{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GS372SF5JG34ZQSVCFTFFHQWHG","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":"d1fc4ff7ee0c85ea0a4bca7b6a3d3bea78629ddb6c02d3a16fd15ed0fedb3f91","cross_cats_sorted":["cs.DM","cs.SI","math.PR","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-21T17:49:26Z","title_canon_sha256":"61b2f29e4a591bb64e311cf7111155fb81aa4c6b8cf0e8911c1c883f36f66688"},"schema_version":"1.0","source":{"id":"1409.6022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6022","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6022v2","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6022","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"GS372SF5JG34","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GS372SF5JG34ZQSV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GS372SF5","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:3b45221fc20253320d86d4aaf4663c16a36a2bd8e1143896d886760bfd0e3fb8","target":"graph","created_at":"2026-05-18T02:27:50Z","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":"The Eschenauer--Gligor (EG) random key predistribution scheme has been widely recognized as a typical approach to secure communications in wireless sensor networks (WSNs). However, there is a lack of precise probability analysis on the reliable connectivity of WSNs under the EG scheme. To address this, we rigorously derive the asymptotically exact probability of $k$-connectivity in WSNs employing the EG scheme with unreliable links represented by independent on/off channels, where $k$-connectivity ensures that the network remains connected despite the failure of any $(k-1)$ sensors or links. O","authors_text":"Jun Zhao, Osman Ya\\u{g}an, Virgil Gligor","cross_cats":["cs.DM","cs.SI","math.PR","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-21T17:49:26Z","title":"Exact Analysis of k-Connectivity in Secure Sensor Networks with Unreliable Links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6022","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:cd920dc491fd2187da2e917f2eb2fbad1603178575d7851d9f7a1011c83e8935","target":"record","created_at":"2026-05-18T02:27:50Z","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":"d1fc4ff7ee0c85ea0a4bca7b6a3d3bea78629ddb6c02d3a16fd15ed0fedb3f91","cross_cats_sorted":["cs.DM","cs.SI","math.PR","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-21T17:49:26Z","title_canon_sha256":"61b2f29e4a591bb64e311cf7111155fb81aa4c6b8cf0e8911c1c883f36f66688"},"schema_version":"1.0","source":{"id":"1409.6022","kind":"arxiv","version":2}},"canonical_sha256":"34b7fd48bd49b7ccc2551166529e1639b9707231dcc45c5e13d1882419bc41d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34b7fd48bd49b7ccc2551166529e1639b9707231dcc45c5e13d1882419bc41d6","first_computed_at":"2026-05-18T02:27:50.968266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:50.968266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTXtocD0XhivhFZ3sU/htcPeVLGUPYjTmxQwIjwrsvn0mA16ecyc8iropR5Rc2AY0CnAbmf0KswM+t1g6sgDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:50.968660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd920dc491fd2187da2e917f2eb2fbad1603178575d7851d9f7a1011c83e8935","sha256:3b45221fc20253320d86d4aaf4663c16a36a2bd8e1143896d886760bfd0e3fb8"],"state_sha256":"a1c8011a7e2faafeaf33ddb2fd25fbfa710efea39e4525d87ebd3bf988409268"}