{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VIMFXYY3XDBK4MCOL6FCN2ZIFC","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":"64967d9e6271e53523e729924ecdb6aa26b0598f331c5203948d11ba694c2942","cross_cats_sorted":["math.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-02T03:02:33Z","title_canon_sha256":"ab06e650f772d36518fafd38ab62d809da787a77a3328be95281316757da7f56"},"schema_version":"1.0","source":{"id":"1904.01187","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01187","created_at":"2026-05-17T23:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01187v2","created_at":"2026-05-17T23:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01187","created_at":"2026-05-17T23:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"VIMFXYY3XDBK","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VIMFXYY3XDBK4MCO","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VIMFXYY3","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:aa9df91909638586c98185b8817ce60843d7fe88aa152dd53b9c047c6003749e","target":"graph","created_at":"2026-05-17T23:45:20Z","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 a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential moment, we show that the equality is achieved if and only if the Gibbs density is equivalent to the hitting measure. As a corollary, if the action is not convex cocompact, any hitting measure is singular to any Gibbs density.","authors_text":"Giulio Tiozzo, Ilya Gekhtman","cross_cats":["math.GT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-02T03:02:33Z","title":"Entropy and drift for Gibbs measures on geometrically finite manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01187","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:a6353f810c30b6c2cfce6fc248cd3a0562a10bcde39d6eab45f8cc767428c947","target":"record","created_at":"2026-05-17T23:45:20Z","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":"64967d9e6271e53523e729924ecdb6aa26b0598f331c5203948d11ba694c2942","cross_cats_sorted":["math.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-02T03:02:33Z","title_canon_sha256":"ab06e650f772d36518fafd38ab62d809da787a77a3328be95281316757da7f56"},"schema_version":"1.0","source":{"id":"1904.01187","kind":"arxiv","version":2}},"canonical_sha256":"aa185be31bb8c2ae304e5f8a26eb28289b3b1949089362e2451ca07c51567ffe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa185be31bb8c2ae304e5f8a26eb28289b3b1949089362e2451ca07c51567ffe","first_computed_at":"2026-05-17T23:45:20.005647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:20.005647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kn8evA2rSllRSbiQMf0qhsbwwd8QehWNtDPXsAqZEP6AvPnEEJv+LvOpQV6v7tAKefAnO8wJzKAiMwzGaC5eDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:20.006249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01187","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6353f810c30b6c2cfce6fc248cd3a0562a10bcde39d6eab45f8cc767428c947","sha256:aa9df91909638586c98185b8817ce60843d7fe88aa152dd53b9c047c6003749e"],"state_sha256":"4723850a6be46fef8b292ca8608bc567f0c4c351d50d3a334f57ea4e304da9ce"}