{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:4HJQWDODUJ3UHRUD67KRPKL2UH","short_pith_number":"pith:4HJQWDOD","schema_version":"1.0","canonical_sha256":"e1d30b0dc3a27743c683f7d517a97aa1dd4898afa6d220ab055868293017286c","source":{"kind":"arxiv","id":"2007.09793","version":1},"attestation_state":"computed","paper":{"title":"$2$-blocks in strongly biconnected directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Raed Jaberi","submitted_at":"2020-07-19T21:59:52Z","abstract_excerpt":"A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. A strongly biconnected component of a strongly connected graph $G=(V,E)$ is a maximal vertex subset $L\\subseteq V$ such that the induced subgraph on $L$ is strongly biconnected. Let $G=(V,E)$ be a strongly biconnected directed graph. A $2$-edge-biconnected block in $G$ is a maximal vertex subset $U\\subseteq V$ such that for any two distict vertices $v,w \\in U$ and for each edge $b\\in E$, the vertices $v,w$ are in the same strongly biconnected components of $G\\s"},"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":"2007.09793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-07-19T21:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"00fe747723d0366682568b53a3f8a931d758c6b90083c2b241bfb2d273cf61f7","abstract_canon_sha256":"fcb8edc2598a005ef2cc96e3bf873ab479e56960e9ad755dfdcd11128670a3f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:20:29.225758Z","signature_b64":"cmEz1xsM2XHxxl9bj+lI6Nvx48OPzB43iiwTK/D30A+X3LlRCo16L2WGq/NR3azXlEMIf2KLoE9mWO/3XN4GAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d30b0dc3a27743c683f7d517a97aa1dd4898afa6d220ab055868293017286c","last_reissued_at":"2026-07-05T01:20:29.225355Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:20:29.225355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$2$-blocks in strongly biconnected directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Raed Jaberi","submitted_at":"2020-07-19T21:59:52Z","abstract_excerpt":"A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. A strongly biconnected component of a strongly connected graph $G=(V,E)$ is a maximal vertex subset $L\\subseteq V$ such that the induced subgraph on $L$ is strongly biconnected. Let $G=(V,E)$ be a strongly biconnected directed graph. A $2$-edge-biconnected block in $G$ is a maximal vertex subset $U\\subseteq V$ such that for any two distict vertices $v,w \\in U$ and for each edge $b\\in E$, the vertices $v,w$ are in the same strongly biconnected components of $G\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.09793","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.09793/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2007.09793","created_at":"2026-07-05T01:20:29.225411+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.09793v1","created_at":"2026-07-05T01:20:29.225411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.09793","created_at":"2026-07-05T01:20:29.225411+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HJQWDODUJ3U","created_at":"2026-07-05T01:20:29.225411+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HJQWDODUJ3UHRUD","created_at":"2026-07-05T01:20:29.225411+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HJQWDOD","created_at":"2026-07-05T01:20:29.225411+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.16087","citing_title":"Problems related to strong connectivity and strong biconnectivity","ref_index":47,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH","json":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH.json","graph_json":"https://pith.science/api/pith-number/4HJQWDODUJ3UHRUD67KRPKL2UH/graph.json","events_json":"https://pith.science/api/pith-number/4HJQWDODUJ3UHRUD67KRPKL2UH/events.json","paper":"https://pith.science/paper/4HJQWDOD"},"agent_actions":{"view_html":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH","download_json":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH.json","view_paper":"https://pith.science/paper/4HJQWDOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.09793&json=true","fetch_graph":"https://pith.science/api/pith-number/4HJQWDODUJ3UHRUD67KRPKL2UH/graph.json","fetch_events":"https://pith.science/api/pith-number/4HJQWDODUJ3UHRUD67KRPKL2UH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH/action/storage_attestation","attest_author":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH/action/author_attestation","sign_citation":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH/action/citation_signature","submit_replication":"https://pith.science/pith/4HJQWDODUJ3UHRUD67KRPKL2UH/action/replication_record"}},"created_at":"2026-07-05T01:20:29.225411+00:00","updated_at":"2026-07-05T01:20:29.225411+00:00"}