{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BYW5B7VMH2KUIUQR4ZT2WVDVPS","short_pith_number":"pith:BYW5B7VM","schema_version":"1.0","canonical_sha256":"0e2dd0feac3e95445211e667ab54757c8a71c48e563c35acc042aaccc39c141e","source":{"kind":"arxiv","id":"1210.1357","version":2},"attestation_state":"computed","paper":{"title":"A quantitative method for determining the robustness of complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Bojin Zheng, Hongrun Wu, Jun Qin, Xiaonian Tong","submitted_at":"2012-10-04T09:46:26Z","abstract_excerpt":"Most current studies estimate the invulnerability of complex networks using a qualitative method that analyzes the inaccurate decay rate of network efficiency. This method results in confusion over the invulnerability of various types of complex networks. By normalizing network efficiency and defining a baseline, this paper defines the invulnerability index as the integral of the difference between the normalized network efficiency curve and the baseline. This quantitative method seeks to establish a benchmark for the robustness and fragility of networks and to measure network invulnerability "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.1357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-10-04T09:46:26Z","cross_cats_sorted":["nlin.AO","physics.soc-ph"],"title_canon_sha256":"ae290939a050dcb1b4a33b9024128417bfeae93420064ad90bff5384602d8b4d","abstract_canon_sha256":"713c55024a9017fdfb5ac19a18701d3449eaaf30816fdcb0ddf97595ea1b0847"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:57.717987Z","signature_b64":"CnWn7sb6TqpMa8X+g4eqlQJaOLhxYgi+vBRVFX3rH3lhhW0on70tscXTRNrQjpvPoOGy5juTebUK9sXm9E/kCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e2dd0feac3e95445211e667ab54757c8a71c48e563c35acc042aaccc39c141e","last_reissued_at":"2026-05-18T02:58:57.717077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:57.717077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quantitative method for determining the robustness of complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Bojin Zheng, Hongrun Wu, Jun Qin, Xiaonian Tong","submitted_at":"2012-10-04T09:46:26Z","abstract_excerpt":"Most current studies estimate the invulnerability of complex networks using a qualitative method that analyzes the inaccurate decay rate of network efficiency. This method results in confusion over the invulnerability of various types of complex networks. By normalizing network efficiency and defining a baseline, this paper defines the invulnerability index as the integral of the difference between the normalized network efficiency curve and the baseline. This quantitative method seeks to establish a benchmark for the robustness and fragility of networks and to measure network invulnerability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1357","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.1357","created_at":"2026-05-18T02:58:57.717242+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1357v2","created_at":"2026-05-18T02:58:57.717242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1357","created_at":"2026-05-18T02:58:57.717242+00:00"},{"alias_kind":"pith_short_12","alias_value":"BYW5B7VMH2KU","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BYW5B7VMH2KUIUQR","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BYW5B7VM","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS","json":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS.json","graph_json":"https://pith.science/api/pith-number/BYW5B7VMH2KUIUQR4ZT2WVDVPS/graph.json","events_json":"https://pith.science/api/pith-number/BYW5B7VMH2KUIUQR4ZT2WVDVPS/events.json","paper":"https://pith.science/paper/BYW5B7VM"},"agent_actions":{"view_html":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS","download_json":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS.json","view_paper":"https://pith.science/paper/BYW5B7VM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1357&json=true","fetch_graph":"https://pith.science/api/pith-number/BYW5B7VMH2KUIUQR4ZT2WVDVPS/graph.json","fetch_events":"https://pith.science/api/pith-number/BYW5B7VMH2KUIUQR4ZT2WVDVPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS/action/storage_attestation","attest_author":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS/action/author_attestation","sign_citation":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS/action/citation_signature","submit_replication":"https://pith.science/pith/BYW5B7VMH2KUIUQR4ZT2WVDVPS/action/replication_record"}},"created_at":"2026-05-18T02:58:57.717242+00:00","updated_at":"2026-05-18T02:58:57.717242+00:00"}