{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3NC57EV74IKX2FTJ3ZTXEQWO4F","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":"445a8e4b9d735642b99a56208586d9dc70a641e22dd6a29bb8408f6f4b0121d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T15:03:02Z","title_canon_sha256":"d8e0c5854ed1bf5a19251bd5520fa368b24fa08d367624c6ca931f209dd514c6"},"schema_version":"1.0","source":{"id":"1509.07019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07019","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07019v1","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07019","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"3NC57EV74IKX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3NC57EV74IKX2FTJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3NC57EV7","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:e85c6afdbdbd09cff2b09e87152a09584e5ad5dfb09e178bd345583b3eb11763","target":"graph","created_at":"2026-05-18T01:32:17Z","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":"A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in which each vertex is given a random weight, and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is characterized and is shown to depend on the weight of the vertex. In particular, if the weight distribution is a power law, the degree distribution will be so as well. Furthermore, an as","authors_text":"Maria Deijfen, Willemien Kets","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T15:03:02Z","title":"Random intersection graphs with tunable degree distribution and clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07019","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:c5f582d18cc7e07da8c2f06cc8dd681e44b0c35a6afe1589c7b0dace0b851d2c","target":"record","created_at":"2026-05-18T01:32:17Z","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":"445a8e4b9d735642b99a56208586d9dc70a641e22dd6a29bb8408f6f4b0121d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T15:03:02Z","title_canon_sha256":"d8e0c5854ed1bf5a19251bd5520fa368b24fa08d367624c6ca931f209dd514c6"},"schema_version":"1.0","source":{"id":"1509.07019","kind":"arxiv","version":1}},"canonical_sha256":"db45df92bfe2157d1669de677242cee169249c57adaafbf6925b0b8ff5e1f504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db45df92bfe2157d1669de677242cee169249c57adaafbf6925b0b8ff5e1f504","first_computed_at":"2026-05-18T01:32:17.185865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:17.185865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IhAqqBtViUyHEizANugZG7xOlwfajZ0nGtYcxakrFTDp4V3tjJ8uUeQJJTiCsItKGumFSAyOx0uq1z09pQrkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:17.186521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5f582d18cc7e07da8c2f06cc8dd681e44b0c35a6afe1589c7b0dace0b851d2c","sha256:e85c6afdbdbd09cff2b09e87152a09584e5ad5dfb09e178bd345583b3eb11763"],"state_sha256":"e2107fd35223992f025948f8dd37ec4f295e7277c057fbaeea930e40b6dd8726"}