{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HW6EXLDS7CORW47IFE6LGBZXAK","short_pith_number":"pith:HW6EXLDS","schema_version":"1.0","canonical_sha256":"3dbc4bac72f89d1b73e8293cb30737029ae7dfef6adef02be678a1524ab801cf","source":{"kind":"arxiv","id":"1811.12528","version":1},"attestation_state":"computed","paper":{"title":"Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack E. Graver, Mark E. Watkins","submitted_at":"2018-11-29T23:01:31Z","abstract_excerpt":"We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph $\\Lambda$ and a \"code\" assigned to each orbit of Aut($\\Lambda$), there exists a unique lobe-transitive graph $\\Gamma$ of connectivity 1 whose lobes are copies of $\\Lambda$ and is consistent with the given code at every vertex of $\\Gamma$. These results lead to necessary and sufficient conditions for a graph of connectivity $1$ to be edge-transitive and to be arc-transitive. Countable graphs of connectivit"},"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":"1811.12528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T23:01:31Z","cross_cats_sorted":[],"title_canon_sha256":"059b10f3dffbdc85a106f2f7c14ae66c8bd9a3786dbb4495763b982954eedde5","abstract_canon_sha256":"6b86223a102b17514093a86b18166d2af4329232a62edd73158af5bdce8c3b7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:29.359400Z","signature_b64":"d4R6il2JPm7H9saDkrtbEvFqQ+m52cMyIjMzfnZOu3xE3XFR2R8bp5RC0Voo+lgM/gHpWPA5jzkQ1LcCuP76DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dbc4bac72f89d1b73e8293cb30737029ae7dfef6adef02be678a1524ab801cf","last_reissued_at":"2026-05-17T23:59:29.358970Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:29.358970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack E. Graver, Mark E. Watkins","submitted_at":"2018-11-29T23:01:31Z","abstract_excerpt":"We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph $\\Lambda$ and a \"code\" assigned to each orbit of Aut($\\Lambda$), there exists a unique lobe-transitive graph $\\Gamma$ of connectivity 1 whose lobes are copies of $\\Lambda$ and is consistent with the given code at every vertex of $\\Gamma$. These results lead to necessary and sufficient conditions for a graph of connectivity $1$ to be edge-transitive and to be arc-transitive. Countable graphs of connectivit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12528","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":"1811.12528","created_at":"2026-05-17T23:59:29.359038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.12528v1","created_at":"2026-05-17T23:59:29.359038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12528","created_at":"2026-05-17T23:59:29.359038+00:00"},{"alias_kind":"pith_short_12","alias_value":"HW6EXLDS7COR","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HW6EXLDS7CORW47I","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HW6EXLDS","created_at":"2026-05-18T12:32:28.185984+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/HW6EXLDS7CORW47IFE6LGBZXAK","json":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK.json","graph_json":"https://pith.science/api/pith-number/HW6EXLDS7CORW47IFE6LGBZXAK/graph.json","events_json":"https://pith.science/api/pith-number/HW6EXLDS7CORW47IFE6LGBZXAK/events.json","paper":"https://pith.science/paper/HW6EXLDS"},"agent_actions":{"view_html":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK","download_json":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK.json","view_paper":"https://pith.science/paper/HW6EXLDS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.12528&json=true","fetch_graph":"https://pith.science/api/pith-number/HW6EXLDS7CORW47IFE6LGBZXAK/graph.json","fetch_events":"https://pith.science/api/pith-number/HW6EXLDS7CORW47IFE6LGBZXAK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/action/storage_attestation","attest_author":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/action/author_attestation","sign_citation":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/action/citation_signature","submit_replication":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/action/replication_record"}},"created_at":"2026-05-17T23:59:29.359038+00:00","updated_at":"2026-05-17T23:59:29.359038+00:00"}