{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VNQY3ALGISODNTUJSGL2SLQBFO","short_pith_number":"pith:VNQY3ALG","canonical_record":{"source":{"id":"1602.06238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2016-02-18T16:34:39Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"title_canon_sha256":"006a83d7f17f29a341ca995868b1152214044fb92c8eccbd8583540e6868d877","abstract_canon_sha256":"7be6140a072b9fc3d776a0a2310d4c4b44058c3326836188e2fbff2cfd3df172"},"schema_version":"1.0"},"canonical_sha256":"ab618d8166449c36ce899197a92e012baf49c2004fa8a5bb4a7f499b2c49f0c2","source":{"kind":"arxiv","id":"1602.06238","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06238","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06238v2","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06238","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"VNQY3ALGISOD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VNQY3ALGISODNTUJ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VNQY3ALG","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VNQY3ALGISODNTUJSGL2SLQBFO","target":"record","payload":{"canonical_record":{"source":{"id":"1602.06238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2016-02-18T16:34:39Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"title_canon_sha256":"006a83d7f17f29a341ca995868b1152214044fb92c8eccbd8583540e6868d877","abstract_canon_sha256":"7be6140a072b9fc3d776a0a2310d4c4b44058c3326836188e2fbff2cfd3df172"},"schema_version":"1.0"},"canonical_sha256":"ab618d8166449c36ce899197a92e012baf49c2004fa8a5bb4a7f499b2c49f0c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:02.238975Z","signature_b64":"tsvuVMCcRZW7q0zaapJPEkNSPhOZ2fcjZoAh6lmtA4ccpp8TWuhkb1+kt7gP4Bk+qFyVgeII3g8A7zLDzO3jCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab618d8166449c36ce899197a92e012baf49c2004fa8a5bb4a7f499b2c49f0c2","last_reissued_at":"2026-05-18T00:41:02.238234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:02.238234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.06238","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YKNdKqNkk3m/fqyadz2ryJBJyxfGQAI14Fqua8r2A/syRrPSPiX/mlnC/OasIzRfDeuYStGYdF/gegh5CmPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:31:40.231732Z"},"content_sha256":"6fb23b4f84c5dd8e5466428d24395c91a2a25af530dff1422ed6422394bf0502","schema_version":"1.0","event_id":"sha256:6fb23b4f84c5dd8e5466428d24395c91a2a25af530dff1422ed6422394bf0502"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VNQY3ALGISODNTUJSGL2SLQBFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of Robustness in Network of Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"primary_cat":"q-bio.NC","authors_text":"Byungjoon Min, Flaviano Morone, Hern\\'an A. Makse, Kevin Roth","submitted_at":"2016-02-18T16:34:39Z","abstract_excerpt":"A model of interdependent networks of networks (NoN) has been introduced recently in the context of brain activation to identify the neural collective influencers in the brain NoN. Here we develop a new approach to derive an exact expression for the random percolation transition in Erd\\\"{o}s-R\\'enyi NoN. Analytical calculations are in excellent agreement with numerical simulations and highlight the robustness of the NoN against random node failures. Interestingly, the phase diagram of the model unveils particular patterns of interconnectivity for which the NoN is most vulnerable. Our results h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06238","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTCJSIqHjq22zVJzYaGE0yRfltM5zDxyTRU2cP/UcgklNW9CGUFfS8qdbqy3Nv8SL68vBjSMRU5/AvF4CkRbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:31:40.232259Z"},"content_sha256":"b4dd85f93b6600a2133bb567824dc14cb5b7f470ecad24047c649103b2fd4cbd","schema_version":"1.0","event_id":"sha256:b4dd85f93b6600a2133bb567824dc14cb5b7f470ecad24047c649103b2fd4cbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNQY3ALGISODNTUJSGL2SLQBFO/bundle.json","state_url":"https://pith.science/pith/VNQY3ALGISODNTUJSGL2SLQBFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNQY3ALGISODNTUJSGL2SLQBFO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T14:31:40Z","links":{"resolver":"https://pith.science/pith/VNQY3ALGISODNTUJSGL2SLQBFO","bundle":"https://pith.science/pith/VNQY3ALGISODNTUJSGL2SLQBFO/bundle.json","state":"https://pith.science/pith/VNQY3ALGISODNTUJSGL2SLQBFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNQY3ALGISODNTUJSGL2SLQBFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VNQY3ALGISODNTUJSGL2SLQBFO","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":"7be6140a072b9fc3d776a0a2310d4c4b44058c3326836188e2fbff2cfd3df172","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2016-02-18T16:34:39Z","title_canon_sha256":"006a83d7f17f29a341ca995868b1152214044fb92c8eccbd8583540e6868d877"},"schema_version":"1.0","source":{"id":"1602.06238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06238","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06238v2","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06238","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"VNQY3ALGISOD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VNQY3ALGISODNTUJ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VNQY3ALG","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:b4dd85f93b6600a2133bb567824dc14cb5b7f470ecad24047c649103b2fd4cbd","target":"graph","created_at":"2026-05-18T00:41:02Z","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":"A model of interdependent networks of networks (NoN) has been introduced recently in the context of brain activation to identify the neural collective influencers in the brain NoN. Here we develop a new approach to derive an exact expression for the random percolation transition in Erd\\\"{o}s-R\\'enyi NoN. Analytical calculations are in excellent agreement with numerical simulations and highlight the robustness of the NoN against random node failures. Interestingly, the phase diagram of the model unveils particular patterns of interconnectivity for which the NoN is most vulnerable. Our results h","authors_text":"Byungjoon Min, Flaviano Morone, Hern\\'an A. Makse, Kevin Roth","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2016-02-18T16:34:39Z","title":"Emergence of Robustness in Network of Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06238","kind":"arxiv","version":2},"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":"sha256:6fb23b4f84c5dd8e5466428d24395c91a2a25af530dff1422ed6422394bf0502","target":"record","created_at":"2026-05-18T00:41:02Z","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":"7be6140a072b9fc3d776a0a2310d4c4b44058c3326836188e2fbff2cfd3df172","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2016-02-18T16:34:39Z","title_canon_sha256":"006a83d7f17f29a341ca995868b1152214044fb92c8eccbd8583540e6868d877"},"schema_version":"1.0","source":{"id":"1602.06238","kind":"arxiv","version":2}},"canonical_sha256":"ab618d8166449c36ce899197a92e012baf49c2004fa8a5bb4a7f499b2c49f0c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab618d8166449c36ce899197a92e012baf49c2004fa8a5bb4a7f499b2c49f0c2","first_computed_at":"2026-05-18T00:41:02.238234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:02.238234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tsvuVMCcRZW7q0zaapJPEkNSPhOZ2fcjZoAh6lmtA4ccpp8TWuhkb1+kt7gP4Bk+qFyVgeII3g8A7zLDzO3jCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:02.238975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fb23b4f84c5dd8e5466428d24395c91a2a25af530dff1422ed6422394bf0502","sha256:b4dd85f93b6600a2133bb567824dc14cb5b7f470ecad24047c649103b2fd4cbd"],"state_sha256":"f68bca650acef1dfd57c253357ee6353a29f953b39141d723eb0a88b1aabff41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TIJIqXqYo9dGJrTikea67w155b2jt984t1/K5K01TfH/6cedKEM5KLTDRrAS60hEXMIiyixEvPlIBsN+YN2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:31:40.235698Z","bundle_sha256":"a86228c34af67c714e6c07f7a55c4afc8d012af9800fca94186788224a8445bf"}}