{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:THEGJ75UWIW4YGKFPTTWF4WS4K","short_pith_number":"pith:THEGJ75U","canonical_record":{"source":{"id":"1601.02843","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-12T13:10:09Z","cross_cats_sorted":[],"title_canon_sha256":"1d0e66c7b991bb71268a06234f8dc9b90d800fef74d1f483f66cf08b011d7e9c","abstract_canon_sha256":"ac9d8fa031a4ba8005392dd4fd8eda2e8e1c01a6c46bb7503a67ed1314b06b29"},"schema_version":"1.0"},"canonical_sha256":"99c864ffb4b22dcc19457ce762f2d2e298b0caf8e987ac717257d7cc2c38f7f0","source":{"kind":"arxiv","id":"1601.02843","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02843","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02843v3","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02843","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"THEGJ75UWIW4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"THEGJ75UWIW4YGKF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"THEGJ75U","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:THEGJ75UWIW4YGKFPTTWF4WS4K","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02843","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-12T13:10:09Z","cross_cats_sorted":[],"title_canon_sha256":"1d0e66c7b991bb71268a06234f8dc9b90d800fef74d1f483f66cf08b011d7e9c","abstract_canon_sha256":"ac9d8fa031a4ba8005392dd4fd8eda2e8e1c01a6c46bb7503a67ed1314b06b29"},"schema_version":"1.0"},"canonical_sha256":"99c864ffb4b22dcc19457ce762f2d2e298b0caf8e987ac717257d7cc2c38f7f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:02.382223Z","signature_b64":"cA2qXMwj+fK6/J/LLBXe8bMdb1ux3PHpsMFHt8zGT/Hc8M1Hfq7lntmNQGjdvSjzdHb74s5HKJvfu6lHw+PpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99c864ffb4b22dcc19457ce762f2d2e298b0caf8e987ac717257d7cc2c38f7f0","last_reissued_at":"2026-05-18T00:26:02.381541Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:02.381541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02843","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aMYJPh+oPz5r2Wi+sFWGMdSFTXjDQ1xwIKlSGtljmqvj8Qo0ig+AEM1T4vDat/0Ufop8bCZZ+mz2CIKkQvFjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:13:10.220301Z"},"content_sha256":"23be1697b8c33a08935c4898d1225cb5c08b27a59a78a3b0248c519a2cbcccf7","schema_version":"1.0","event_id":"sha256:23be1697b8c33a08935c4898d1225cb5c08b27a59a78a3b0248c519a2cbcccf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:THEGJ75UWIW4YGKFPTTWF4WS4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ruelle's inequality in negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Felipe Riquelme","submitted_at":"2016-01-12T13:10:09Z","abstract_excerpt":"In this paper we study different notions of entropy for measure-preserving dynamical systems defined on noncompact spaces. We see that some classical results for compact spaces remain partially valid in this setting. We define a new kind of entropy for dynamical systems defined on noncompact Riemannian manifolds, which satisfies similar properties to the classical ones. As an application, we prove Ruelle's inequality and Pesin's entropy formula for the geodesic flow in manifolds with pinched negative sectional curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02843","kind":"arxiv","version":3},"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":"2026-05-18T00:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8jIS+O721Qdfc3asTr2Oj41fxG1N00/5SG4XGon1NK2WIzeocUsgvbWlblYckianuBLzL8u6dtUDwJAeeZbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:13:10.220667Z"},"content_sha256":"327ebdc67902dc6b90efcb058e83194e931ba3dcc6df088615be4bc1db5ea9b6","schema_version":"1.0","event_id":"sha256:327ebdc67902dc6b90efcb058e83194e931ba3dcc6df088615be4bc1db5ea9b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THEGJ75UWIW4YGKFPTTWF4WS4K/bundle.json","state_url":"https://pith.science/pith/THEGJ75UWIW4YGKFPTTWF4WS4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THEGJ75UWIW4YGKFPTTWF4WS4K/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":"2026-07-02T19:13:10Z","links":{"resolver":"https://pith.science/pith/THEGJ75UWIW4YGKFPTTWF4WS4K","bundle":"https://pith.science/pith/THEGJ75UWIW4YGKFPTTWF4WS4K/bundle.json","state":"https://pith.science/pith/THEGJ75UWIW4YGKFPTTWF4WS4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THEGJ75UWIW4YGKFPTTWF4WS4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:THEGJ75UWIW4YGKFPTTWF4WS4K","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":"ac9d8fa031a4ba8005392dd4fd8eda2e8e1c01a6c46bb7503a67ed1314b06b29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-12T13:10:09Z","title_canon_sha256":"1d0e66c7b991bb71268a06234f8dc9b90d800fef74d1f483f66cf08b011d7e9c"},"schema_version":"1.0","source":{"id":"1601.02843","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02843","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02843v3","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02843","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"THEGJ75UWIW4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"THEGJ75UWIW4YGKF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"THEGJ75U","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:327ebdc67902dc6b90efcb058e83194e931ba3dcc6df088615be4bc1db5ea9b6","target":"graph","created_at":"2026-05-18T00:26:02Z","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":"In this paper we study different notions of entropy for measure-preserving dynamical systems defined on noncompact spaces. We see that some classical results for compact spaces remain partially valid in this setting. We define a new kind of entropy for dynamical systems defined on noncompact Riemannian manifolds, which satisfies similar properties to the classical ones. As an application, we prove Ruelle's inequality and Pesin's entropy formula for the geodesic flow in manifolds with pinched negative sectional curvature.","authors_text":"Felipe Riquelme","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-12T13:10:09Z","title":"Ruelle's inequality in negative curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02843","kind":"arxiv","version":3},"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":"sha256:23be1697b8c33a08935c4898d1225cb5c08b27a59a78a3b0248c519a2cbcccf7","target":"record","created_at":"2026-05-18T00:26:02Z","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":"ac9d8fa031a4ba8005392dd4fd8eda2e8e1c01a6c46bb7503a67ed1314b06b29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-12T13:10:09Z","title_canon_sha256":"1d0e66c7b991bb71268a06234f8dc9b90d800fef74d1f483f66cf08b011d7e9c"},"schema_version":"1.0","source":{"id":"1601.02843","kind":"arxiv","version":3}},"canonical_sha256":"99c864ffb4b22dcc19457ce762f2d2e298b0caf8e987ac717257d7cc2c38f7f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99c864ffb4b22dcc19457ce762f2d2e298b0caf8e987ac717257d7cc2c38f7f0","first_computed_at":"2026-05-18T00:26:02.381541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:02.381541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cA2qXMwj+fK6/J/LLBXe8bMdb1ux3PHpsMFHt8zGT/Hc8M1Hfq7lntmNQGjdvSjzdHb74s5HKJvfu6lHw+PpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:02.382223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02843","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23be1697b8c33a08935c4898d1225cb5c08b27a59a78a3b0248c519a2cbcccf7","sha256:327ebdc67902dc6b90efcb058e83194e931ba3dcc6df088615be4bc1db5ea9b6"],"state_sha256":"f5e9cbf9271f483491f5729658baadfa79bb00f62fcd42242e56b7a77e5d3c92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6y04zD5dfn+IuDSVlFVX4BMn/T0hmUXUYG9ehULduEr/4bdRY3QBu64Iy67gwNBSNw3xedfMdkiUuVvJ1UMbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:13:10.222570Z","bundle_sha256":"6ffbe9ddc76191a664ef730062771adf0bea3729bf576f0092985a4f25b58c55"}}