{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NYND77X5GK2XMGBFRWVT6WWZ4J","short_pith_number":"pith:NYND77X5","schema_version":"1.0","canonical_sha256":"6e1a3ffefd32b57618258dab3f5ad9e274e01abbbe8fe91502c29c24d8d0f9bf","source":{"kind":"arxiv","id":"1404.4734","version":1},"attestation_state":"computed","paper":{"title":"Random directed graphs are robustly Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Benny Sudakov, Dan Hefetz","submitted_at":"2014-04-18T09:56:54Z","abstract_excerpt":"A classical theorem of Ghouila-Houri from 1960 asserts that every directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$ contains a directed Hamilton cycle. In this paper we extend this theorem to a random directed graph ${\\mathcal D}(n,p)$, that is, a directed graph in which every ordered pair $(u,v)$ becomes an arc with probability $p$ independently of all other pairs. Motivated by the study of resilience of properties of random graphs, we prove that if $p \\gg \\log n/\\sqrt{n}$, then a.a.s. every subdigraph of ${\\mathcal D}(n,p)$ with minimum out-degree and in-deg"},"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":"1404.4734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-18T09:56:54Z","cross_cats_sorted":[],"title_canon_sha256":"8670418325db0b97881181416f8a77b4bef236b9a357381fe0738e96ae7877e7","abstract_canon_sha256":"3e3b0b97d0f4bb89acf6e3aa026854a2bdc710791c357f040990507cfc78b50c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:55.186602Z","signature_b64":"AQpouySrPO5qSpIB17CwstdMRzsTqv6fwmtXQXDC12ekdP/YcQ4Cgcder9fd/KCDGVhSI4e7FyOMv7c8+vr+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e1a3ffefd32b57618258dab3f5ad9e274e01abbbe8fe91502c29c24d8d0f9bf","last_reissued_at":"2026-05-18T02:53:55.185897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:55.185897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random directed graphs are robustly Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Benny Sudakov, Dan Hefetz","submitted_at":"2014-04-18T09:56:54Z","abstract_excerpt":"A classical theorem of Ghouila-Houri from 1960 asserts that every directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$ contains a directed Hamilton cycle. In this paper we extend this theorem to a random directed graph ${\\mathcal D}(n,p)$, that is, a directed graph in which every ordered pair $(u,v)$ becomes an arc with probability $p$ independently of all other pairs. Motivated by the study of resilience of properties of random graphs, we prove that if $p \\gg \\log n/\\sqrt{n}$, then a.a.s. every subdigraph of ${\\mathcal D}(n,p)$ with minimum out-degree and in-deg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4734","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":"1404.4734","created_at":"2026-05-18T02:53:55.186007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4734v1","created_at":"2026-05-18T02:53:55.186007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4734","created_at":"2026-05-18T02:53:55.186007+00:00"},{"alias_kind":"pith_short_12","alias_value":"NYND77X5GK2X","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NYND77X5GK2XMGBF","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NYND77X5","created_at":"2026-05-18T12:28:41.024544+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/NYND77X5GK2XMGBFRWVT6WWZ4J","json":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J.json","graph_json":"https://pith.science/api/pith-number/NYND77X5GK2XMGBFRWVT6WWZ4J/graph.json","events_json":"https://pith.science/api/pith-number/NYND77X5GK2XMGBFRWVT6WWZ4J/events.json","paper":"https://pith.science/paper/NYND77X5"},"agent_actions":{"view_html":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J","download_json":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J.json","view_paper":"https://pith.science/paper/NYND77X5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4734&json=true","fetch_graph":"https://pith.science/api/pith-number/NYND77X5GK2XMGBFRWVT6WWZ4J/graph.json","fetch_events":"https://pith.science/api/pith-number/NYND77X5GK2XMGBFRWVT6WWZ4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J/action/storage_attestation","attest_author":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J/action/author_attestation","sign_citation":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J/action/citation_signature","submit_replication":"https://pith.science/pith/NYND77X5GK2XMGBFRWVT6WWZ4J/action/replication_record"}},"created_at":"2026-05-18T02:53:55.186007+00:00","updated_at":"2026-05-18T02:53:55.186007+00:00"}