{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ERKU67SNW3IK4PRXH4BOV5S2J6","short_pith_number":"pith:ERKU67SN","schema_version":"1.0","canonical_sha256":"24554f7e4db6d0ae3e373f02eaf65a4fbdbc468dc4d9728382f180ef005fac91","source":{"kind":"arxiv","id":"2411.04250","version":1},"attestation_state":"computed","paper":{"title":"A Tits alternative for $\\mathbb{R}$-buildings of type $\\tilde{A}_2$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Corentin Le Bars, Jean L\\'ecureux, Jeroen Schillewaert","submitted_at":"2024-11-06T20:42:40Z","abstract_excerpt":"Let $G$ be a group with a non-elementary action on a (not necessarily discrete) $\\tilde{A}_2$-buildings. We prove that, given a random walk on $G$, isometries in $G$ are strongly regular hyperbolic with high probability. As a consequence, we prove a Tits alternative for $G$, as well as a local-to-global fixed point result. We also prove that isometries of (not necessarily complete) $\\mathbb{R}$-buildings are semi-simple."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.04250","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2024-11-06T20:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"6563a2794a9c94a19b7d840f2c6e4566d567f817fcb68480727f9b23d665c98f","abstract_canon_sha256":"425c96298f3566fc12180376f2ce4c02a6ece0ad4ac5b8ecb96e6e5d42be3a89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:32:16.302247Z","signature_b64":"XM69k+xu+NKhPiYToUid/tD6tCo4/FrlQkqPi2MAyJlH22ZH3YF1itexs8xq9KnF+LPw2mrvyMHG4IWzfO/7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24554f7e4db6d0ae3e373f02eaf65a4fbdbc468dc4d9728382f180ef005fac91","last_reissued_at":"2026-07-05T09:32:16.301868Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:32:16.301868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Tits alternative for $\\mathbb{R}$-buildings of type $\\tilde{A}_2$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Corentin Le Bars, Jean L\\'ecureux, Jeroen Schillewaert","submitted_at":"2024-11-06T20:42:40Z","abstract_excerpt":"Let $G$ be a group with a non-elementary action on a (not necessarily discrete) $\\tilde{A}_2$-buildings. We prove that, given a random walk on $G$, isometries in $G$ are strongly regular hyperbolic with high probability. As a consequence, we prove a Tits alternative for $G$, as well as a local-to-global fixed point result. We also prove that isometries of (not necessarily complete) $\\mathbb{R}$-buildings are semi-simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04250","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.04250/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.04250","created_at":"2026-07-05T09:32:16.301923+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.04250v1","created_at":"2026-07-05T09:32:16.301923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.04250","created_at":"2026-07-05T09:32:16.301923+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERKU67SNW3IK","created_at":"2026-07-05T09:32:16.301923+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERKU67SNW3IK4PRX","created_at":"2026-07-05T09:32:16.301923+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERKU67SN","created_at":"2026-07-05T09:32:16.301923+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6","json":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6.json","graph_json":"https://pith.science/api/pith-number/ERKU67SNW3IK4PRXH4BOV5S2J6/graph.json","events_json":"https://pith.science/api/pith-number/ERKU67SNW3IK4PRXH4BOV5S2J6/events.json","paper":"https://pith.science/paper/ERKU67SN"},"agent_actions":{"view_html":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6","download_json":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6.json","view_paper":"https://pith.science/paper/ERKU67SN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.04250&json=true","fetch_graph":"https://pith.science/api/pith-number/ERKU67SNW3IK4PRXH4BOV5S2J6/graph.json","fetch_events":"https://pith.science/api/pith-number/ERKU67SNW3IK4PRXH4BOV5S2J6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6/action/storage_attestation","attest_author":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6/action/author_attestation","sign_citation":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6/action/citation_signature","submit_replication":"https://pith.science/pith/ERKU67SNW3IK4PRXH4BOV5S2J6/action/replication_record"}},"created_at":"2026-07-05T09:32:16.301923+00:00","updated_at":"2026-07-05T09:32:16.301923+00:00"}