{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VH43TBW2D3K4DVO42OVCKZ4QYF","short_pith_number":"pith:VH43TBW2","schema_version":"1.0","canonical_sha256":"a9f9b986da1ed5c1d5dcd3aa256790c17d31c8bb440a40c8fa70544715b749c1","source":{"kind":"arxiv","id":"1009.3721","version":1},"attestation_state":"computed","paper":{"title":"Long cycles in subgraphs of (pseudo)random directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Ido Ben-Eliezer, Michael Krivelevich","submitted_at":"2010-09-20T07:47:18Z","abstract_excerpt":"We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every $0 < \\gamma < 1/2$ we find a constant $c=c(\\gamma)$ such that the following holds. Let $G=(V,E)$ be a (pseudo)random directed graph on $n$ vertices, and let $G'$ be a subgraph of $G$ with $(1/2+\\gamma)|E|$ edges. Then $G'$ contains a directed cycle of length at least $(c-o(1))n$. Moreover, there is a subgraph $G''$ of $G$ with $(1/2+\\gamma-o(1))|E|$ edges that does not contain a cycle of length at least $cn$."},"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":"1009.3721","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-20T07:47:18Z","cross_cats_sorted":[],"title_canon_sha256":"2edf66b4f33af8742c907e28066cd28aa3d2e2efffc8b0f96332f503ce54bee4","abstract_canon_sha256":"8064b2dd27b4118bd338d126755bb3cb517b9cf9bd6df7cd10d5c560c8be4181"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:43.997268Z","signature_b64":"VhRsOrhvqlPrhGnr9HC1QxTPwd3pC7dHamp+Gv0hg1BJhAsKN+e/JkT2ktvOsvHODJyhJloi5SJ9I6ssI9WEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9f9b986da1ed5c1d5dcd3aa256790c17d31c8bb440a40c8fa70544715b749c1","last_reissued_at":"2026-05-18T04:40:43.996669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:43.996669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long cycles in subgraphs of (pseudo)random directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Ido Ben-Eliezer, Michael Krivelevich","submitted_at":"2010-09-20T07:47:18Z","abstract_excerpt":"We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every $0 < \\gamma < 1/2$ we find a constant $c=c(\\gamma)$ such that the following holds. Let $G=(V,E)$ be a (pseudo)random directed graph on $n$ vertices, and let $G'$ be a subgraph of $G$ with $(1/2+\\gamma)|E|$ edges. Then $G'$ contains a directed cycle of length at least $(c-o(1))n$. Moreover, there is a subgraph $G''$ of $G$ with $(1/2+\\gamma-o(1))|E|$ edges that does not contain a cycle of length at least $cn$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3721","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":"1009.3721","created_at":"2026-05-18T04:40:43.996777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3721v1","created_at":"2026-05-18T04:40:43.996777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3721","created_at":"2026-05-18T04:40:43.996777+00:00"},{"alias_kind":"pith_short_12","alias_value":"VH43TBW2D3K4","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VH43TBW2D3K4DVO4","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VH43TBW2","created_at":"2026-05-18T12:26:15.391820+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/VH43TBW2D3K4DVO42OVCKZ4QYF","json":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF.json","graph_json":"https://pith.science/api/pith-number/VH43TBW2D3K4DVO42OVCKZ4QYF/graph.json","events_json":"https://pith.science/api/pith-number/VH43TBW2D3K4DVO42OVCKZ4QYF/events.json","paper":"https://pith.science/paper/VH43TBW2"},"agent_actions":{"view_html":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF","download_json":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF.json","view_paper":"https://pith.science/paper/VH43TBW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3721&json=true","fetch_graph":"https://pith.science/api/pith-number/VH43TBW2D3K4DVO42OVCKZ4QYF/graph.json","fetch_events":"https://pith.science/api/pith-number/VH43TBW2D3K4DVO42OVCKZ4QYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF/action/storage_attestation","attest_author":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF/action/author_attestation","sign_citation":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF/action/citation_signature","submit_replication":"https://pith.science/pith/VH43TBW2D3K4DVO42OVCKZ4QYF/action/replication_record"}},"created_at":"2026-05-18T04:40:43.996777+00:00","updated_at":"2026-05-18T04:40:43.996777+00:00"}