{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:V3EHG5RWJF5BT5LFCOZNUXN4PM","short_pith_number":"pith:V3EHG5RW","schema_version":"1.0","canonical_sha256":"aec8737636497a19f56513b2da5dbc7b3925b33cf10eaf29c8c0344bca1cf707","source":{"kind":"arxiv","id":"2310.19976","version":2},"attestation_state":"computed","paper":{"title":"Ergodic dichotomy for subspace flows in higher rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Dongryul M. Kim, Hee Oh, Yahui Wang","submitted_at":"2023-10-30T19:48:21Z","abstract_excerpt":"In this paper, we study the ergodicity of a one-parameter diagonalizable subgroup of a connected semisimple real algebraic group $G$ acting on a homogeneous space or, more generally, a homogeneous-like space, equipped with a Bowen-Margulis-Sullivan type measure. These flow spaces are associated with Anosov subgroups of $G$, or more generally, with transverse subgroups of $G$.\n  We obtain an ergodicity criterion similar to the Hopf-Tsuji-Sullivan dichotomy for the ergodicity of the geodesic flow on hyperbolic manifolds. In addition, we extend this criterion to the action of any connected diagon"},"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":"2310.19976","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-10-30T19:48:21Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"9d061c56a08c2ab124e02ab72485e3761f44a9e3f8e4d1ddbb5f6e8c754e1186","abstract_canon_sha256":"a1852155d2e3035ea38745a905685147eb95de573159eda849b6964a9e9cfdc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:05:07.861931Z","signature_b64":"ZL2vY0otu/P+8hRTC+qCKGp8Aw+oNZFlv/B+v68Dk6XZocKSl8k3rqTgQyYG1fhZbWanjQQZcGC1ZI8iJidSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec8737636497a19f56513b2da5dbc7b3925b33cf10eaf29c8c0344bca1cf707","last_reissued_at":"2026-07-05T10:05:07.861461Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:05:07.861461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic dichotomy for subspace flows in higher rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Dongryul M. Kim, Hee Oh, Yahui Wang","submitted_at":"2023-10-30T19:48:21Z","abstract_excerpt":"In this paper, we study the ergodicity of a one-parameter diagonalizable subgroup of a connected semisimple real algebraic group $G$ acting on a homogeneous space or, more generally, a homogeneous-like space, equipped with a Bowen-Margulis-Sullivan type measure. These flow spaces are associated with Anosov subgroups of $G$, or more generally, with transverse subgroups of $G$.\n  We obtain an ergodicity criterion similar to the Hopf-Tsuji-Sullivan dichotomy for the ergodicity of the geodesic flow on hyperbolic manifolds. In addition, we extend this criterion to the action of any connected diagon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19976","kind":"arxiv","version":2},"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/2310.19976/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":"2310.19976","created_at":"2026-07-05T10:05:07.861518+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.19976v2","created_at":"2026-07-05T10:05:07.861518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19976","created_at":"2026-07-05T10:05:07.861518+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3EHG5RWJF5B","created_at":"2026-07-05T10:05:07.861518+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3EHG5RWJF5BT5LF","created_at":"2026-07-05T10:05:07.861518+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3EHG5RW","created_at":"2026-07-05T10:05:07.861518+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.07271","citing_title":"Geometry and Dynamics of Transverse Groups","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM","json":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM.json","graph_json":"https://pith.science/api/pith-number/V3EHG5RWJF5BT5LFCOZNUXN4PM/graph.json","events_json":"https://pith.science/api/pith-number/V3EHG5RWJF5BT5LFCOZNUXN4PM/events.json","paper":"https://pith.science/paper/V3EHG5RW"},"agent_actions":{"view_html":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM","download_json":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM.json","view_paper":"https://pith.science/paper/V3EHG5RW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.19976&json=true","fetch_graph":"https://pith.science/api/pith-number/V3EHG5RWJF5BT5LFCOZNUXN4PM/graph.json","fetch_events":"https://pith.science/api/pith-number/V3EHG5RWJF5BT5LFCOZNUXN4PM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM/action/storage_attestation","attest_author":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM/action/author_attestation","sign_citation":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM/action/citation_signature","submit_replication":"https://pith.science/pith/V3EHG5RWJF5BT5LFCOZNUXN4PM/action/replication_record"}},"created_at":"2026-07-05T10:05:07.861518+00:00","updated_at":"2026-07-05T10:05:07.861518+00:00"}