{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:J5DQWW2EAPWGLL43563YFFH4TU","short_pith_number":"pith:J5DQWW2E","schema_version":"1.0","canonical_sha256":"4f470b5b4403ec65af9befb78294fc9d10cd11f8117f1fabb458b3d11902afa7","source":{"kind":"arxiv","id":"1607.08496","version":1},"attestation_state":"computed","paper":{"title":"On the roots of the node reliability polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.CO","authors_text":"Jason Brown, Lucas Mol","submitted_at":"2016-07-28T15:12:35Z","abstract_excerpt":"Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce; it is the analogous node measure of robustness to the well studied \\textit{all-terminal reliability}, where the nodes are perfectly reliable but the edges fail randomly. In sharp contrast to what is known about the roots of the all-terminal reliability polynomial, we show that the node reliability polyn"},"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":"1607.08496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-28T15:12:35Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"880a98e708feb3989b666c3146207db623d8a678b3eaaa4c610435cc77f2559a","abstract_canon_sha256":"091b9603273b24b442cda1db3eff52fbfecf0699a9c95ae957c08769f165970b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:19.613864Z","signature_b64":"4WPF78wefZ85OVr3EgOrfLkrKgVgjr0qroBO7E3Ep3OpuZOqYIyca3461rCYHVVAgHcxl/99+R+b7/vdIKg0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f470b5b4403ec65af9befb78294fc9d10cd11f8117f1fabb458b3d11902afa7","last_reissued_at":"2026-05-18T00:40:19.613246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:19.613246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the roots of the node reliability polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.CO","authors_text":"Jason Brown, Lucas Mol","submitted_at":"2016-07-28T15:12:35Z","abstract_excerpt":"Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce; it is the analogous node measure of robustness to the well studied \\textit{all-terminal reliability}, where the nodes are perfectly reliable but the edges fail randomly. In sharp contrast to what is known about the roots of the all-terminal reliability polynomial, we show that the node reliability polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08496","kind":"arxiv","version":1},"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":"1607.08496","created_at":"2026-05-18T00:40:19.613349+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.08496v1","created_at":"2026-05-18T00:40:19.613349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08496","created_at":"2026-05-18T00:40:19.613349+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5DQWW2EAPWG","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5DQWW2EAPWGLL43","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5DQWW2E","created_at":"2026-05-18T12:30:22.444734+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/J5DQWW2EAPWGLL43563YFFH4TU","json":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU.json","graph_json":"https://pith.science/api/pith-number/J5DQWW2EAPWGLL43563YFFH4TU/graph.json","events_json":"https://pith.science/api/pith-number/J5DQWW2EAPWGLL43563YFFH4TU/events.json","paper":"https://pith.science/paper/J5DQWW2E"},"agent_actions":{"view_html":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU","download_json":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU.json","view_paper":"https://pith.science/paper/J5DQWW2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.08496&json=true","fetch_graph":"https://pith.science/api/pith-number/J5DQWW2EAPWGLL43563YFFH4TU/graph.json","fetch_events":"https://pith.science/api/pith-number/J5DQWW2EAPWGLL43563YFFH4TU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU/action/storage_attestation","attest_author":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU/action/author_attestation","sign_citation":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU/action/citation_signature","submit_replication":"https://pith.science/pith/J5DQWW2EAPWGLL43563YFFH4TU/action/replication_record"}},"created_at":"2026-05-18T00:40:19.613349+00:00","updated_at":"2026-05-18T00:40:19.613349+00:00"}