{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ULLRAONJ5RVZGP4UDWFBQ446VQ","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":"84ac0a9d159ac92e1d290c781f8adbd60e2ece81c953ed46e8852425f8ebebd4","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-08-07T04:04:26Z","title_canon_sha256":"9710624aebafbf5e4968ca9ee48fa0b31fd9c3288036d78c5ff8705a5d0caac8"},"schema_version":"1.0","source":{"id":"2108.03361","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.03361","created_at":"2026-07-05T10:28:08Z"},{"alias_kind":"arxiv_version","alias_value":"2108.03361v4","created_at":"2026-07-05T10:28:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.03361","created_at":"2026-07-05T10:28:08Z"},{"alias_kind":"pith_short_12","alias_value":"ULLRAONJ5RVZ","created_at":"2026-07-05T10:28:08Z"},{"alias_kind":"pith_short_16","alias_value":"ULLRAONJ5RVZGP4U","created_at":"2026-07-05T10:28:08Z"},{"alias_kind":"pith_short_8","alias_value":"ULLRAONJ","created_at":"2026-07-05T10:28:08Z"}],"graph_snapshots":[{"event_id":"sha256:fd068c242494a9544a3da84a3d7d9c52320a4ac07fb3165aa0f253e971b0f07b","target":"graph","created_at":"2026-07-05T10:28:08Z","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/2108.03361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"According to Bestvina-Bromberg-Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasi-trees so that orbital maps are quasi-isometric embeddings. We prove that the fundamental group $\\pi_1(M)$ of a compact, connected, orientable 3-manifold $M$ has property (QT) if and only if no summand in the sphere-disc decomposition of $M$ supports either Sol or Nil geometry. In particular, all compact, orientable, irreducible 3-manifold groups with nontrivial torus decomposition and not supporting Sol geometry have property (QT). In the cours","authors_text":"Hoang Thanh Nguyen, Suzhen Han, Wenyuan Yang","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-08-07T04:04:26Z","title":"Property (QT) for 3-manifold groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.03361","kind":"arxiv","version":4},"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":"sha256:306ecb4abc38f936a9feffc74b4772436a51812ede86d2fe0328c43ceeeb3e04","target":"record","created_at":"2026-07-05T10:28:08Z","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":"84ac0a9d159ac92e1d290c781f8adbd60e2ece81c953ed46e8852425f8ebebd4","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-08-07T04:04:26Z","title_canon_sha256":"9710624aebafbf5e4968ca9ee48fa0b31fd9c3288036d78c5ff8705a5d0caac8"},"schema_version":"1.0","source":{"id":"2108.03361","kind":"arxiv","version":4}},"canonical_sha256":"a2d71039a9ec6b933f941d8a18739eac07f99407785fc084a134b850cecf60d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2d71039a9ec6b933f941d8a18739eac07f99407785fc084a134b850cecf60d1","first_computed_at":"2026-07-05T10:28:08.961033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:28:08.961033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4Kr66uNADKfobKSEtklHZ0lz7C/Vsx4/B250oev6/itSnIcuU2MWzSbhKmlGDIQXOlywo2XwBBfmejUWjO0Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:28:08.961514Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.03361","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:306ecb4abc38f936a9feffc74b4772436a51812ede86d2fe0328c43ceeeb3e04","sha256:fd068c242494a9544a3da84a3d7d9c52320a4ac07fb3165aa0f253e971b0f07b"],"state_sha256":"24ba9986fc6e779dfbc8e17858b9c89dac91982489239fe7641bfdd52d83698a"}