{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EMG6KVC3LKIZFESEYW6OH232DQ","short_pith_number":"pith:EMG6KVC3","schema_version":"1.0","canonical_sha256":"230de5545b5a91929244c5bce3eb7a1c0c880b26647a5d4ae78e9f371729d7da","source":{"kind":"arxiv","id":"1306.3454","version":2},"attestation_state":"computed","paper":{"title":"Vulnerability of robust preferential attachment networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Maren Eckhoff, Peter M\\\"orters","submitted_at":"2013-06-14T16:49:50Z","abstract_excerpt":"Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the science literature that such networks are highly vulnerable to a targeted attack, and removing a small number of key nodes in the network will dramatically change the topological structure. Here we analyse a class of preferential attachment networks in the robust regime and prove four main results supporting this claim: After removal of an arbitrarily small p"},"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":"1306.3454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-14T16:49:50Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b7d069d90b6b41984bd6a606cbf631d4c2060a82b651114973a02c28100e4048","abstract_canon_sha256":"fda8ccfb8b529341817443208346dab987d75c4c1e381f033abf1cbde83986c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:20.513076Z","signature_b64":"QCxLCJoAbpPzVpefx/9bWy+YDIJNdv02Jxkr78/VRf9O/ayk90+DJeIayo0l9gK6R/BxMI2CLixcmsthjefkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230de5545b5a91929244c5bce3eb7a1c0c880b26647a5d4ae78e9f371729d7da","last_reissued_at":"2026-05-18T03:15:20.512485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:20.512485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vulnerability of robust preferential attachment networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Maren Eckhoff, Peter M\\\"orters","submitted_at":"2013-06-14T16:49:50Z","abstract_excerpt":"Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the science literature that such networks are highly vulnerable to a targeted attack, and removing a small number of key nodes in the network will dramatically change the topological structure. Here we analyse a class of preferential attachment networks in the robust regime and prove four main results supporting this claim: After removal of an arbitrarily small p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3454","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":"1306.3454","created_at":"2026-05-18T03:15:20.512582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3454v2","created_at":"2026-05-18T03:15:20.512582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3454","created_at":"2026-05-18T03:15:20.512582+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMG6KVC3LKIZ","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMG6KVC3LKIZFESE","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMG6KVC3","created_at":"2026-05-18T12:27:43.054852+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/EMG6KVC3LKIZFESEYW6OH232DQ","json":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ.json","graph_json":"https://pith.science/api/pith-number/EMG6KVC3LKIZFESEYW6OH232DQ/graph.json","events_json":"https://pith.science/api/pith-number/EMG6KVC3LKIZFESEYW6OH232DQ/events.json","paper":"https://pith.science/paper/EMG6KVC3"},"agent_actions":{"view_html":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ","download_json":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ.json","view_paper":"https://pith.science/paper/EMG6KVC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3454&json=true","fetch_graph":"https://pith.science/api/pith-number/EMG6KVC3LKIZFESEYW6OH232DQ/graph.json","fetch_events":"https://pith.science/api/pith-number/EMG6KVC3LKIZFESEYW6OH232DQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ/action/storage_attestation","attest_author":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ/action/author_attestation","sign_citation":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ/action/citation_signature","submit_replication":"https://pith.science/pith/EMG6KVC3LKIZFESEYW6OH232DQ/action/replication_record"}},"created_at":"2026-05-18T03:15:20.512582+00:00","updated_at":"2026-05-18T03:15:20.512582+00:00"}