{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VTJ5EEJAXSL2RKL43MUZ4H52PJ","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":"eea9be04b404557267d623e5b5b4349b6324679bff159f48ac77b1ad2d8097e2","cross_cats_sorted":["cs.SI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-12-09T21:28:13Z","title_canon_sha256":"9ab258c40e42c01c6d323fadaead7f1a34245b1fe9569043c9121e83a3300749"},"schema_version":"1.0","source":{"id":"1412.3124","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3124","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3124v1","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3124","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"VTJ5EEJAXSL2","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VTJ5EEJAXSL2RKL4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VTJ5EEJA","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:51f212d22b6fc722bd1101a079d83ed375c024254eb43fffe271454ecb4db500","target":"graph","created_at":"2026-05-18T01:41:20Z","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":"The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks are neither random nor hub-targeted, but localized, where a group of neighboring nodes in a network are attacked and fail. In this paper we develop a percolation framework to analytically and numerically study the robustness of complex networks against such localized attack. In particular, we investigate this robustness in Erd\\H{o}s-R\\'{e}nyi networks, random-","authors_text":"H Eugene Stanley, Shlomo Havlin, Shuai Shao, Xuqing Huang","cross_cats":["cs.SI","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-12-09T21:28:13Z","title":"Percolation of localized attack on complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3124","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":"sha256:4c08ed61215a6f5099f9cb2559cc22f2c647e7548c9d8f5a8aff0d8529408558","target":"record","created_at":"2026-05-18T01:41:20Z","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":"eea9be04b404557267d623e5b5b4349b6324679bff159f48ac77b1ad2d8097e2","cross_cats_sorted":["cs.SI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-12-09T21:28:13Z","title_canon_sha256":"9ab258c40e42c01c6d323fadaead7f1a34245b1fe9569043c9121e83a3300749"},"schema_version":"1.0","source":{"id":"1412.3124","kind":"arxiv","version":1}},"canonical_sha256":"acd3d21120bc97a8a97cdb299e1fba7a6e7339aa5491c5bd0be6b84b31219c4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acd3d21120bc97a8a97cdb299e1fba7a6e7339aa5491c5bd0be6b84b31219c4c","first_computed_at":"2026-05-18T01:41:20.249128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:20.249128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wGctejW1/yYSv7uuCv52OyUTqfT3FC1LzCH6k0xhPAeAU3+7Ya6wuIkMwq+Wou4DQ1tnFQc4V6oEYo/7S+p5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:20.249545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3124","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c08ed61215a6f5099f9cb2559cc22f2c647e7548c9d8f5a8aff0d8529408558","sha256:51f212d22b6fc722bd1101a079d83ed375c024254eb43fffe271454ecb4db500"],"state_sha256":"d33a48ada51d9031d4899e2fac8f98d8c0e8f6582b35a373205789c070ada7c4"}