{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:U3G4ZMG5YIKPWL2KF6RXDML2HG","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":"1ffb380188818889edb9b78fe7d89665c1d3ef76e8ae079c10f4641e528a7c34","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-28T09:21:52Z","title_canon_sha256":"1e79c44aef801fdb600116711ebc634166431ab3cc9cfe0ba629d6152e6a915b"},"schema_version":"1.0","source":{"id":"0910.5311","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5311","created_at":"2026-05-18T02:29:44Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5311v2","created_at":"2026-05-18T02:29:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5311","created_at":"2026-05-18T02:29:44Z"},{"alias_kind":"pith_short_12","alias_value":"U3G4ZMG5YIKP","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"U3G4ZMG5YIKPWL2K","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"U3G4ZMG5","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:f0faf7e4076a2d1875849fcc8e5563f2140bef14addb9d94c97af7a025ef56f1","target":"graph","created_at":"2026-05-18T02:29:44Z","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 solve the conjecture posed by Fill, Scheinerman and Singer-Cohen and show the equivalence of the sharp threshold functions of the random intersection graph G(n,m,p) with $m >= n^3$ and a graph in which each edge appears independently. Moreover we prove sharper equivalence results under some additional assumptions.","authors_text":"Katarzyna Rybarczyk","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-28T09:21:52Z","title":"Equivalence of the random intersection graph and G(n,p)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5311","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:c7acdcd79e853ff035b167082d65fd5d05b02aa913c0b099327486352abf3eb3","target":"record","created_at":"2026-05-18T02:29:44Z","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":"1ffb380188818889edb9b78fe7d89665c1d3ef76e8ae079c10f4641e528a7c34","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-28T09:21:52Z","title_canon_sha256":"1e79c44aef801fdb600116711ebc634166431ab3cc9cfe0ba629d6152e6a915b"},"schema_version":"1.0","source":{"id":"0910.5311","kind":"arxiv","version":2}},"canonical_sha256":"a6cdccb0ddc214fb2f4a2fa371b17a39826828bc3dde4c2476d9268f1aef7c22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6cdccb0ddc214fb2f4a2fa371b17a39826828bc3dde4c2476d9268f1aef7c22","first_computed_at":"2026-05-18T02:29:44.496255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:44.496255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q6HCIgkaswyOMU8c5FQ6EpjDdcMA9Tubfe/SkiZIWW7s4jCWW/vDy/B1KRg1fszqJj6O7DKl3KLTE/M/IfFIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:44.496681Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5311","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7acdcd79e853ff035b167082d65fd5d05b02aa913c0b099327486352abf3eb3","sha256:f0faf7e4076a2d1875849fcc8e5563f2140bef14addb9d94c97af7a025ef56f1"],"state_sha256":"14ed10b9e3f7b89dcb47444015ec81a2938448c842d1d8bff304360dfb0e5922"}