{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6T663VXFTNV7JMLDMPL3ZOG6P7","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":"bc475a790912ea8ff0c6c3da4b338ca442328ca139dc1f2d66bd2156d75bd2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T20:28:02Z","title_canon_sha256":"ea66621c59315b8ed219bd20d21e063d73e50e35c929749a97e236ee6c098e87"},"schema_version":"1.0","source":{"id":"1204.3211","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3211","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3211v3","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3211","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"6T663VXFTNV7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6T663VXFTNV7JMLD","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6T663VXF","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:6a92b667c6372e5b2ef13a5f6790c3924ea0f5e85a14122c44b6c709cd0d06ad","target":"graph","created_at":"2026-05-18T03:56:09Z","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 describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of combinatorial group theory, and connected with Garside theory, here in a non-Noetherian context. As an application we describe several families of ordered groups whose space of left-invariant orderings has an isolated point, including torus knot groups and some of their amalgamated products.","authors_text":"Patrick Dehornoy (LMNO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T20:28:02Z","title":"Monoids of O-type, subword reversing, and ordered groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3211","kind":"arxiv","version":3},"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":"sha256:947bfdc7f55c46e94b0f0335673fb211be14c3275f0133cf9719db9150b87389","target":"record","created_at":"2026-05-18T03:56:09Z","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":"bc475a790912ea8ff0c6c3da4b338ca442328ca139dc1f2d66bd2156d75bd2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-14T20:28:02Z","title_canon_sha256":"ea66621c59315b8ed219bd20d21e063d73e50e35c929749a97e236ee6c098e87"},"schema_version":"1.0","source":{"id":"1204.3211","kind":"arxiv","version":3}},"canonical_sha256":"f4fdedd6e59b6bf4b16363d7bcb8de7fdbe217fb7dd08b3077fa7452595e5cba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4fdedd6e59b6bf4b16363d7bcb8de7fdbe217fb7dd08b3077fa7452595e5cba","first_computed_at":"2026-05-18T03:56:09.139077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.139077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D+PIjX9jLy23fuFkXCoPnLgNnnYX07IXwfhw6uIODT5MqAycZr68QuRe75royb4aOuDN0xx8KTDX0Q8DUVuHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.139749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3211","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:947bfdc7f55c46e94b0f0335673fb211be14c3275f0133cf9719db9150b87389","sha256:6a92b667c6372e5b2ef13a5f6790c3924ea0f5e85a14122c44b6c709cd0d06ad"],"state_sha256":"82da59b99f789b8f161358374806fc61b2c327a100a552ca3f763b4f7fabd9d8"}