{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TPH2OTHUHCAFFRUILYNHSBL4PC","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":"9b4a1a5b78c9cd65b368bcfec6b57ce17e6d9de204d9ce86b63c2c112458a9c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-27T02:38:36Z","title_canon_sha256":"2593604b41f8133027ca2fa0e0595c829930823fb26d958eeb3a7d43bb8e9611"},"schema_version":"1.0","source":{"id":"1703.08907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08907","created_at":"2026-05-18T00:47:55Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08907v1","created_at":"2026-05-18T00:47:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08907","created_at":"2026-05-18T00:47:55Z"},{"alias_kind":"pith_short_12","alias_value":"TPH2OTHUHCAF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TPH2OTHUHCAFFRUI","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TPH2OTHU","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:22e425187a7c70ab71fee5424ace30f31f01f0e922aa7db456766ed26a8a5056","target":"graph","created_at":"2026-05-18T00:47:55Z","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":"The Baumslag-Solitar group is an example of an HNN extension. Spielberg showed that it has a natural positive cone, and that it is then a quasi-lattice ordered group in the sense of Nica. We give conditions for an HNN extension of a quasi-lattice ordered group $(G,P)$ to be quasi-lattice ordered. In that case, if $(G,P)$ is amenable as a quasi-lattice ordered group, then so is the HNN extension.","authors_text":"Astrid an Huef, Iain Raeburn, Ilija Tolich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-27T02:38:36Z","title":"HNN extensions of quasi-lattice ordered groups and their operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08907","kind":"arxiv","version":1},"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":"sha256:522266b21b42b08fae0268e64993765aaa1ca92a0f01ce058f4ee7b3f74afdb3","target":"record","created_at":"2026-05-18T00:47:55Z","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":"9b4a1a5b78c9cd65b368bcfec6b57ce17e6d9de204d9ce86b63c2c112458a9c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-27T02:38:36Z","title_canon_sha256":"2593604b41f8133027ca2fa0e0595c829930823fb26d958eeb3a7d43bb8e9611"},"schema_version":"1.0","source":{"id":"1703.08907","kind":"arxiv","version":1}},"canonical_sha256":"9bcfa74cf4388052c6885e1a79057c788861faf038af4d15a079acf8ed34e9f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bcfa74cf4388052c6885e1a79057c788861faf038af4d15a079acf8ed34e9f8","first_computed_at":"2026-05-18T00:47:55.189665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:55.189665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b1pDwlXS1j+oipo1VzkWf2jquCAd9f8LRTBwUElCor08DOcFxJf2gHDme68Nl4nhWiKfraFXVFDL9feUvG2MAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:55.190165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:522266b21b42b08fae0268e64993765aaa1ca92a0f01ce058f4ee7b3f74afdb3","sha256:22e425187a7c70ab71fee5424ace30f31f01f0e922aa7db456766ed26a8a5056"],"state_sha256":"6310543bada3d33dcec03c81d8e533e2d77e1c151e098a62d63b3f88a214699d"}