{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HZ3BNVYMNQW4L5ZHDSB7S4FZTC","short_pith_number":"pith:HZ3BNVYM","schema_version":"1.0","canonical_sha256":"3e7616d70c6c2dc5f7271c83f970b998be5798f4a25655428f2bf291048de0f7","source":{"kind":"arxiv","id":"1103.3983","version":2},"attestation_state":"computed","paper":{"title":"Simplified existence theorems on all fractional [a,b]-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2011-03-21T11:37:04Z","abstract_excerpt":"Let $G$ be a graph with order $n$ and let $g, f : V (G)\\rightarrow N$ such that $g(v)\\leq f(v)$ for all $v\\in V(G)$. We say that $G$ has all fractional $(g, f)$-factors if $G$ has a fractional $p$-factor for every $p: V (G)\\rightarrow N$ such that $g(v)\\leq p(v)\\leq f (v)$ for every $v\\in V(G)$. Let $a<b$ be two positive integers. %and $G$ \\textbf{a graph} of order $n$ sufficiently large %for $a$ and $b$. If $g\\equiv a$, $f\\equiv b$ and $G$ has all fractional $(g,f)$-factors, then we say that $G$ has all fractional $[a,b]$-factors. Suppose that $n$ is sufficiently large for $a$ and $b$.\n  This"},"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":"1103.3983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-21T11:37:04Z","cross_cats_sorted":[],"title_canon_sha256":"c5b4846f3d52bbb6f612cf7dad34be1234b3c7df2af537fffa5737741bdeebbb","abstract_canon_sha256":"e054edf81cda80551bdea50b5f716a29355635bbc56b99a97a9294c8ad361001"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.891957Z","signature_b64":"ZBC40Z5/KYnpbVTTZO+M68xjzKnQfWLEp7EsO0j9eo29w7OZeHMREaI8ZFmB734uw4F2uW2ivKQAIRvKWXq9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e7616d70c6c2dc5f7271c83f970b998be5798f4a25655428f2bf291048de0f7","last_reissued_at":"2026-05-18T03:37:41.891475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.891475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simplified existence theorems on all fractional [a,b]-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2011-03-21T11:37:04Z","abstract_excerpt":"Let $G$ be a graph with order $n$ and let $g, f : V (G)\\rightarrow N$ such that $g(v)\\leq f(v)$ for all $v\\in V(G)$. We say that $G$ has all fractional $(g, f)$-factors if $G$ has a fractional $p$-factor for every $p: V (G)\\rightarrow N$ such that $g(v)\\leq p(v)\\leq f (v)$ for every $v\\in V(G)$. Let $a<b$ be two positive integers. %and $G$ \\textbf{a graph} of order $n$ sufficiently large %for $a$ and $b$. If $g\\equiv a$, $f\\equiv b$ and $G$ has all fractional $(g,f)$-factors, then we say that $G$ has all fractional $[a,b]$-factors. Suppose that $n$ is sufficiently large for $a$ and $b$.\n  This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3983","kind":"arxiv","version":2},"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":"1103.3983","created_at":"2026-05-18T03:37:41.891537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.3983v2","created_at":"2026-05-18T03:37:41.891537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3983","created_at":"2026-05-18T03:37:41.891537+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZ3BNVYMNQW4","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZ3BNVYMNQW4L5ZH","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZ3BNVYM","created_at":"2026-05-18T12:26:30.835961+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/HZ3BNVYMNQW4L5ZHDSB7S4FZTC","json":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC.json","graph_json":"https://pith.science/api/pith-number/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/graph.json","events_json":"https://pith.science/api/pith-number/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/events.json","paper":"https://pith.science/paper/HZ3BNVYM"},"agent_actions":{"view_html":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC","download_json":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC.json","view_paper":"https://pith.science/paper/HZ3BNVYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.3983&json=true","fetch_graph":"https://pith.science/api/pith-number/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/graph.json","fetch_events":"https://pith.science/api/pith-number/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/action/storage_attestation","attest_author":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/action/author_attestation","sign_citation":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/action/citation_signature","submit_replication":"https://pith.science/pith/HZ3BNVYMNQW4L5ZHDSB7S4FZTC/action/replication_record"}},"created_at":"2026-05-18T03:37:41.891537+00:00","updated_at":"2026-05-18T03:37:41.891537+00:00"}