{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q7GF3WLRFR6765O2MMCB666TZZ","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":"00d07f9f4afdaec3c59285e72fba4d34d2f045ee6e006d5ecb19fc148d0dc4cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-09-26T12:35:19Z","title_canon_sha256":"99ad546cc852dd0e84c88e57638e4ed9419622b7c8677a6e5f6857d23762b130"},"schema_version":"1.0","source":{"id":"1610.00997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00997","created_at":"2026-05-18T00:32:26Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00997v1","created_at":"2026-05-18T00:32:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00997","created_at":"2026-05-18T00:32:26Z"},{"alias_kind":"pith_short_12","alias_value":"Q7GF3WLRFR67","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q7GF3WLRFR6765O2","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q7GF3WLR","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:37a0e39ce64b8e64de143665eaa4b774d1853a019a2a9a861721afa99a50425f","target":"graph","created_at":"2026-05-18T00:32:26Z","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":"Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component.We identify","authors_text":"Hans J. Herrmann, Jan Nagler, Lucas B\\\"ottcher, Mirko Lukovic, Shlomo Havlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-09-26T12:35:19Z","title":"Impact of embedding on predictability of failure-recovery dynamics in networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00997","kind":"arxiv","version":1},"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":"sha256:5d965cd8afebb1b8324309d20c0354fac968538a8ce4000048c3b11230d6b1c6","target":"record","created_at":"2026-05-18T00:32:26Z","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":"00d07f9f4afdaec3c59285e72fba4d34d2f045ee6e006d5ecb19fc148d0dc4cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-09-26T12:35:19Z","title_canon_sha256":"99ad546cc852dd0e84c88e57638e4ed9419622b7c8677a6e5f6857d23762b130"},"schema_version":"1.0","source":{"id":"1610.00997","kind":"arxiv","version":1}},"canonical_sha256":"87cc5dd9712c7dff75da63041f7bd3ce6c8a31e4e72b7e64f189b9919077c237","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87cc5dd9712c7dff75da63041f7bd3ce6c8a31e4e72b7e64f189b9919077c237","first_computed_at":"2026-05-18T00:32:26.034157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:26.034157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nuMI4sTP9KynrOQLqPVTkYSQWFUx0rjk8Qj8aqHEBqM2izvlomyD/3F/SkhBNip6nCKEtYGs6+zn1SutjS20DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:26.034843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d965cd8afebb1b8324309d20c0354fac968538a8ce4000048c3b11230d6b1c6","sha256:37a0e39ce64b8e64de143665eaa4b774d1853a019a2a9a861721afa99a50425f"],"state_sha256":"aa4f168ed0565fa22c5a709f9250d8326635127abcc334a7986eeddb8bf9dd33"}