{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:COXBHLOA3XZZGIMFT3NGIY65QW","short_pith_number":"pith:COXBHLOA","canonical_record":{"source":{"id":"1407.4339","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-16T15:18:15Z","cross_cats_sorted":[],"title_canon_sha256":"2aba39f245b0da73c1c0b89aa2c846586e5f10128d0084692d87247edd3118fc","abstract_canon_sha256":"71780b3ab98f2bc0cde38b28db73f18131781a7cf0f9b8ae3ef394b53f594602"},"schema_version":"1.0"},"canonical_sha256":"13ae13adc0ddf39321859eda6463dd85bdc2cae30094e123a3c7536836a707a0","source":{"kind":"arxiv","id":"1407.4339","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4339","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4339v3","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4339","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"COXBHLOA3XZZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"COXBHLOA3XZZGIMF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"COXBHLOA","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:COXBHLOA3XZZGIMFT3NGIY65QW","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4339","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-16T15:18:15Z","cross_cats_sorted":[],"title_canon_sha256":"2aba39f245b0da73c1c0b89aa2c846586e5f10128d0084692d87247edd3118fc","abstract_canon_sha256":"71780b3ab98f2bc0cde38b28db73f18131781a7cf0f9b8ae3ef394b53f594602"},"schema_version":"1.0"},"canonical_sha256":"13ae13adc0ddf39321859eda6463dd85bdc2cae30094e123a3c7536836a707a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:57.643712Z","signature_b64":"twOxmGaSDlLR77bOPqRBsWfvTyWyQxtRillNKY+zIBb13lWGruUztv2gXswUUUWzLjM4s/65XVEX3TiB5fW1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13ae13adc0ddf39321859eda6463dd85bdc2cae30094e123a3c7536836a707a0","last_reissued_at":"2026-05-18T00:14:57.643042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:57.643042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4339","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sCLYvb1w0E/go7Ri5OseNi4FDjsQIstmz3sS2SKNlz6Cl0PEwcxwnOdqGeBiohDCrTyvBku8US00fPPJ8MkZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:42:40.273565Z"},"content_sha256":"9a77355aab45ba7ecec693b5a3248b2e9990c0f9140b6d6ef839dfbfd79a127a","schema_version":"1.0","event_id":"sha256:9a77355aab45ba7ecec693b5a3248b2e9990c0f9140b6d6ef839dfbfd79a127a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:COXBHLOA3XZZGIMFT3NGIY65QW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension from Precoloured Sets of Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ant\\'onio Gir\\~ao, Gregory J. Puleo, Jan van den Heuvel, Jean-S\\'ebastien Sereni, Katherine Edwards, Ross J. Kang","submitted_at":"2014-07-16T15:18:15Z","abstract_excerpt":"We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree $\\Delta$. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? This question turns out to be related to the notorious List Colouring Conjecture and other classic notions of choosability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4339","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RQ9RNft27O5VJVDcm807JqVtOAhjoO56Rp8+gfq024Jrtg5qAPaJ2G6BVfvPz9qoQy44aS8v+m6mUqDw64aABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:42:40.273953Z"},"content_sha256":"e6cd288b50208c2c1deff5180b950f1d323899841932491f14c73612574c67a6","schema_version":"1.0","event_id":"sha256:e6cd288b50208c2c1deff5180b950f1d323899841932491f14c73612574c67a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COXBHLOA3XZZGIMFT3NGIY65QW/bundle.json","state_url":"https://pith.science/pith/COXBHLOA3XZZGIMFT3NGIY65QW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COXBHLOA3XZZGIMFT3NGIY65QW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T08:42:40Z","links":{"resolver":"https://pith.science/pith/COXBHLOA3XZZGIMFT3NGIY65QW","bundle":"https://pith.science/pith/COXBHLOA3XZZGIMFT3NGIY65QW/bundle.json","state":"https://pith.science/pith/COXBHLOA3XZZGIMFT3NGIY65QW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COXBHLOA3XZZGIMFT3NGIY65QW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:COXBHLOA3XZZGIMFT3NGIY65QW","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":"71780b3ab98f2bc0cde38b28db73f18131781a7cf0f9b8ae3ef394b53f594602","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-16T15:18:15Z","title_canon_sha256":"2aba39f245b0da73c1c0b89aa2c846586e5f10128d0084692d87247edd3118fc"},"schema_version":"1.0","source":{"id":"1407.4339","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4339","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4339v3","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4339","created_at":"2026-05-18T00:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"COXBHLOA3XZZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"COXBHLOA3XZZGIMF","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"COXBHLOA","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:e6cd288b50208c2c1deff5180b950f1d323899841932491f14c73612574c67a6","target":"graph","created_at":"2026-05-18T00:14:57Z","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 consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree $\\Delta$. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? This question turns out to be related to the notorious List Colouring Conjecture and other classic notions of choosability.","authors_text":"Ant\\'onio Gir\\~ao, Gregory J. Puleo, Jan van den Heuvel, Jean-S\\'ebastien Sereni, Katherine Edwards, Ross J. Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-16T15:18:15Z","title":"Extension from Precoloured Sets of Edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4339","kind":"arxiv","version":3},"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":"sha256:9a77355aab45ba7ecec693b5a3248b2e9990c0f9140b6d6ef839dfbfd79a127a","target":"record","created_at":"2026-05-18T00:14:57Z","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":"71780b3ab98f2bc0cde38b28db73f18131781a7cf0f9b8ae3ef394b53f594602","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-16T15:18:15Z","title_canon_sha256":"2aba39f245b0da73c1c0b89aa2c846586e5f10128d0084692d87247edd3118fc"},"schema_version":"1.0","source":{"id":"1407.4339","kind":"arxiv","version":3}},"canonical_sha256":"13ae13adc0ddf39321859eda6463dd85bdc2cae30094e123a3c7536836a707a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13ae13adc0ddf39321859eda6463dd85bdc2cae30094e123a3c7536836a707a0","first_computed_at":"2026-05-18T00:14:57.643042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:57.643042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"twOxmGaSDlLR77bOPqRBsWfvTyWyQxtRillNKY+zIBb13lWGruUztv2gXswUUUWzLjM4s/65XVEX3TiB5fW1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:57.643712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4339","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a77355aab45ba7ecec693b5a3248b2e9990c0f9140b6d6ef839dfbfd79a127a","sha256:e6cd288b50208c2c1deff5180b950f1d323899841932491f14c73612574c67a6"],"state_sha256":"ec58ab6a890288de4e9f3825f9481e36d98a17aa1ccaf6c5e4730d74ccf77702"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ymRig6Aoj3EUxOKY3qEvrBwFYyCUa921aD8zJAdLErfgEXDkkpOIzVumTK1SR/JzQL5QhwFvTdN8QtBf2MwCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:42:40.277658Z","bundle_sha256":"3c387cde07d09319ede1851252b32fe48e3f079669b9e273beb31f73c981d49f"}}