{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HURDLWZOX5IVCCTMIR3VY3YYOR","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":"00db22bcd4fb3458b9577d8537280573cb3698e8b3fcc7c15d6976bffc0759e6","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-08T16:44:40Z","title_canon_sha256":"441c48a5eb3bd3ea580a3fa713d7c4a848911dc9f1253ed7aa380215127ace43"},"schema_version":"1.0","source":{"id":"1504.02031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02031","created_at":"2026-05-18T00:21:15Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02031v2","created_at":"2026-05-18T00:21:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02031","created_at":"2026-05-18T00:21:15Z"},{"alias_kind":"pith_short_12","alias_value":"HURDLWZOX5IV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HURDLWZOX5IVCCTM","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HURDLWZO","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:36e9c948943040e551e5d71d6e8568021f7a931f5b4499117beeb19b586f293e","target":"graph","created_at":"2026-05-18T00:21:15Z","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 study the properties of the potential overlap between two networks $A,B$ sharing the same set of $N$ nodes (a two-layer network) whose respective degree distributions $p_A(k), p_B(k)$ are given. Defining the overlap coefficient $\\alpha$ as the Jaccard index, we derive upper bounds for the minimum and maximum overlap coefficient in terms of $p_A(k)$, $p_B(k)$ and $N$. We also present an algorithm based on cross-rewiring of links to obtain a two-layer network with any prescribed $\\alpha$ inside the permitted range. Finally, to illustrate the importance of the overlap for the dynamics of inter","authors_text":"David Juher, Joan Salda\\~na","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-08T16:44:40Z","title":"Creating and controlling overlap in two-layer networks. Application to a mean-field SIS epidemic model with awareness dissemination"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02031","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":"sha256:1de3639af094f5a1fe78b47624acc8ca2a4f77a68315aca22bc13afd49c248b8","target":"record","created_at":"2026-05-18T00:21:15Z","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":"00db22bcd4fb3458b9577d8537280573cb3698e8b3fcc7c15d6976bffc0759e6","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-08T16:44:40Z","title_canon_sha256":"441c48a5eb3bd3ea580a3fa713d7c4a848911dc9f1253ed7aa380215127ace43"},"schema_version":"1.0","source":{"id":"1504.02031","kind":"arxiv","version":2}},"canonical_sha256":"3d2235db2ebf51510a6c44775c6f187458eff224e6ef083969c2a65b7ebd12ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d2235db2ebf51510a6c44775c6f187458eff224e6ef083969c2a65b7ebd12ef","first_computed_at":"2026-05-18T00:21:15.027253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:15.027253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"moG5ILTgyq1MsDIpL+Pn+iMyy0N2WZprcGPfW5uXdCeP2ATawiB4Zjeom3lzwR1c9Fkg7sfapnG8dygmjwdJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:15.027667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de3639af094f5a1fe78b47624acc8ca2a4f77a68315aca22bc13afd49c248b8","sha256:36e9c948943040e551e5d71d6e8568021f7a931f5b4499117beeb19b586f293e"],"state_sha256":"5b359d860e7a1ba3beea282f7a455760d665965fc09dd584ad419413a8edacd8"}