{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3Z772IMUJ6X7IOVKOU5KWZ236G","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":"b8cd11919772dbac11663bf7bbd993554e4f0827e018d68051c82f4260ced963","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-26T14:44:17Z","title_canon_sha256":"1dfa6dc815dcd62ae65bd586c4e64e45d99325823fc887b5eac9ede895c35a99"},"schema_version":"1.0","source":{"id":"1907.11600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11600","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11600v1","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11600","created_at":"2026-05-17T23:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"3Z772IMUJ6X7","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"3Z772IMUJ6X7IOVK","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"3Z772IMU","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:89de6917ccf18f956dc4ba4a55e0e8f4e69bf113ace7be85d8eef83a9c7620c3","target":"graph","created_at":"2026-05-17T23:39:28Z","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":"We show that for every l, there exists d_l such that every 3-edge-connected graph with minimum degree d_l can be edge-partitioned into paths of length l (provided that its number of edges is divisible by l). This improves a result asserting that 24-edge-connectivity and high minimum degree provides such a partition. This is best possible as 3-edge-connectivity cannot be replaced by 2-edge connectivity.","authors_text":"St\\'ephan Thomass\\'e, Tereza Klimo\\v{s}ov\\'a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-26T14:44:17Z","title":"Edge-partitioning 3-edge-connected graphs into paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11600","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":"sha256:3d9070759332a1ee6794e91d9c7f5ce335881a984ec584533a4766b9474e52fe","target":"record","created_at":"2026-05-17T23:39:28Z","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":"b8cd11919772dbac11663bf7bbd993554e4f0827e018d68051c82f4260ced963","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-26T14:44:17Z","title_canon_sha256":"1dfa6dc815dcd62ae65bd586c4e64e45d99325823fc887b5eac9ede895c35a99"},"schema_version":"1.0","source":{"id":"1907.11600","kind":"arxiv","version":1}},"canonical_sha256":"de7ffd21944faff43aaa753aab675bf19a743a14e7e8089f0e281da21715571b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de7ffd21944faff43aaa753aab675bf19a743a14e7e8089f0e281da21715571b","first_computed_at":"2026-05-17T23:39:28.582475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:28.582475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qiqkyLiPFSQ2UjQsiGVnZbU8MTAg53rIK9nBAPDcnWZ++ZMfjqtzx5DXzsKuUxiiLwGK/aky9TmkLF+h5mu0Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:28.583077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d9070759332a1ee6794e91d9c7f5ce335881a984ec584533a4766b9474e52fe","sha256:89de6917ccf18f956dc4ba4a55e0e8f4e69bf113ace7be85d8eef83a9c7620c3"],"state_sha256":"610f4ce311823207ba086497056de5e2611684de009e37baffb34fe6a1dc9fd9"}