"record","created_at":"2026-05-17T23:55:02Z","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":"db62ed27d840e6a0232b3102d0de3c84ae45ad9f78d5a6ab1b1314b4255b3373","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-31T13:09:24Z","title_canon_sha256":"4e9661b69c42d124d196b77ebf03d0b8da0e7fe00552d9a31df136b76fc74da2"},"schema_version":"1.0","source":{"id":"1901.11339","kind":"arxiv","version":1}},"canonical_sha256":"5a1cd95f4af9fe14ead9d4e89b695cbf11c35931ee59af8719a6fa1f942ea8c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a1cd95f4af9fe14ead9d4e89b695cbf11c35931ee59af8719a6fa1f942ea8c2","first_computed_at":"2026-05-17T23:55:02.141380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:02.141380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nD9iJudInxEQexJWWQzXtvEyxsn6KecMkHS1VW+2TbjdMPDikStwSLumk02gngPOlzvohUBJfyBoaMF+N605Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:02.141994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.11339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee982aa15d0ca06a6245d9ac7199129a55d7a0afe3b8756842bec87f13d9ace1","sha256:9690d5126b1fb89705769ba5733e38c3d92ac758b7319d798788a6643bb79081"],"state_sha256":"e5aa5dfe2334325562eff49222930e884372ca72cd7d11abca8ef2a4d94d533e"}