{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HW6EXLDS7CORW47IFE6LGBZXAK","short_pith_number":"pith:HW6EXLDS","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"},"canonical_sha256":"3dbc4bac72f89d1b73e8293cb30737029ae7dfef6adef02be678a1524ab801cf","source":{"kind":"arxiv","id":"1811.12528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12528","created_at":"2026-05-17T23:59:29Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12528v1","created_at":"2026-05-17T23:59:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12528","created_at":"2026-05-17T23:59:29Z"},{"alias_kind":"pith_short_12","alias_value":"HW6EXLDS7COR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HW6EXLDS7CORW47I","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HW6EXLDS","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HW6EXLDS7CORW47IFE6LGBZXAK","target":"record","payload":{"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"},"canonical_sha256":"3dbc4bac72f89d1b73e8293cb30737029ae7dfef6adef02be678a1524ab801cf","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"},"source_kind":"arxiv","source_id":"1811.12528","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGf1K2A5gg/FA/2zWW7rZtgqoGWudYj/Cq7Z/IhkWjt7X6BLHjyyN0+uBOIeMTcGP6NMNdxW6BeHsAIzwoelCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:37:42.441816Z"},"content_sha256":"b8b78ea60e13004b40f17e3cb2a832af078bf099913c4f4cd30946f959295bfb","schema_version":"1.0","event_id":"sha256:b8b78ea60e13004b40f17e3cb2a832af078bf099913c4f4cd30946f959295bfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HW6EXLDS7CORW47IFE6LGBZXAK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCXLeAPyFPu5XOi0OYnufi3rPkED2HKGdvB13IcZ4gnfJYhKo5cFg21SUDuVOOhlbKJIpT+VpRRiuaElS3JrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:37:42.442154Z"},"content_sha256":"74e0564a2a08dc22058052fc031ba2f6d217a0b9c0fa3d691ca804f8fd3538c6","schema_version":"1.0","event_id":"sha256:74e0564a2a08dc22058052fc031ba2f6d217a0b9c0fa3d691ca804f8fd3538c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/bundle.json","state_url":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HW6EXLDS7CORW47IFE6LGBZXAK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T20:37:42Z","links":{"resolver":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK","bundle":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/bundle.json","state":"https://pith.science/pith/HW6EXLDS7CORW47IFE6LGBZXAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HW6EXLDS7CORW47IFE6LGBZXAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HW6EXLDS7CORW47IFE6LGBZXAK","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":"6b86223a102b17514093a86b18166d2af4329232a62edd73158af5bdce8c3b7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T23:01:31Z","title_canon_sha256":"059b10f3dffbdc85a106f2f7c14ae66c8bd9a3786dbb4495763b982954eedde5"},"schema_version":"1.0","source":{"id":"1811.12528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12528","created_at":"2026-05-17T23:59:29Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12528v1","created_at":"2026-05-17T23:59:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12528","created_at":"2026-05-17T23:59:29Z"},{"alias_kind":"pith_short_12","alias_value":"HW6EXLDS7COR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HW6EXLDS7CORW47I","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HW6EXLDS","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:74e0564a2a08dc22058052fc031ba2f6d217a0b9c0fa3d691ca804f8fd3538c6","target":"graph","created_at":"2026-05-17T23:59:29Z","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":"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","authors_text":"Jack E. Graver, Mark E. Watkins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T23:01:31Z","title":"Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12528","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:b8b78ea60e13004b40f17e3cb2a832af078bf099913c4f4cd30946f959295bfb","target":"record","created_at":"2026-05-17T23:59:29Z","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":"6b86223a102b17514093a86b18166d2af4329232a62edd73158af5bdce8c3b7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T23:01:31Z","title_canon_sha256":"059b10f3dffbdc85a106f2f7c14ae66c8bd9a3786dbb4495763b982954eedde5"},"schema_version":"1.0","source":{"id":"1811.12528","kind":"arxiv","version":1}},"canonical_sha256":"3dbc4bac72f89d1b73e8293cb30737029ae7dfef6adef02be678a1524ab801cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dbc4bac72f89d1b73e8293cb30737029ae7dfef6adef02be678a1524ab801cf","first_computed_at":"2026-05-17T23:59:29.358970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:29.358970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d4R6il2JPm7H9saDkrtbEvFqQ+m52cMyIjMzfnZOu3xE3XFR2R8bp5RC0Voo+lgM/gHpWPA5jzkQ1LcCuP76DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:29.359400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8b78ea60e13004b40f17e3cb2a832af078bf099913c4f4cd30946f959295bfb","sha256:74e0564a2a08dc22058052fc031ba2f6d217a0b9c0fa3d691ca804f8fd3538c6"],"state_sha256":"f4d0e954caf8f1cb416d37819ebd459fb78b5ce9336e755818e4553538bc554d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGrLyOn75lpSrS1f/yIzavwVrnZc5trZKGht6J0f8lwHxua9nVJXpU8nh+unnTJtKJvHeEzhC+DnOftRUTJrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:37:42.444073Z","bundle_sha256":"813d64dbce4ac175b136c325cb5dd8d333816b4248931d7007e823556eb3ed1a"}}