{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:66XT4S4OMAMU6FM3SGVMNLC63Q","short_pith_number":"pith:66XT4S4O","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"},"canonical_sha256":"f7af3e4b8e60194f159b91aac6ac5edc208011891d9a6e5aa51b071d67f7559f","source":{"kind":"arxiv","id":"2201.00841","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.00841","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"2201.00841v2","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.00841","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"66XT4S4OMAMU","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"pith_short_16","alias_value":"66XT4S4OMAMU6FM3","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"pith_short_8","alias_value":"66XT4S4O","created_at":"2026-07-05T05:46:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:66XT4S4OMAMU6FM3SGVMNLC63Q","target":"record","payload":{"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"},"canonical_sha256":"f7af3e4b8e60194f159b91aac6ac5edc208011891d9a6e5aa51b071d67f7559f","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"},"source_kind":"arxiv","source_id":"2201.00841","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:46:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYoDSnpGSAajXjZ/02A/A+fIJCbXimM19/+GaBYuQvYlhAlYMrPPqKdLCKYQKHf/SV6cpt6fRU9WzvO+JUiXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T01:43:58.465996Z"},"content_sha256":"3115f852658883201d45043dea16dd8f91ee2c912bc55b9d7cccc8f069484fbb","schema_version":"1.0","event_id":"sha256:3115f852658883201d45043dea16dd8f91ee2c912bc55b9d7cccc8f069484fbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:66XT4S4OMAMU6FM3SGVMNLC63Q","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:46:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MT4X2F9z7DXQE81YRH8E6EyU5cjCfqHFHN7dKIfTbXm83ZlZRRZCsUanR4J/uYK1UuutLGZdMu1j51WtaJiKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T01:43:58.466544Z"},"content_sha256":"16449e52d022e7bfd028ba66fcf0b4b1b82852b0147fdb3b251df78ed2949f4f","schema_version":"1.0","event_id":"sha256:16449e52d022e7bfd028ba66fcf0b4b1b82852b0147fdb3b251df78ed2949f4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/bundle.json","state_url":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T01:43:58Z","links":{"resolver":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q","bundle":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/bundle.json","state":"https://pith.science/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66XT4S4OMAMU6FM3SGVMNLC63Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:66XT4S4OMAMU6FM3SGVMNLC63Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"74e20a6fb8c9d3f9f84753f41480e5b49047ba58c28bc0a3fa4fd53ad6b3509d","cross_cats_sorted":["math.MG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-01-03T19:06:38Z","title_canon_sha256":"5a8324253dcee0b2f2843a92ba55513706370838bfe08923caf282c820b86ae8"},"schema_version":"1.0","source":{"id":"2201.00841","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.00841","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"2201.00841v2","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.00841","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"66XT4S4OMAMU","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"pith_short_16","alias_value":"66XT4S4OMAMU6FM3","created_at":"2026-07-05T05:46:12Z"},{"alias_kind":"pith_short_8","alias_value":"66XT4S4O","created_at":"2026-07-05T05:46:12Z"}],"graph_snapshots":[{"event_id":"sha256:16449e52d022e7bfd028ba66fcf0b4b1b82852b0147fdb3b251df78ed2949f4f","target":"graph","created_at":"2026-07-05T05:46:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.00841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Christian Weiss, Max Goering","cross_cats":["math.MG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-01-03T19:06:38Z","title":"A study in quantitative equidistribution on the unit square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.00841","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3115f852658883201d45043dea16dd8f91ee2c912bc55b9d7cccc8f069484fbb","target":"record","created_at":"2026-07-05T05:46:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"74e20a6fb8c9d3f9f84753f41480e5b49047ba58c28bc0a3fa4fd53ad6b3509d","cross_cats_sorted":["math.MG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-01-03T19:06:38Z","title_canon_sha256":"5a8324253dcee0b2f2843a92ba55513706370838bfe08923caf282c820b86ae8"},"schema_version":"1.0","source":{"id":"2201.00841","kind":"arxiv","version":2}},"canonical_sha256":"f7af3e4b8e60194f159b91aac6ac5edc208011891d9a6e5aa51b071d67f7559f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7af3e4b8e60194f159b91aac6ac5edc208011891d9a6e5aa51b071d67f7559f","first_computed_at":"2026-07-05T05:46:12.140371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:46:12.140371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9kA/LCcyDeFDZla1CQLQ6COC5kd9i7UkDoUhvf+63QpEq5ImWgrcpHv4nbv6T47qD4BptkAcr9bxW9IuYpc1Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:46:12.140834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.00841","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3115f852658883201d45043dea16dd8f91ee2c912bc55b9d7cccc8f069484fbb","sha256:16449e52d022e7bfd028ba66fcf0b4b1b82852b0147fdb3b251df78ed2949f4f"],"state_sha256":"7f060fade5f6b7c1e39d60988ec044f46b861ad76d5e51b6b05768648e3adca1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBJ//KxIYp9FktsDYrg16kCmwR0HluIbbhuMa4g18quxyXKglcFk4+vYr7H8G6pHwhvGKEojBNlUeTRvDH69AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T01:43:58.471720Z","bundle_sha256":"8d5f37726146c14925a50fb4e40250fd7bf76ef291be1102663e6bad7da43a46"}}