{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:66XT4S4OMAMU6FM3SGVMNLC63Q","short_pith_number":"pith:66XT4S4O","schema_version":"1.0","canonical_sha256":"f7af3e4b8e60194f159b91aac6ac5edc208011891d9a6e5aa51b071d67f7559f","source":{"kind":"arxiv","id":"2201.00841","version":2},"attestation_state":"computed","paper":{"title":"A study in quantitative equidistribution on the unit square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.DS","authors_text":"Christian Weiss, Max Goering","submitted_at":"2022-01-03T19:06:38Z","abstract_excerpt":"The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is to compare the error between the actual time the translation flow spent in specific sets $E \\subset [0,1]^2$ to the expected time. In this article, we prove that when $E$ is in the algebra generated by convex sets the error is of order at most $\\log(T)^{1+\\varepsilon}$ for all but countably many directions. Whenever the direction is badly approximable the bound can be sha"},"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":"2201.00841","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-01-03T19:06:38Z","cross_cats_sorted":["math.MG","math.NT"],"title_canon_sha256":"5a8324253dcee0b2f2843a92ba55513706370838bfe08923caf282c820b86ae8","abstract_canon_sha256":"74e20a6fb8c9d3f9f84753f41480e5b49047ba58c28bc0a3fa4fd53ad6b3509d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:46:12.140834Z","signature_b64":"9kA/LCcyDeFDZla1CQLQ6COC5kd9i7UkDoUhvf+63QpEq5ImWgrcpHv4nbv6T47qD4BptkAcr9bxW9IuYpc1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7af3e4b8e60194f159b91aac6ac5edc208011891d9a6e5aa51b071d67f7559f","last_reissued_at":"2026-07-05T05:46:12.140371Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:46:12.140371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A study in quantitative equidistribution on the unit square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.DS","authors_text":"Christian Weiss, Max Goering","submitted_at":"2022-01-03T19:06:38Z","abstract_excerpt":"The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is to compare the error between the actual time the translation flow spent in specific sets $E \\subset [0,1]^2$ to the expected time. In this article, we prove that when $E$ is in the algebra generated by convex sets the error is of order at most $\\log(T)^{1+\\varepsilon}$ for all but countably many directions. Whenever the direction is badly approximable the bound can be sha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.00841","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/2201.00841/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":"2201.00841","created_at":"2026-07-05T05:46:12.140438+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.00841v2","created_at":"2026-07-05T05:46:12.140438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.00841","created_at":"2026-07-05T05:46:12.140438+00:00"},{"alias_kind":"pith_short_12","alias_value":"66XT4S4OMAMU","created_at":"2026-07-05T05:46:12.140438+00:00"},{"alias_kind":"pith_short_16","alias_value":"66XT4S4OMAMU6FM3","created_at":"2026-07-05T05:46:12.140438+00:00"},{"alias_kind":"pith_short_8","alias_value":"66XT4S4O","created_at":"2026-07-05T05:46:12.140438+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/66XT4S4OMAMU6FM3SGVMNLC63Q","json":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q.json","graph_json":"https://pith.science/api/pith-number/66XT4S4OMAMU6FM3SGVMNLC63Q/graph.json","events_json":"https://pith.science/api/pith-number/66XT4S4OMAMU6FM3SGVMNLC63Q/events.json","paper":"https://pith.science/paper/66XT4S4O"},"agent_actions":{"view_html":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q","download_json":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q.json","view_paper":"https://pith.science/paper/66XT4S4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.00841&json=true","fetch_graph":"https://pith.science/api/pith-number/66XT4S4OMAMU6FM3SGVMNLC63Q/graph.json","fetch_events":"https://pith.science/api/pith-number/66XT4S4OMAMU6FM3SGVMNLC63Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/action/storage_attestation","attest_author":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/action/author_attestation","sign_citation":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/action/citation_signature","submit_replication":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/action/replication_record"}},"created_at":"2026-07-05T05:46:12.140438+00:00","updated_at":"2026-07-05T05:46:12.140438+00:00"}