{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:S6SEUX3JVEOLZXL7OIAFBFO7XC","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":"4d30434ae34a42793ffb58c321d31d677132814aa98ec55529d06c78a25c520b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-01-03T10:49:33Z","title_canon_sha256":"b974dca205d5908600e199c117490a9eae783721f83d907b9dd3f6b348041e0d"},"schema_version":"1.0","source":{"id":"1101.0486","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0486","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0486v2","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0486","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"S6SEUX3JVEOL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S6SEUX3JVEOLZXL7","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S6SEUX3J","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:0d2a39a18de10507ead0d45cf052e851562db2a8986e2ea0bd05d75205f31493","target":"graph","created_at":"2026-05-18T04:10:47Z","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 show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of compact variable negative sectional curvature manifolds, establishing a logarithm law for such kind of flow.","authors_text":"Isaia Nisoli, Stefano Galatolo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-01-03T10:49:33Z","title":"Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0486","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":"sha256:28791e7445809b1886539bbe384e8cce7e807fd0898d3bdb50bd5955a6711116","target":"record","created_at":"2026-05-18T04:10:47Z","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":"4d30434ae34a42793ffb58c321d31d677132814aa98ec55529d06c78a25c520b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-01-03T10:49:33Z","title_canon_sha256":"b974dca205d5908600e199c117490a9eae783721f83d907b9dd3f6b348041e0d"},"schema_version":"1.0","source":{"id":"1101.0486","kind":"arxiv","version":2}},"canonical_sha256":"97a44a5f69a91cbcdd7f72005095dfb88254902881b701a25130f73b181096c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97a44a5f69a91cbcdd7f72005095dfb88254902881b701a25130f73b181096c3","first_computed_at":"2026-05-18T04:10:47.119208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:47.119208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0lIP4ONX70Kk0FZ0ZKx3a/Qxfb5BEM460yHkZAM0h5vuwk0sh7womT35L3tijeVSKOF2zRtyJ8ZzYd6XyEAwBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:47.119673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0486","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28791e7445809b1886539bbe384e8cce7e807fd0898d3bdb50bd5955a6711116","sha256:0d2a39a18de10507ead0d45cf052e851562db2a8986e2ea0bd05d75205f31493"],"state_sha256":"0bd47a8a28327cc08a0a2eeaab9a9f66107fd188c37b7d16ef3741e49ab60c40"}