{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:LY5LKQHHNP6ONVOMUYV5JCPVH3","short_pith_number":"pith:LY5LKQHH","schema_version":"1.0","canonical_sha256":"5e3ab540e76bfce6d5cca62bd489f53ec87fe9350a63b940d282646f7ec50f44","source":{"kind":"arxiv","id":"2205.07594","version":1},"attestation_state":"computed","paper":{"title":"Random walks and rank one isometries on CAT(0) spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Corentin Le Bars","submitted_at":"2022-05-16T11:53:36Z","abstract_excerpt":"Let $G$ be a discrete group, $\\mu$ a measure on $G$ and $X$ a proper CAT(0) space. We show that if $G$ acts non-elementarily with a rank one element on $X$, then the pushforward $\\{Z_n o \\}_n$ to $X$ of the random walk generated by $\\mu$ converges almost surely to a rank one point of the boundary. We also show that in this context, there is a unique stationary measure on the visual boundary $\\partial_\\infty X$ of $X$, and that the drift of the random walk is almost surely positive."},"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":"2205.07594","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2022-05-16T11:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"99e75b28b34b46d66ab4123e9f0c2da4dfab6611d0fef0d0a07b37ca42e0b0f8","abstract_canon_sha256":"66be8ccf3c706300c18c631b08ec38cd12514eabab42ac9419b79f57ef98e741"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:23:30.446107Z","signature_b64":"M5kM7RLDg4ekTNjFLPPqM3eDh3nt7+yIDVJNs7e29hfHjZQV7SyETEbm695GnVgBDptnxrViJRT64PDHtOApAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e3ab540e76bfce6d5cca62bd489f53ec87fe9350a63b940d282646f7ec50f44","last_reissued_at":"2026-07-05T04:23:30.445719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:23:30.445719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random walks and rank one isometries on CAT(0) spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Corentin Le Bars","submitted_at":"2022-05-16T11:53:36Z","abstract_excerpt":"Let $G$ be a discrete group, $\\mu$ a measure on $G$ and $X$ a proper CAT(0) space. We show that if $G$ acts non-elementarily with a rank one element on $X$, then the pushforward $\\{Z_n o \\}_n$ to $X$ of the random walk generated by $\\mu$ converges almost surely to a rank one point of the boundary. We also show that in this context, there is a unique stationary measure on the visual boundary $\\partial_\\infty X$ of $X$, and that the drift of the random walk is almost surely positive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.07594","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/2205.07594/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":"2205.07594","created_at":"2026-07-05T04:23:30.445779+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.07594v1","created_at":"2026-07-05T04:23:30.445779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.07594","created_at":"2026-07-05T04:23:30.445779+00:00"},{"alias_kind":"pith_short_12","alias_value":"LY5LKQHHNP6O","created_at":"2026-07-05T04:23:30.445779+00:00"},{"alias_kind":"pith_short_16","alias_value":"LY5LKQHHNP6ONVOM","created_at":"2026-07-05T04:23:30.445779+00:00"},{"alias_kind":"pith_short_8","alias_value":"LY5LKQHH","created_at":"2026-07-05T04:23:30.445779+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.07859","citing_title":"Sublinear Morse Geodesics and First Passage Percolation","ref_index":55,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3","json":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3.json","graph_json":"https://pith.science/api/pith-number/LY5LKQHHNP6ONVOMUYV5JCPVH3/graph.json","events_json":"https://pith.science/api/pith-number/LY5LKQHHNP6ONVOMUYV5JCPVH3/events.json","paper":"https://pith.science/paper/LY5LKQHH"},"agent_actions":{"view_html":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3","download_json":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3.json","view_paper":"https://pith.science/paper/LY5LKQHH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.07594&json=true","fetch_graph":"https://pith.science/api/pith-number/LY5LKQHHNP6ONVOMUYV5JCPVH3/graph.json","fetch_events":"https://pith.science/api/pith-number/LY5LKQHHNP6ONVOMUYV5JCPVH3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3/action/storage_attestation","attest_author":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3/action/author_attestation","sign_citation":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3/action/citation_signature","submit_replication":"https://pith.science/pith/LY5LKQHHNP6ONVOMUYV5JCPVH3/action/replication_record"}},"created_at":"2026-07-05T04:23:30.445779+00:00","updated_at":"2026-07-05T04:23:30.445779+00:00"}