{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:N7WDXMEUZD44WLVRNKPDUMPKBS","short_pith_number":"pith:N7WDXMEU","schema_version":"1.0","canonical_sha256":"6fec3bb094c8f9cb2eb16a9e3a31ea0ca910ca2dfd64be1dd6cc31d89a690084","source":{"kind":"arxiv","id":"1203.6119","version":6},"attestation_state":"computed","paper":{"title":"Robustness of Complex Networks with Implications for Consensus and Contagion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Elaheh Fata, Haotian Zhang, Shreyas Sundaram","submitted_at":"2012-03-28T00:36:17Z","abstract_excerpt":"We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph properties such as connectivity and minimum degree in that one can construct graphs with high connectivity and minimum degree but low robustness. However, we show that the notions of connectivity and robustness coincide on common random graph models for complex networks (Erdos-Renyi, geometric random, and preferential attachment graphs). More specifically, the pro"},"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":"1203.6119","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-03-28T00:36:17Z","cross_cats_sorted":["cs.SY","physics.soc-ph"],"title_canon_sha256":"8de8823208bf4bd351f3e8480386c8925389ce368e6df1715448543113962f7e","abstract_canon_sha256":"5fa2dcbc77597e0c518103f47529f27b81b035c23f08fc472c9ba9690410fa54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:16.804778Z","signature_b64":"0eFd6Uz8wrxC0sVA3AhdOi3pfIlylqvc7n+yEHP/Ek51pfgd4rRwB7J8pi9Ib9ePM18b5O57tleBIsBaPPD3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fec3bb094c8f9cb2eb16a9e3a31ea0ca910ca2dfd64be1dd6cc31d89a690084","last_reissued_at":"2026-05-18T02:21:16.804247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:16.804247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robustness of Complex Networks with Implications for Consensus and Contagion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Elaheh Fata, Haotian Zhang, Shreyas Sundaram","submitted_at":"2012-03-28T00:36:17Z","abstract_excerpt":"We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph properties such as connectivity and minimum degree in that one can construct graphs with high connectivity and minimum degree but low robustness. However, we show that the notions of connectivity and robustness coincide on common random graph models for complex networks (Erdos-Renyi, geometric random, and preferential attachment graphs). More specifically, the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6119","kind":"arxiv","version":6},"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":"1203.6119","created_at":"2026-05-18T02:21:16.804327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.6119v6","created_at":"2026-05-18T02:21:16.804327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6119","created_at":"2026-05-18T02:21:16.804327+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7WDXMEUZD44","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7WDXMEUZD44WLVR","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7WDXMEU","created_at":"2026-05-18T12:27:16.716162+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/N7WDXMEUZD44WLVRNKPDUMPKBS","json":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS.json","graph_json":"https://pith.science/api/pith-number/N7WDXMEUZD44WLVRNKPDUMPKBS/graph.json","events_json":"https://pith.science/api/pith-number/N7WDXMEUZD44WLVRNKPDUMPKBS/events.json","paper":"https://pith.science/paper/N7WDXMEU"},"agent_actions":{"view_html":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS","download_json":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS.json","view_paper":"https://pith.science/paper/N7WDXMEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.6119&json=true","fetch_graph":"https://pith.science/api/pith-number/N7WDXMEUZD44WLVRNKPDUMPKBS/graph.json","fetch_events":"https://pith.science/api/pith-number/N7WDXMEUZD44WLVRNKPDUMPKBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS/action/storage_attestation","attest_author":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS/action/author_attestation","sign_citation":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS/action/citation_signature","submit_replication":"https://pith.science/pith/N7WDXMEUZD44WLVRNKPDUMPKBS/action/replication_record"}},"created_at":"2026-05-18T02:21:16.804327+00:00","updated_at":"2026-05-18T02:21:16.804327+00:00"}