{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4D3PBZ3KZMHZJRQQHRUWM3FWKZ","short_pith_number":"pith:4D3PBZ3K","schema_version":"1.0","canonical_sha256":"e0f6f0e76acb0f94c6103c69666cb656500574c2434d1cc73a4cf52018c1385a","source":{"kind":"arxiv","id":"1608.05741","version":2},"attestation_state":"computed","paper":{"title":"A stability version for a theorem of Erd\\H{o}s on nonhamiltonian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Ruth Luo, Zolt\\'an F\\\"uredi","submitted_at":"2016-08-19T21:30:30Z","abstract_excerpt":"Let $n, d$ be integers with $1 \\leq d \\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, and set $h(n,d):={n-d \\choose 2} + d^2$ and $e(n,d):= \\max\\{h(n,d),h(n, \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor)\\}$. Because $h(n,d)$ is quadratic in $d$, there exists a $d_0(n)=(n/6)+O(1)$ such that $e(n,1)> e(n, 2)> \\dots >e(n,d_0)=e(n, d_0+1)=\\dots = e(n,\\left \\lfloor \\frac{n-1}{2} \\right \\rfloor)$. A theorem by Erd\\H{o}s states that for $d\\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, any $n$-vertex nonhamiltonian graph $G$ with minimum degree $\\delta(G) \\geq d$ has at most $e(n,d)$ edges, and for"},"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":"1608.05741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T21:30:30Z","cross_cats_sorted":[],"title_canon_sha256":"ea893125ab44bb7dc7bc9801967aafeda84c6ac59bc478b5443345224e5177f2","abstract_canon_sha256":"ae76a967b7181bac847fedd3775aefddfd74d6285450469660dab12742054312"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:55.606395Z","signature_b64":"FxsKVPvrWTsFFezh7NhijeAjCR/FGelRREc3cFNJcPHxs4B23DcJN8DkfMGgxlkkGnZqPm4f4IAVMswO5XX0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f6f0e76acb0f94c6103c69666cb656500574c2434d1cc73a4cf52018c1385a","last_reissued_at":"2026-05-18T00:46:55.605819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:55.605819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stability version for a theorem of Erd\\H{o}s on nonhamiltonian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Ruth Luo, Zolt\\'an F\\\"uredi","submitted_at":"2016-08-19T21:30:30Z","abstract_excerpt":"Let $n, d$ be integers with $1 \\leq d \\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, and set $h(n,d):={n-d \\choose 2} + d^2$ and $e(n,d):= \\max\\{h(n,d),h(n, \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor)\\}$. Because $h(n,d)$ is quadratic in $d$, there exists a $d_0(n)=(n/6)+O(1)$ such that $e(n,1)> e(n, 2)> \\dots >e(n,d_0)=e(n, d_0+1)=\\dots = e(n,\\left \\lfloor \\frac{n-1}{2} \\right \\rfloor)$. A theorem by Erd\\H{o}s states that for $d\\leq \\left \\lfloor \\frac{n-1}{2} \\right \\rfloor$, any $n$-vertex nonhamiltonian graph $G$ with minimum degree $\\delta(G) \\geq d$ has at most $e(n,d)$ edges, and for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05741","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":"1608.05741","created_at":"2026-05-18T00:46:55.605907+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.05741v2","created_at":"2026-05-18T00:46:55.605907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05741","created_at":"2026-05-18T00:46:55.605907+00:00"},{"alias_kind":"pith_short_12","alias_value":"4D3PBZ3KZMHZ","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4D3PBZ3KZMHZJRQQ","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4D3PBZ3K","created_at":"2026-05-18T12:29:58.707656+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/4D3PBZ3KZMHZJRQQHRUWM3FWKZ","json":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ.json","graph_json":"https://pith.science/api/pith-number/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/graph.json","events_json":"https://pith.science/api/pith-number/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/events.json","paper":"https://pith.science/paper/4D3PBZ3K"},"agent_actions":{"view_html":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ","download_json":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ.json","view_paper":"https://pith.science/paper/4D3PBZ3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.05741&json=true","fetch_graph":"https://pith.science/api/pith-number/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/graph.json","fetch_events":"https://pith.science/api/pith-number/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/action/storage_attestation","attest_author":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/action/author_attestation","sign_citation":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/action/citation_signature","submit_replication":"https://pith.science/pith/4D3PBZ3KZMHZJRQQHRUWM3FWKZ/action/replication_record"}},"created_at":"2026-05-18T00:46:55.605907+00:00","updated_at":"2026-05-18T00:46:55.605907+00:00"}