{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4OS4ARCYIWGUO3ZNASEYOVFFDH","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":"36e013d83dca5945e96a42c32abe137683a7245dbd1a38e1c065c946fbd97bfe","cross_cats_sorted":["math-ph","math.DG","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-09T19:10:54Z","title_canon_sha256":"5b99d75b9189d49b8cf4fc1aa08bcf9c6579386beae6f08392a56abaa2ab3a36"},"schema_version":"1.0","source":{"id":"1405.2320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2320","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2320v1","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2320","created_at":"2026-05-18T02:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"4OS4ARCYIWGU","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4OS4ARCYIWGUO3ZN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4OS4ARCY","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:48fcec15cf0a0c5f315f66d38e202cb54e6c5d3c133577449fa26061efd12c9a","target":"graph","created_at":"2026-05-18T02:52:13Z","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 $M$ be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure $m_F$ associated to a potential $F$. We compute the Hausdorff dimension of the conditional measures of $m_F$. We study the $m_F$-almost sure asymptotic penetration behaviour of locally geodesic lines of $M$ into small neighbourhoods of closed geodesics, and of other compact (locally) convex subsets of $M$. We prove Khintchine-type and logarithm law-type results for the spiraling of geodesic lines around these objects. As an arithmetic consequence, we give almost sure Diophantin","authors_text":"Fr\\'ed\\'eric Paulin (LM-Orsay), Mark Pollicott (WMI)","cross_cats":["math-ph","math.DG","math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-09T19:10:54Z","title":"Logarithm laws for equilibrium states in negative curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2320","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:b7ee4e76b08fe9c328d7aaf0d448dd99aff734de047ac0e04f5e9b0bde8c4900","target":"record","created_at":"2026-05-18T02:52:13Z","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":"36e013d83dca5945e96a42c32abe137683a7245dbd1a38e1c065c946fbd97bfe","cross_cats_sorted":["math-ph","math.DG","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-09T19:10:54Z","title_canon_sha256":"5b99d75b9189d49b8cf4fc1aa08bcf9c6579386beae6f08392a56abaa2ab3a36"},"schema_version":"1.0","source":{"id":"1405.2320","kind":"arxiv","version":1}},"canonical_sha256":"e3a5c04458458d476f2d04898754a519e415c6137948603d689b7110a58d07d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3a5c04458458d476f2d04898754a519e415c6137948603d689b7110a58d07d4","first_computed_at":"2026-05-18T02:52:13.114842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:13.114842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"azR8S83kj29sTvIWBMIZN7njTBp3JCHyFGO4WoHGzJjSs6avgc+AubEZj9Zh4RoRNofupLQASUdDLTwNXAmHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:13.115360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7ee4e76b08fe9c328d7aaf0d448dd99aff734de047ac0e04f5e9b0bde8c4900","sha256:48fcec15cf0a0c5f315f66d38e202cb54e6c5d3c133577449fa26061efd12c9a"],"state_sha256":"e80dca3f3205a45d8833065234a928b8f7ecdb94510fc9be11575bd0d4fc9441"}