{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A4Y3EWLQNLRVDSQ7SUYGRM5ZSB","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":"ee37d8a7bcbe5fa076db0254937939b064370fdc687a5405fa7e30b2a0c0a069","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T19:07:00Z","title_canon_sha256":"e3a2bbcbd46222bb20ef8ccd267da98a67bf66a70afb905b46a67060919f1183"},"schema_version":"1.0","source":{"id":"1609.01699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01699","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01699v1","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01699","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"A4Y3EWLQNLRV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A4Y3EWLQNLRVDSQ7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A4Y3EWLQ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:2913afae99d23ebc6c907c13ae647e7bcbebbf29a3fe0afea47413379ab5532e","target":"graph","created_at":"2026-05-18T01:05:38Z","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":"Random intersection graphs are characterized by three parameters: $n$, $m$ and $p$, where $n$ is the number of vertices, $m$ is the number of objects, and $p$ is the probability that a given object is associated with a given vertex. Two vertices in a random intersection graph are adjacent if and only if they have an associated object in common. When $m=\\lfloor n^\\alpha\\rfloor$ for constant $\\alpha$, we provide a condition, called {\\em strictly $\\alpha$-balanced}, for the Poisson convergence of the number of induced copies of a fixed subgraph.","authors_text":"Dudley Stark, Katarzyna Rybarczyk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T19:07:00Z","title":"Poisson approximation of counts of subgraphs in random intersection graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01699","kind":"arxiv","version":1},"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:c6a95c75dc54371e2c7ecf13df92dfd3e4bc1bb48e2fa25c3095577c4af606f2","target":"record","created_at":"2026-05-18T01:05:38Z","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":"ee37d8a7bcbe5fa076db0254937939b064370fdc687a5405fa7e30b2a0c0a069","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-06T19:07:00Z","title_canon_sha256":"e3a2bbcbd46222bb20ef8ccd267da98a67bf66a70afb905b46a67060919f1183"},"schema_version":"1.0","source":{"id":"1609.01699","kind":"arxiv","version":1}},"canonical_sha256":"0731b259706ae351ca1f953068b3b9906b321f5b9ec577d56408b490f26f703e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0731b259706ae351ca1f953068b3b9906b321f5b9ec577d56408b490f26f703e","first_computed_at":"2026-05-18T01:05:38.968940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:38.968940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q2CuR09s5As/8IYyQuZAN0oifOmlGyuQZdTy85YtaRN6o1qjCsRL/uyi55MWif7LSHI8rX2W64gj8fCP7lFjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:38.969520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6a95c75dc54371e2c7ecf13df92dfd3e4bc1bb48e2fa25c3095577c4af606f2","sha256:2913afae99d23ebc6c907c13ae647e7bcbebbf29a3fe0afea47413379ab5532e"],"state_sha256":"0651607c20f025195e8e8e8682781bdcac5ffbe92d20856ea4d33ed185dac365"}