{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5RBDALRHJBJVOOTRI2VLLRMCOR","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":"449237f95fa4b93a77e7f294bd491ac70295c47dd296ff1a507638bc372ed36b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-07T17:27:15Z","title_canon_sha256":"c3d92a01cdf8618a142567c28cf19ae4e5a280a25c6e52c04ad38112f7581e33"},"schema_version":"1.0","source":{"id":"0901.0880","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0880","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0880v2","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0880","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"5RBDALRHJBJV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5RBDALRHJBJVOOTR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5RBDALRH","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:dc33b1e2686ea221411f9e37573038b8d4eeda35b412e26490619a5d132b7d6e","target":"graph","created_at":"2026-05-18T02:41:51Z","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 provide a pure algebraic version of the dynamical characterization of Conrad's property. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof of a theorem first established by Linnell: an orderable group having infinitely many orderings has uncountably many. This proof is achieved by extending to uncountable orderable groups a result about orderings which may be approximated by their conjugates. This last result is illustrated by an example of an exotic ordering on the free group given in the Appen","authors_text":"Adam Clay, Andr\\'es Navas, Crist\\'obal Rivas","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-07T17:27:15Z","title":"A new characterization of Conrad's property for group orderings, with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0880","kind":"arxiv","version":2},"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":"sha256:7d37f36c2301ffef0ed6f33e4c963f20f8ed803bcc0b6e0fa8c7df1bd606725b","target":"record","created_at":"2026-05-18T02:41:51Z","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":"449237f95fa4b93a77e7f294bd491ac70295c47dd296ff1a507638bc372ed36b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-07T17:27:15Z","title_canon_sha256":"c3d92a01cdf8618a142567c28cf19ae4e5a280a25c6e52c04ad38112f7581e33"},"schema_version":"1.0","source":{"id":"0901.0880","kind":"arxiv","version":2}},"canonical_sha256":"ec42302e274853573a7146aab5c582745c49f70f5b67fc83c68e7a5ec7a62da7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec42302e274853573a7146aab5c582745c49f70f5b67fc83c68e7a5ec7a62da7","first_computed_at":"2026-05-18T02:41:51.392120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.392120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqZiuFDfLPIHcX20Lt1Ef2KfTeollnHCqFxp0onP4XxUmKt+0zQNYothPhISyh9DjdQgWKVIp75aeUoVXOEkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.392564Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0880","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d37f36c2301ffef0ed6f33e4c963f20f8ed803bcc0b6e0fa8c7df1bd606725b","sha256:dc33b1e2686ea221411f9e37573038b8d4eeda35b412e26490619a5d132b7d6e"],"state_sha256":"0286f50c5dca5b09d406a9ca758ad0ca3ab4ccda9a122a0e183741c51a0e0b1b"}