{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AMNMXZ7MCXEBKVU5GAOLVHPZG6","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":"8c9f08267387c1e34ef5fa26912ffa659ba465dd351e15bf6ab7b15a375cac83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-18T05:38:40Z","title_canon_sha256":"84a52fae9893cc83d83ddf1554597faaf6ba20050649ffe6b2d561992692bef7"},"schema_version":"1.0","source":{"id":"1507.05147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05147","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05147v1","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05147","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"AMNMXZ7MCXEB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AMNMXZ7MCXEBKVU5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AMNMXZ7M","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:b4758739671c5e86fb5de2ec3ae43213f72950c4635991427876eb4e67cb597d","target":"graph","created_at":"2026-05-18T01:36:41Z","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":"We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive effective equidistribution results for horocycle maps. As an application of our main theorems in the compact case we further improve on a result of A. Venkatesh, recently already improved by J. Tanis and P. Vishe, on a sparse equidistribution problem for classical horocycle flows proposed by N. Shah and G. Margulis, and in the general non-compact, finite area case we prove bounds on Fourier coefficients of cups forms w","authors_text":"Giovanni Forni, James Tanis, Livio Flaminio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-18T05:38:40Z","title":"Effective equidistribution of twisted horocycle flows and horocycle maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05147","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":"sha256:11ab62c91aee0ec96cbc81fbb2aa10d4a60eba7ebd959b9ad49b431e6cf441e2","target":"record","created_at":"2026-05-18T01:36:41Z","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":"8c9f08267387c1e34ef5fa26912ffa659ba465dd351e15bf6ab7b15a375cac83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-18T05:38:40Z","title_canon_sha256":"84a52fae9893cc83d83ddf1554597faaf6ba20050649ffe6b2d561992692bef7"},"schema_version":"1.0","source":{"id":"1507.05147","kind":"arxiv","version":1}},"canonical_sha256":"031acbe7ec15c815569d301cba9df937b2a668a571faa212ef7c64c6f3c112ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"031acbe7ec15c815569d301cba9df937b2a668a571faa212ef7c64c6f3c112ae","first_computed_at":"2026-05-18T01:36:41.325994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:41.325994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vRX3MrjSHNvI237Lc8/36S7zoRrN8aPjOwai2bcX79VqrHMVHRFVdLsAmMhoVkouTvTmt5TkcG3o9+yN7UzAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:41.326695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11ab62c91aee0ec96cbc81fbb2aa10d4a60eba7ebd959b9ad49b431e6cf441e2","sha256:b4758739671c5e86fb5de2ec3ae43213f72950c4635991427876eb4e67cb597d"],"state_sha256":"c0237fb042a2c88ff3dd3790fd9d18079a7a6e440e694e870071b007b5c475bf"}