{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5Z5FMTBUTOIWDYBQHMMPMSOTMO","short_pith_number":"pith:5Z5FMTBU","canonical_record":{"source":{"id":"1104.4502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-22T20:10:38Z","cross_cats_sorted":["math.PR","math.RT"],"title_canon_sha256":"72b8bedead1e66c0425bc7b114bdbc0693545bc6a93a1c16e2badd31e6198ae6","abstract_canon_sha256":"fa305e400492bfe820e5c6f3473738ac565e060eaacc0a5aead33f885df1b259"},"schema_version":"1.0"},"canonical_sha256":"ee7a564c349b9161e0303b18f649d3638de45c4d5daa016c0e3f64f1d9a65885","source":{"kind":"arxiv","id":"1104.4502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4502","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4502v1","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4502","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"5Z5FMTBUTOIW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5Z5FMTBUTOIWDYBQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5Z5FMTBU","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5Z5FMTBUTOIWDYBQHMMPMSOTMO","target":"record","payload":{"canonical_record":{"source":{"id":"1104.4502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-22T20:10:38Z","cross_cats_sorted":["math.PR","math.RT"],"title_canon_sha256":"72b8bedead1e66c0425bc7b114bdbc0693545bc6a93a1c16e2badd31e6198ae6","abstract_canon_sha256":"fa305e400492bfe820e5c6f3473738ac565e060eaacc0a5aead33f885df1b259"},"schema_version":"1.0"},"canonical_sha256":"ee7a564c349b9161e0303b18f649d3638de45c4d5daa016c0e3f64f1d9a65885","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:33.925764Z","signature_b64":"ry6enfQ3kIVm7TxIw0RO2//N2pELAds3UZKDYiHNdgl54geqUCpV6FKdeBbRIeoug9Chzf1c2l1vwH7ZBSdiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee7a564c349b9161e0303b18f649d3638de45c4d5daa016c0e3f64f1d9a65885","last_reissued_at":"2026-05-18T04:23:33.925334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:33.925334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.4502","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eXXoOD/YFT+mFgQrwZHOcdF6ZBB/E7mtbk8mC7Nwg86IF/qnKhP9l+/uNwuGEW5X85xB8NdgVnvi/OdO/vtaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:02:25.580456Z"},"content_sha256":"39df3c8704ba018e49dfaa1199b4e0c84a36f3a83182a5fefacb7fef5c287da8","schema_version":"1.0","event_id":"sha256:39df3c8704ba018e49dfaa1199b4e0c84a36f3a83182a5fefacb7fef5c287da8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5Z5FMTBUTOIWDYBQHMMPMSOTMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Theorems for Horocycle Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.RT"],"primary_cat":"math.DS","authors_text":"Alexander Bufetov, Giovanni Forni","submitted_at":"2011-04-22T20:10:38Z","abstract_excerpt":"The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on rectifiable arcs. An asymptotic formula for ergodic integrals for horocycle flows is obtained in terms of the finitely-additive measures, and limit theorems follow as a corollary of the asymptotic formula. The objects and results of this paper are similar to those in [15], [16], [4] and [5] for translation flows on flat surfaces. The arguments are based on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4502","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T04:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROGxGzJFItxVALDlZRoHmRs15kmKZmuOLMp0GQ/IXYyNRx0lOuFSdraamoIO7Lj2V6chFCoghWQf0LckB4gsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:02:25.580805Z"},"content_sha256":"942fa94415094d3d9bc007c64728a6bba244f55cd9f30caed4646d0c5bf411ca","schema_version":"1.0","event_id":"sha256:942fa94415094d3d9bc007c64728a6bba244f55cd9f30caed4646d0c5bf411ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO/bundle.json","state_url":"https://pith.science/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO/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":"2026-06-30T07:02:25Z","links":{"resolver":"https://pith.science/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO","bundle":"https://pith.science/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO/bundle.json","state":"https://pith.science/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Z5FMTBUTOIWDYBQHMMPMSOTMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5Z5FMTBUTOIWDYBQHMMPMSOTMO","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":"fa305e400492bfe820e5c6f3473738ac565e060eaacc0a5aead33f885df1b259","cross_cats_sorted":["math.PR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-22T20:10:38Z","title_canon_sha256":"72b8bedead1e66c0425bc7b114bdbc0693545bc6a93a1c16e2badd31e6198ae6"},"schema_version":"1.0","source":{"id":"1104.4502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4502","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4502v1","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4502","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"5Z5FMTBUTOIW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5Z5FMTBUTOIWDYBQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5Z5FMTBU","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:942fa94415094d3d9bc007c64728a6bba244f55cd9f30caed4646d0c5bf411ca","target":"graph","created_at":"2026-05-18T04:23:33Z","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":"The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on rectifiable arcs. An asymptotic formula for ergodic integrals for horocycle flows is obtained in terms of the finitely-additive measures, and limit theorems follow as a corollary of the asymptotic formula. The objects and results of this paper are similar to those in [15], [16], [4] and [5] for translation flows on flat surfaces. The arguments are based on t","authors_text":"Alexander Bufetov, Giovanni Forni","cross_cats":["math.PR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-22T20:10:38Z","title":"Limit Theorems for Horocycle Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4502","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":"sha256:39df3c8704ba018e49dfaa1199b4e0c84a36f3a83182a5fefacb7fef5c287da8","target":"record","created_at":"2026-05-18T04:23:33Z","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":"fa305e400492bfe820e5c6f3473738ac565e060eaacc0a5aead33f885df1b259","cross_cats_sorted":["math.PR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-22T20:10:38Z","title_canon_sha256":"72b8bedead1e66c0425bc7b114bdbc0693545bc6a93a1c16e2badd31e6198ae6"},"schema_version":"1.0","source":{"id":"1104.4502","kind":"arxiv","version":1}},"canonical_sha256":"ee7a564c349b9161e0303b18f649d3638de45c4d5daa016c0e3f64f1d9a65885","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7a564c349b9161e0303b18f649d3638de45c4d5daa016c0e3f64f1d9a65885","first_computed_at":"2026-05-18T04:23:33.925334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:33.925334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ry6enfQ3kIVm7TxIw0RO2//N2pELAds3UZKDYiHNdgl54geqUCpV6FKdeBbRIeoug9Chzf1c2l1vwH7ZBSdiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:33.925764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39df3c8704ba018e49dfaa1199b4e0c84a36f3a83182a5fefacb7fef5c287da8","sha256:942fa94415094d3d9bc007c64728a6bba244f55cd9f30caed4646d0c5bf411ca"],"state_sha256":"4692c65322a7facbaffb005bf14ea72590671fc5febd0e759253661f340feb43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0iD20FOGnkf5nRipPJlQXraHeoc/ZyvIrLaQ42epzTwyBvK8iuDBNI2shpTQy78TAwM4vQIG81BfIolCeuQaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T07:02:25.583037Z","bundle_sha256":"24ccc6cbb1ebedf2b568a2ee49048682c268e91303a02ac142e4a7a6cf7ea844"}}