{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ETMKPTA7M7VNYJU7H5RHXKLNKB","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":"c8d6050100636846e541f62b68b311797aa2f6764c45ba8b986b28d3f41d566e","cross_cats_sorted":["math.CO","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-23T18:01:01Z","title_canon_sha256":"77bccbaa1d77c58ec692178c78689f6d42309da2e0a685e615c5a3e38ff36786"},"schema_version":"1.0","source":{"id":"2310.15242","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.15242","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"2310.15242v6","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.15242","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"ETMKPTA7M7VN","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ETMKPTA7M7VNYJU7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ETMKPTA7","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:4f17f2528d681f223e178e2121a4aad3fd880ec952f1bc751ceb3d40238fa824","target":"graph","created_at":"2026-05-18T03:10:13Z","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 prove that a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph is necessarily accessible. This leads to a complete classification of the finitely generated groups which are quasi-isometric to planar graphs. In particular, such a group is virtually a free product of free and surface groups, and thus virtually admits a planar Cayley graph.","authors_text":"Joseph Paul MacManus","cross_cats":["math.CO","math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-23T18:01:01Z","title":"Accessibility, planar graphs, and quasi-isometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.15242","kind":"arxiv","version":6},"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":"sha256:3e9b38efe21c0b01700ad51dd7c4fa9d454530686c1c1b24229a14f50fb656ef","target":"record","created_at":"2026-05-18T03:10:13Z","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":"c8d6050100636846e541f62b68b311797aa2f6764c45ba8b986b28d3f41d566e","cross_cats_sorted":["math.CO","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2023-10-23T18:01:01Z","title_canon_sha256":"77bccbaa1d77c58ec692178c78689f6d42309da2e0a685e615c5a3e38ff36786"},"schema_version":"1.0","source":{"id":"2310.15242","kind":"arxiv","version":6}},"canonical_sha256":"24d8a7cc1f67eadc269f3f627ba96d5069c12024c2ceba6a52dfadc10aaa5bf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24d8a7cc1f67eadc269f3f627ba96d5069c12024c2ceba6a52dfadc10aaa5bf3","first_computed_at":"2026-05-18T03:10:13.246589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:13.246589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8GEPV2B4tIzoE5yozs9vB1ddFVBmPbZ9QJsOO6ikcMV1puCHBgJg/JBOKfnLCiKnQvzPCVdmjAbDR6GYhWp8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:13.247151Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.15242","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e9b38efe21c0b01700ad51dd7c4fa9d454530686c1c1b24229a14f50fb656ef","sha256:4f17f2528d681f223e178e2121a4aad3fd880ec952f1bc751ceb3d40238fa824"],"state_sha256":"41bd7548937c5217349e2a569fd9de66464809b0bbc357b247f08d9e0a0a4969"}