{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WWORTMF4J6UHPL4LOF3ZKGQPBS","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":"0ec04601efcddda861790eff74dc985adafeea0d952e8da8ea2b1a0099d3d141","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T17:53:00Z","title_canon_sha256":"b8adf98127e9a6a0ccc840f405843e39d8544cf565101ba095d5941450c57b0c"},"schema_version":"1.0","source":{"id":"1107.0400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0400","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0400v1","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0400","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"WWORTMF4J6UH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WWORTMF4J6UHPL4L","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WWORTMF4","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:619d03a885dd009340e24f55c57bc2ff1c1c86dfda1e4941bcf5fbb650814600","target":"graph","created_at":"2026-05-18T03:25:25Z","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":"In this paper we introduce the nullity of signed graphs, and give some results on the nullity of signed graphs with pendant trees. We characterize the unicyclic signed graphs of order n with nullity n-2; n-3; n-4; n-5 respectively.","authors_text":"Yi Wang, Yi-Zheng Fan, Yue Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T17:53:00Z","title":"The nullity of unicyclic signed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0400","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:fd455a6beac0029f6136a5e1da4286c967b0412295f1272cbad9f2212d2babac","target":"record","created_at":"2026-05-18T03:25:25Z","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":"0ec04601efcddda861790eff74dc985adafeea0d952e8da8ea2b1a0099d3d141","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T17:53:00Z","title_canon_sha256":"b8adf98127e9a6a0ccc840f405843e39d8544cf565101ba095d5941450c57b0c"},"schema_version":"1.0","source":{"id":"1107.0400","kind":"arxiv","version":1}},"canonical_sha256":"b59d19b0bc4fa877af8b7177951a0f0cb0ef37be213e91365bc2cb45fc56ca3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b59d19b0bc4fa877af8b7177951a0f0cb0ef37be213e91365bc2cb45fc56ca3f","first_computed_at":"2026-05-18T03:25:25.932853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:25.932853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FUnNpbdvkjYM5HzqYXSH3kERDSrkE6FCj0JTcjEBtOOWXrG59mFCDk9id9QQvIJVgIlQY3MB62vLvbCE88obCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:25.933382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd455a6beac0029f6136a5e1da4286c967b0412295f1272cbad9f2212d2babac","sha256:619d03a885dd009340e24f55c57bc2ff1c1c86dfda1e4941bcf5fbb650814600"],"state_sha256":"ff8843e1824e2533d72772c540537908218bb6f23d195bddcd980d5e4562a78f"}