{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DJUCBNMD2MAYM4FEP3EA5MWK2F","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":"9a507c91bedf073783767e1ebf2833dde1b01408853dd883e911838079aebdfc","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-01-28T12:14:08Z","title_canon_sha256":"f37bba25a26ad8f3abca85cabce887b7c8cf277f34923976a4e0fe50cfefe2be"},"schema_version":"1.0","source":{"id":"2001.10286","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.10286","created_at":"2026-07-05T03:52:10Z"},{"alias_kind":"arxiv_version","alias_value":"2001.10286v2","created_at":"2026-07-05T03:52:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.10286","created_at":"2026-07-05T03:52:10Z"},{"alias_kind":"pith_short_12","alias_value":"DJUCBNMD2MAY","created_at":"2026-07-05T03:52:10Z"},{"alias_kind":"pith_short_16","alias_value":"DJUCBNMD2MAYM4FE","created_at":"2026-07-05T03:52:10Z"},{"alias_kind":"pith_short_8","alias_value":"DJUCBNMD","created_at":"2026-07-05T03:52:10Z"}],"graph_snapshots":[{"event_id":"sha256:08c9b14f6ad43f67f4661a010aa60bd745bab67f92850cfadedf36f97ff68761","target":"graph","created_at":"2026-07-05T03:52:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.10286/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the geometry of positive cones of left-invariant total orders (left-order, for short) in finitely generated groups. We introduce the \\textit{Hucha property} and the \\texit{Prieto property} for left-orderable groups. The first one means that in any left-order the corresponding positive cone is not coarsely connected, and the second one that in any left-order the corresponding positive cone is coarsely connected. We show that all left-orderable free products have the Hucha property, and that the Hucha property is stable under certain free products with amalgamatation over Prieto subgrou","authors_text":"C. Rivas, J. Alonso, J. Brum, Y. Antol\\'in","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-01-28T12:14:08Z","title":"On the geometry of positive cones in finitely generated groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.10286","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:d2d3c658c4a698a68574e2158b47bb5a7bba07ad92296da19edf6299fe470e52","target":"record","created_at":"2026-07-05T03:52:10Z","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":"9a507c91bedf073783767e1ebf2833dde1b01408853dd883e911838079aebdfc","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-01-28T12:14:08Z","title_canon_sha256":"f37bba25a26ad8f3abca85cabce887b7c8cf277f34923976a4e0fe50cfefe2be"},"schema_version":"1.0","source":{"id":"2001.10286","kind":"arxiv","version":2}},"canonical_sha256":"1a6820b583d3018670a47ec80eb2cad1598e92ee2d4618c9bcb6a6f034a9c345","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a6820b583d3018670a47ec80eb2cad1598e92ee2d4618c9bcb6a6f034a9c345","first_computed_at":"2026-07-05T03:52:10.575668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:52:10.575668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TjjFttKaARUHJVylPKbV9ANxsMBQZW/TeP8Zmg0p6czYviVgTpJLn/MyHtfQ6v3qvBR+LHfRJgIPSpTDOgs3Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T03:52:10.576033Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.10286","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2d3c658c4a698a68574e2158b47bb5a7bba07ad92296da19edf6299fe470e52","sha256:08c9b14f6ad43f67f4661a010aa60bd745bab67f92850cfadedf36f97ff68761"],"state_sha256":"68c9f44f463cc9470f7cc6b4c9a93957f74ceb5c2d11f42d55040e9403075ea1"}