{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UQEY5BBF5DONQVYDLCYQYOO2TE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"77a59902547c9a6273d275568a087fcbe288f524c4557894b386f8ed3725e897","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-30T09:23:46Z","title_canon_sha256":"f3166883a8f945fbbdf4fb41afe320e0463db817be52a41ee8f78c2932204751"},"schema_version":"1.0","source":{"id":"1105.5913","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5913","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5913v2","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5913","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"pith_short_12","alias_value":"UQEY5BBF5DON","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UQEY5BBF5DONQVYD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UQEY5BBF","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:d7342f8ad1098d15281d885f507acebc74d21090ee7f2551fe71b2ebdccc0784","target":"graph","created_at":"2026-05-18T02:29:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We describe a general approach of determining the distribution of spanning subgraphs in the random graph $\\G(n,p)$. In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a generalisation of the $d$-factors, of spanning triangle-free subgraphs, of (directed) Hamilton cycles and of spanning subgraphs that are isomorphic to a collection of vertex disjoint (directed) triangles.","authors_text":"Pu Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-30T09:23:46Z","title":"Distributions of sparse spanning subgraphs in random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5913","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:af045ec809ef87041186e26c079a403dbf4ae4b8b165870986d192f0f700a32c","target":"record","created_at":"2026-05-18T02:29:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"77a59902547c9a6273d275568a087fcbe288f524c4557894b386f8ed3725e897","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-30T09:23:46Z","title_canon_sha256":"f3166883a8f945fbbdf4fb41afe320e0463db817be52a41ee8f78c2932204751"},"schema_version":"1.0","source":{"id":"1105.5913","kind":"arxiv","version":2}},"canonical_sha256":"a4098e8425e8dcd8570358b10c39da99211d857c825416d3527e52c771749b85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4098e8425e8dcd8570358b10c39da99211d857c825416d3527e52c771749b85","first_computed_at":"2026-05-18T02:29:23.806295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:23.806295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VTFod4e7kcq5WpB9KovDBtRT1cWNy8YaoCO1uwUXgFiQgxMbxgpMkrg0U5UuYspMqLu7h59d6HqNSEpJ+Z33Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:23.806779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5913","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af045ec809ef87041186e26c079a403dbf4ae4b8b165870986d192f0f700a32c","sha256:d7342f8ad1098d15281d885f507acebc74d21090ee7f2551fe71b2ebdccc0784"],"state_sha256":"3b66c489113e54ed4fa5d37b4d741853791c0cd50fd98b4f3d988eae36f597f6"}