{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CAIDSPBPFN27FCVXP4WHTM4WM2","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":"575e99856a2f63119c5b650357252aad9d609b1011e67e8e12f376aff85a7f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-06T12:18:55Z","title_canon_sha256":"5e546eb786474bb3ee3351525a7d66662b5283722966e1d99f1b598074ccc72e"},"schema_version":"1.0","source":{"id":"1307.1772","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1772","created_at":"2026-05-18T03:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1772v1","created_at":"2026-05-18T03:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1772","created_at":"2026-05-18T03:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"CAIDSPBPFN27","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CAIDSPBPFN27FCVX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CAIDSPBP","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:f31697599ee753565b81ec5753c89189ea72d1236fcad9b258e055df1c4a7bee","target":"graph","created_at":"2026-05-18T03:19:03Z","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":"For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum vertex separator. For a connected graph $G$ with vertex connectivity $k (k \\geq 1)$, the connectivity augmentation refers to a set $S$ of edges whose augmentation to $G$ increases its vertex connectivity by one. A minimum connectivity augmentation of $G$ is the one in which $S$ is minimum. In this paper, we focus our attention on connectivity augmentation of","authors_text":"N.Sadagopan, Surabhi Jain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-06T12:18:55Z","title":"Simpler Sequential and Parallel Biconnectivity Augmentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1772","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:e542d02942f8ee19510ac7e43d3b2683a607e68a3e26e8934487ed7e630fd6e4","target":"record","created_at":"2026-05-18T03:19:03Z","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":"575e99856a2f63119c5b650357252aad9d609b1011e67e8e12f376aff85a7f04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-06T12:18:55Z","title_canon_sha256":"5e546eb786474bb3ee3351525a7d66662b5283722966e1d99f1b598074ccc72e"},"schema_version":"1.0","source":{"id":"1307.1772","kind":"arxiv","version":1}},"canonical_sha256":"1010393c2f2b75f28ab77f2c79b39666a9346e718c384d3ad0be30961a9d6a18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1010393c2f2b75f28ab77f2c79b39666a9346e718c384d3ad0be30961a9d6a18","first_computed_at":"2026-05-18T03:19:03.561806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:03.561806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0iSCDdMgC7vUTPcqaD7yDAmjK7FN3x4lr8OgCwyD77WIwGLQGygGzZA4PpeMjH6CGI+Fc1CrnMz8m+NWQOEfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:03.562511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1772","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e542d02942f8ee19510ac7e43d3b2683a607e68a3e26e8934487ed7e630fd6e4","sha256:f31697599ee753565b81ec5753c89189ea72d1236fcad9b258e055df1c4a7bee"],"state_sha256":"e65f6bc6a8bf521b629ea5b261c5ae6a9f736ca5e6e2cdbf564a1cee353627c1"}