{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7X5V2X6S2KTE7L3EEAB5VZHOQV","short_pith_number":"pith:7X5V2X6S","schema_version":"1.0","canonical_sha256":"fdfb5d5fd2d2a64faf642003dae4ee856d9a26be991d725a3628a756a10174a9","source":{"kind":"arxiv","id":"2409.03300","version":4},"attestation_state":"computed","paper":{"title":"Multislicing and effective equidistribution for random walks on some homogeneous spaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Timoth\\'ee B\\'enard, Weikun He","submitted_at":"2024-09-05T07:10:19Z","abstract_excerpt":"We consider a random walk on a homogeneous space $G/\\Lambda$ where $G$ is $\\mathrm{SO}(2,1)$ or $\\mathrm{SO}(3,1)$ and $\\Lambda$ is a lattice. The walk is driven by a probability measure $\\mu$ on $G$ whose support generates a Zariski-dense subgroup. We show that for every starting point $x \\in G/\\Lambda$ which is not trapped in a finite $\\mu$-invariant set, the $n$-step distribution $\\mu^{*n}*\\delta_{x}$ of the walk equidistributes toward the Haar measure. Moreover, under arithmetic assumptions on the pair $(\\Lambda, \\mu)$, we show the convergence occurs at an exponential rate, tempered by the"},"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":"2409.03300","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2024-09-05T07:10:19Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"903e915d579609200bc488dab9f1874466f555466074805f9648af9d81b43a27","abstract_canon_sha256":"90fe627e3e2b9cdc6530fc60dba592eda020ac49c2042ec2617bdf4ffcb3bd28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:04:47.237241Z","signature_b64":"B63k3D1iLB47Zw6LDIxXCEg+/3yYKdhY4KgFAp8sOuAo6xrGMY7LY2bh0NxmP4dSKfOeXxXTJkiASogDDxfvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdfb5d5fd2d2a64faf642003dae4ee856d9a26be991d725a3628a756a10174a9","last_reissued_at":"2026-05-27T01:04:47.236532Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:04:47.236532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multislicing and effective equidistribution for random walks on some homogeneous spaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Timoth\\'ee B\\'enard, Weikun He","submitted_at":"2024-09-05T07:10:19Z","abstract_excerpt":"We consider a random walk on a homogeneous space $G/\\Lambda$ where $G$ is $\\mathrm{SO}(2,1)$ or $\\mathrm{SO}(3,1)$ and $\\Lambda$ is a lattice. The walk is driven by a probability measure $\\mu$ on $G$ whose support generates a Zariski-dense subgroup. We show that for every starting point $x \\in G/\\Lambda$ which is not trapped in a finite $\\mu$-invariant set, the $n$-step distribution $\\mu^{*n}*\\delta_{x}$ of the walk equidistributes toward the Haar measure. Moreover, under arithmetic assumptions on the pair $(\\Lambda, \\mu)$, we show the convergence occurs at an exponential rate, tempered by the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.03300","kind":"arxiv","version":4},"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/2409.03300/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":"2409.03300","created_at":"2026-05-27T01:04:47.236645+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.03300v4","created_at":"2026-05-27T01:04:47.236645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.03300","created_at":"2026-05-27T01:04:47.236645+00:00"},{"alias_kind":"pith_short_12","alias_value":"7X5V2X6S2KTE","created_at":"2026-05-27T01:04:47.236645+00:00"},{"alias_kind":"pith_short_16","alias_value":"7X5V2X6S2KTE7L3E","created_at":"2026-05-27T01:04:47.236645+00:00"},{"alias_kind":"pith_short_8","alias_value":"7X5V2X6S","created_at":"2026-05-27T01:04:47.236645+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/7X5V2X6S2KTE7L3EEAB5VZHOQV","json":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV.json","graph_json":"https://pith.science/api/pith-number/7X5V2X6S2KTE7L3EEAB5VZHOQV/graph.json","events_json":"https://pith.science/api/pith-number/7X5V2X6S2KTE7L3EEAB5VZHOQV/events.json","paper":"https://pith.science/paper/7X5V2X6S"},"agent_actions":{"view_html":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV","download_json":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV.json","view_paper":"https://pith.science/paper/7X5V2X6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.03300&json=true","fetch_graph":"https://pith.science/api/pith-number/7X5V2X6S2KTE7L3EEAB5VZHOQV/graph.json","fetch_events":"https://pith.science/api/pith-number/7X5V2X6S2KTE7L3EEAB5VZHOQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV/action/storage_attestation","attest_author":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV/action/author_attestation","sign_citation":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV/action/citation_signature","submit_replication":"https://pith.science/pith/7X5V2X6S2KTE7L3EEAB5VZHOQV/action/replication_record"}},"created_at":"2026-05-27T01:04:47.236645+00:00","updated_at":"2026-05-27T01:04:47.236645+00:00"}