{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PMY4IGXUF23L2ZULJU7FLJSAOC","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":"013142cdcfa9ec50a5758fed1f2c633417f6e2053363efdcb0835c0d21b08805","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T16:55:15Z","title_canon_sha256":"500207d12cd703a3b9e3124efda4944b92520d841c46948c673ad0abf323358a"},"schema_version":"1.0","source":{"id":"1501.05228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05228","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05228v1","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05228","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"PMY4IGXUF23L","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PMY4IGXUF23L2ZUL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PMY4IGXU","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:15f038f7bdcf9860ba38b2e0f376dd9963e8d1c0eec52face5b1d49712d1b6d5","target":"graph","created_at":"2026-05-18T02:28:55Z","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"},"paper":{"abstract_excerpt":"Let $M=\\Gamma\\backslash\\mathrm{PSL}(2,\\mathbb{R})$ be a compact manifold, and let $f\\in C^\\infty(M)$ be a function of zero average. We use spectral methods to get uniform (i.e. independent of spectral gap) bounds for twisted averages of $f$ along long horocycle orbit segments. We apply this to obtain an equidistribution result for sparse subsets of horocycles on $M$.","authors_text":"James Tanis, Pankaj Vishe","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T16:55:15Z","title":"Uniform bounds for period integrals and sparse equidistribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05228","kind":"arxiv","version":1},"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":"sha256:95614dc2ada86dff9c549dfc186059c64381c087130efd8f3adfea7841628c25","target":"record","created_at":"2026-05-18T02:28:55Z","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":"013142cdcfa9ec50a5758fed1f2c633417f6e2053363efdcb0835c0d21b08805","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-21T16:55:15Z","title_canon_sha256":"500207d12cd703a3b9e3124efda4944b92520d841c46948c673ad0abf323358a"},"schema_version":"1.0","source":{"id":"1501.05228","kind":"arxiv","version":1}},"canonical_sha256":"7b31c41af42eb6bd668b4d3e55a640709e77e688542cddd9ae6c1fb5a256f6b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b31c41af42eb6bd668b4d3e55a640709e77e688542cddd9ae6c1fb5a256f6b4","first_computed_at":"2026-05-18T02:28:55.704122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:55.704122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RwQnSxgXsVfubBYSLUvJm1NNPvOPrv4SFb9Fmt908uRL8+OYqV5KGTfya35Dmg8dhbmX2tnEWSllferPbFz4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:55.704606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95614dc2ada86dff9c549dfc186059c64381c087130efd8f3adfea7841628c25","sha256:15f038f7bdcf9860ba38b2e0f376dd9963e8d1c0eec52face5b1d49712d1b6d5"],"state_sha256":"31098d02ae91b46af433a126d7ecb2a7381a85ed9301086f297e2d1fd1234e1b"}