{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5RBDALRHJBJVOOTRI2VLLRMCOR","short_pith_number":"pith:5RBDALRH","canonical_record":{"source":{"id":"0901.0880","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-07T17:27:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c3d92a01cdf8618a142567c28cf19ae4e5a280a25c6e52c04ad38112f7581e33","abstract_canon_sha256":"449237f95fa4b93a77e7f294bd491ac70295c47dd296ff1a507638bc372ed36b"},"schema_version":"1.0"},"canonical_sha256":"ec42302e274853573a7146aab5c582745c49f70f5b67fc83c68e7a5ec7a62da7","source":{"kind":"arxiv","id":"0901.0880","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5RBDALRHJBJVOOTRI2VLLRMCOR","target":"record","payload":{"canonical_record":{"source":{"id":"0901.0880","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-07T17:27:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"c3d92a01cdf8618a142567c28cf19ae4e5a280a25c6e52c04ad38112f7581e33","abstract_canon_sha256":"449237f95fa4b93a77e7f294bd491ac70295c47dd296ff1a507638bc372ed36b"},"schema_version":"1.0"},"canonical_sha256":"ec42302e274853573a7146aab5c582745c49f70f5b67fc83c68e7a5ec7a62da7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.392564Z","signature_b64":"gqZiuFDfLPIHcX20Lt1Ef2KfTeollnHCqFxp0onP4XxUmKt+0zQNYothPhISyh9DjdQgWKVIp75aeUoVXOEkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec42302e274853573a7146aab5c582745c49f70f5b67fc83c68e7a5ec7a62da7","last_reissued_at":"2026-05-18T02:41:51.392120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.392120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.0880","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2yKje2+MghjL2hXjmCrp8ZtatSPhPuZbqHNnFlttjEUqFIwAVEQnoLecZSDhUMiJuCm1mY1H04RvUy8o/dhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:26:55.521697Z"},"content_sha256":"7d37f36c2301ffef0ed6f33e4c963f20f8ed803bcc0b6e0fa8c7df1bd606725b","schema_version":"1.0","event_id":"sha256:7d37f36c2301ffef0ed6f33e4c963f20f8ed803bcc0b6e0fa8c7df1bd606725b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5RBDALRHJBJVOOTRI2VLLRMCOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new characterization of Conrad's property for group orderings, with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Adam Clay, Andr\\'es Navas, Crist\\'obal Rivas","submitted_at":"2009-01-07T17:27:15Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0880","kind":"arxiv","version":2},"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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2atfFXok7Mzb7kFjc0Zjso5478yCwK2SeafsVIXH9/U+0AGfgr+3epO+7Syt/J0H1VwDRSUJiNR99wTVDeRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:26:55.522493Z"},"content_sha256":"dc33b1e2686ea221411f9e37573038b8d4eeda35b412e26490619a5d132b7d6e","schema_version":"1.0","event_id":"sha256:dc33b1e2686ea221411f9e37573038b8d4eeda35b412e26490619a5d132b7d6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RBDALRHJBJVOOTRI2VLLRMCOR/bundle.json","state_url":"https://pith.science/pith/5RBDALRHJBJVOOTRI2VLLRMCOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RBDALRHJBJVOOTRI2VLLRMCOR/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":"2026-06-01T12:26:55Z","links":{"resolver":"https://pith.science/pith/5RBDALRHJBJVOOTRI2VLLRMCOR","bundle":"https://pith.science/pith/5RBDALRHJBJVOOTRI2VLLRMCOR/bundle.json","state":"https://pith.science/pith/5RBDALRHJBJVOOTRI2VLLRMCOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RBDALRHJBJVOOTRI2VLLRMCOR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4zBmqctGq8lqjsQTwiZl8/ynxJY9qf76uz4lzpUr3eSJsAMShrLvg+jiLxrIVYalLnCy3sPO8kVwC0NMVV+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:26:55.525369Z","bundle_sha256":"21b48da8778b331953756dbff6e03efa9298e672cb1b6d90cc1fcd7503c75624"}}