{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CZ2FAFUPTP5GMUJ7TTEBXFT5CI","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":"611adf5dbdad319f834df3f443d92775f8806a694fc1eb58bdb8e755aa09293f","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-04-18T14:25:04Z","title_canon_sha256":"7bf72d40e09e4ed329b388f7e9f0944ab67a799afa685cf3e71658b855cc51d9"},"schema_version":"1.0","source":{"id":"1604.05175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05175","created_at":"2026-05-18T01:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05175v2","created_at":"2026-05-18T01:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05175","created_at":"2026-05-18T01:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"CZ2FAFUPTP5G","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CZ2FAFUPTP5GMUJ7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CZ2FAFUP","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e94ef7c5d073623aa22b86de49aaec99454ec69038278faa088bb1aa51e2f711","target":"graph","created_at":"2026-05-18T01:05:43Z","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":"Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers $M$. Specifically we propose and compare two message passing algorithms, that generalize the algorithm widely used to study the","authors_text":"Davide Cellai, Ginestra Bianconi, Sergey N. Dorogovtsev","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-04-18T14:25:04Z","title":"Message passing theory for percolation models on multiplex networks with link overlap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05175","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":"sha256:35f292c436e795aa30066b1ed558fb3141a9f408d2cdba02bca831f62876c6fa","target":"record","created_at":"2026-05-18T01:05:43Z","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":"611adf5dbdad319f834df3f443d92775f8806a694fc1eb58bdb8e755aa09293f","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-04-18T14:25:04Z","title_canon_sha256":"7bf72d40e09e4ed329b388f7e9f0944ab67a799afa685cf3e71658b855cc51d9"},"schema_version":"1.0","source":{"id":"1604.05175","kind":"arxiv","version":2}},"canonical_sha256":"167450168f9bfa66513f9cc81b967d122344d6781d9ad36c5cd89cc9e669e8bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"167450168f9bfa66513f9cc81b967d122344d6781d9ad36c5cd89cc9e669e8bf","first_computed_at":"2026-05-18T01:05:43.467308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:43.467308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uKPyjE5Nr7XpgkNKLmJdZWWqQRNA0UnLS7a6o++Uvpmog8ZKGrT3vaHL7ej125EuyZ6D05hKto/dB87qEIzbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:43.467793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35f292c436e795aa30066b1ed558fb3141a9f408d2cdba02bca831f62876c6fa","sha256:e94ef7c5d073623aa22b86de49aaec99454ec69038278faa088bb1aa51e2f711"],"state_sha256":"1ec1d2099ba4dac53163517dfddbca3909b33ec1d82a5a1e7618d08280923ec2"}