{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BR3VUXIRTHDBRK66W6WFGWSL3P","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":"fc971688ea7089535f9e76bc96b0b9d1072c06d31c292a7da340dce90bb220ff","cross_cats_sorted":["cond-mat.stat-mech","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-14T14:55:18Z","title_canon_sha256":"947a7f2dc94fd7748559367ef891a7a10a918b2f7c3aea89ce512e6b5c6ee592"},"schema_version":"1.0","source":{"id":"1306.3416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3416","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3416v1","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3416","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"BR3VUXIRTHDB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BR3VUXIRTHDBRK66","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BR3VUXIR","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:e05f7609a514f6bcfe4a19126df3807a4695eaedca5f27dc162f98542e9f73e5","target":"graph","created_at":"2026-05-18T03:03:20Z","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":"Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of $","authors_text":"H. Eugene Stanley, Jianxi Gao, Sergey V. Buldyrev, Shlomo Havlin, Xiaoming Xu","cross_cats":["cond-mat.stat-mech","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-14T14:55:18Z","title":"Percolation of a general network of networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3416","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":"sha256:44882c47b387734a536fc2de5748415e9cad684039cd66618037bb509f849822","target":"record","created_at":"2026-05-18T03:03:20Z","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":"fc971688ea7089535f9e76bc96b0b9d1072c06d31c292a7da340dce90bb220ff","cross_cats_sorted":["cond-mat.stat-mech","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2013-06-14T14:55:18Z","title_canon_sha256":"947a7f2dc94fd7748559367ef891a7a10a918b2f7c3aea89ce512e6b5c6ee592"},"schema_version":"1.0","source":{"id":"1306.3416","kind":"arxiv","version":1}},"canonical_sha256":"0c775a5d1199c618abdeb7ac535a4bdbef21f54e0e881c216f0d793cf7f4e062","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c775a5d1199c618abdeb7ac535a4bdbef21f54e0e881c216f0d793cf7f4e062","first_computed_at":"2026-05-18T03:03:20.872211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:20.872211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5UkMyJUYAX2n9A6UKSmccXiDTFzStVWwEJ5haxF4ATa0kEXWudjYUTCrLb8iYHMYPTmeIXMhNTJODCLDL07EAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:20.872777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44882c47b387734a536fc2de5748415e9cad684039cd66618037bb509f849822","sha256:e05f7609a514f6bcfe4a19126df3807a4695eaedca5f27dc162f98542e9f73e5"],"state_sha256":"06c96afd99801e6ccef158354bd971236218ba6cad32cfd741499dd7b7da963f"}