{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7WYXVS2TCUDL2NAAW7P4EDFROM","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":"cfcb34302a8a213102aefad6366de2ca5dfb59550277c32c8c54f31d9f9e7d30","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-05-13T21:06:28Z","title_canon_sha256":"3ad2adb6770d3d2b13092dba3113cdebe4ded51d4b40de4916405d3cee409286"},"schema_version":"1.0","source":{"id":"1205.2909","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2909","created_at":"2026-05-18T03:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2909v3","created_at":"2026-05-18T03:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2909","created_at":"2026-05-18T03:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"7WYXVS2TCUDL","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7WYXVS2TCUDL2NAA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7WYXVS2T","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:eeace88e6f6f20547ad1c07e688afd08bda34445067c81e196a11f98d12bbffe","target":"graph","created_at":"2026-05-18T03:45:00Z","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":"We model the robustness against random failure or intentional attack of networks with arbitrary large-scale structure. We construct a block-based model which incorporates --- in a general fashion --- both connectivity and interdependence links, as well as arbitrary degree distributions and block correlations. By optimizing the percolation properties of this general class of networks, we identify a simple core-periphery structure as the topology most robust against random failure. In such networks, a distinct and small \"core\" of nodes with higher degree is responsible for most of the connectivi","authors_text":"Stefan Bornholdt, Tiago P. Peixoto","cross_cats":["cond-mat.stat-mech","cs.SI","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-05-13T21:06:28Z","title":"Evolution of robust network topologies: Emergence of central backbones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2909","kind":"arxiv","version":3},"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":"sha256:020f8013c9d50e5722e370ea0c0cf56228a0bbcf7eaf77608f4ec8aaff12d495","target":"record","created_at":"2026-05-18T03:45:00Z","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":"cfcb34302a8a213102aefad6366de2ca5dfb59550277c32c8c54f31d9f9e7d30","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-05-13T21:06:28Z","title_canon_sha256":"3ad2adb6770d3d2b13092dba3113cdebe4ded51d4b40de4916405d3cee409286"},"schema_version":"1.0","source":{"id":"1205.2909","kind":"arxiv","version":3}},"canonical_sha256":"fdb17acb531506bd3400b7dfc20cb1733aaf3fc5a9b6b0b27ee955e422e5825c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdb17acb531506bd3400b7dfc20cb1733aaf3fc5a9b6b0b27ee955e422e5825c","first_computed_at":"2026-05-18T03:45:00.369702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:00.369702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+mfgbeN564NQwXZKUh+YpF3b0F+tjCyhZ/BTpZy+VXyyTtlWZCMDtq1s4ZsjX6E2M9KayvyhCTqKV9D3bWULCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:00.370401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2909","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:020f8013c9d50e5722e370ea0c0cf56228a0bbcf7eaf77608f4ec8aaff12d495","sha256:eeace88e6f6f20547ad1c07e688afd08bda34445067c81e196a11f98d12bbffe"],"state_sha256":"16d6d0e7dc207802a60a6c3e9b106fcda5b26154c96ab6d1448e3de2008b4d9b"}