{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GMFLHI67FZ5O3KVZMNNFGWHDAD","short_pith_number":"pith:GMFLHI67","schema_version":"1.0","canonical_sha256":"330ab3a3df2e7aedaab9635a5358e300e08f4728ced7c54de15c45cafb4ddd50","source":{"kind":"arxiv","id":"1904.02482","version":1},"attestation_state":"computed","paper":{"title":"The Extension Degree Conditions for Fractional Factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Juan L.G. Guirao, Weifan Wang, Wei Gao","submitted_at":"2019-04-04T11:09:32Z","abstract_excerpt":"In Gao's previous work, the authors determined several graph degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if $b=f(x)=g(x)=a$ for all vertices $x$ in $G$. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference $\\Delta$ between $g(x)$ and $f(x)$ for every vertex $x$ in $G$. These obtained new degree conditions reformulate Gao's previous conclusions, and show how $\\Delta$ acts in th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.02482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-04T11:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"5d36b0885fd63b3626f4a4e67502b1fe10fe04b9f284ce84f599ef95332b3999","abstract_canon_sha256":"7f1b9bb0fca58bdd83f238b91922cf49c1b5db81442b384355db2db4d5c8db3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:23.504697Z","signature_b64":"X28J8mOsPEil395u8pp7PQWD6zKhC3JaWEP3mmsxRJCTjeHUre9QhI4AD3JCUrUSzV1tVaG0mLCv8PSVQu58Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"330ab3a3df2e7aedaab9635a5358e300e08f4728ced7c54de15c45cafb4ddd50","last_reissued_at":"2026-05-17T23:49:23.504246Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:23.504246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Extension Degree Conditions for Fractional Factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Juan L.G. Guirao, Weifan Wang, Wei Gao","submitted_at":"2019-04-04T11:09:32Z","abstract_excerpt":"In Gao's previous work, the authors determined several graph degree conditions of a graph which admits fractional factor in particular settings. It was revealed that these degree conditions are tight if $b=f(x)=g(x)=a$ for all vertices $x$ in $G$. In this paper, we continue to discuss these degree conditions for admitting fractional factor in the setting that several vertices and edges are removed and there is a difference $\\Delta$ between $g(x)$ and $f(x)$ for every vertex $x$ in $G$. These obtained new degree conditions reformulate Gao's previous conclusions, and show how $\\Delta$ acts in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02482","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.02482","created_at":"2026-05-17T23:49:23.504310+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.02482v1","created_at":"2026-05-17T23:49:23.504310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02482","created_at":"2026-05-17T23:49:23.504310+00:00"},{"alias_kind":"pith_short_12","alias_value":"GMFLHI67FZ5O","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GMFLHI67FZ5O3KVZ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GMFLHI67","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD","json":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD.json","graph_json":"https://pith.science/api/pith-number/GMFLHI67FZ5O3KVZMNNFGWHDAD/graph.json","events_json":"https://pith.science/api/pith-number/GMFLHI67FZ5O3KVZMNNFGWHDAD/events.json","paper":"https://pith.science/paper/GMFLHI67"},"agent_actions":{"view_html":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD","download_json":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD.json","view_paper":"https://pith.science/paper/GMFLHI67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.02482&json=true","fetch_graph":"https://pith.science/api/pith-number/GMFLHI67FZ5O3KVZMNNFGWHDAD/graph.json","fetch_events":"https://pith.science/api/pith-number/GMFLHI67FZ5O3KVZMNNFGWHDAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD/action/storage_attestation","attest_author":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD/action/author_attestation","sign_citation":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD/action/citation_signature","submit_replication":"https://pith.science/pith/GMFLHI67FZ5O3KVZMNNFGWHDAD/action/replication_record"}},"created_at":"2026-05-17T23:49:23.504310+00:00","updated_at":"2026-05-17T23:49:23.504310+00:00"}