{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7GDEP3XMXGBZJJHGEBPJ7CCULY","short_pith_number":"pith:7GDEP3XM","canonical_record":{"source":{"id":"1105.2307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-11T20:21:40Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"faa6c2649a4be93cdf983cb3bd957fde712a2e598ab1a6232b82fce58f12dcda","abstract_canon_sha256":"50d83b4bb07b01ce2646b5ace60bdca95deced4a3b71eb4f24aae23550a81180"},"schema_version":"1.0"},"canonical_sha256":"f98647eeecb98394a4e6205e9f88545e1fdfd7d9e103a0eb479b72d2425124be","source":{"kind":"arxiv","id":"1105.2307","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2307","created_at":"2026-05-18T04:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2307v2","created_at":"2026-05-18T04:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2307","created_at":"2026-05-18T04:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"7GDEP3XMXGBZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7GDEP3XMXGBZJJHG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7GDEP3XM","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7GDEP3XMXGBZJJHGEBPJ7CCULY","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-11T20:21:40Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"faa6c2649a4be93cdf983cb3bd957fde712a2e598ab1a6232b82fce58f12dcda","abstract_canon_sha256":"50d83b4bb07b01ce2646b5ace60bdca95deced4a3b71eb4f24aae23550a81180"},"schema_version":"1.0"},"canonical_sha256":"f98647eeecb98394a4e6205e9f88545e1fdfd7d9e103a0eb479b72d2425124be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:20.513266Z","signature_b64":"EL5didID1uaF0J7mihN0pU/A+AdzYHA9/74Wli8ES3R6T6KGlwcZ6KihLihuIQ5XDWywxO+piC9fuQ3XYIpvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f98647eeecb98394a4e6205e9f88545e1fdfd7d9e103a0eb479b72d2425124be","last_reissued_at":"2026-05-18T04:16:20.512700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:20.512700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2307","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfopc3e7sC48Ujkm15Lpr1MG3yqp1IxVK8Yxn5tiC6joQtrwv+NAB6QBKPU9flSywVbdHXHTwurNBtYnn5/dCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:54:12.266133Z"},"content_sha256":"6ebd0714ceaa14165efec59d7c5294f0eb3e0b027a7d135f3120337f8092679f","schema_version":"1.0","event_id":"sha256:6ebd0714ceaa14165efec59d7c5294f0eb3e0b027a7d135f3120337f8092679f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7GDEP3XMXGBZJJHGEBPJ7CCULY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy for hyperbolic Riemann surface laminations I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Nessim Sibony, Tien-Cuong Dinh, Viet-Anh Nguyen","submitted_at":"2011-05-11T20:21:40Z","abstract_excerpt":"We develop a notion of entropy, using hyperbolic time, for laminations by hyperbolic Riemann surfaces. When the lamination is compact and transversally smooth, we show that the entropy is finite and the Poincare metric on leaves is transversally Holder continuous. A notion of metric entropy is also introduced for harmonic measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2307","kind":"arxiv","version":2},"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":"2026-05-18T04:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7xB4aSvFdqxdOmQKW/OxZqOIB5+x3sWuMrx3Ir7WPzHNVQet5E8sJgnOSRJwImtBjliihXSTPrA2xegohP2tDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:54:12.266550Z"},"content_sha256":"3c378c97a49ccd2bce8533fecd51a9132ce5d8fc4bbc9daa348543a994164387","schema_version":"1.0","event_id":"sha256:3c378c97a49ccd2bce8533fecd51a9132ce5d8fc4bbc9daa348543a994164387"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY/bundle.json","state_url":"https://pith.science/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY/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":"2026-06-02T17:54:12Z","links":{"resolver":"https://pith.science/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY","bundle":"https://pith.science/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY/bundle.json","state":"https://pith.science/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7GDEP3XMXGBZJJHGEBPJ7CCULY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7GDEP3XMXGBZJJHGEBPJ7CCULY","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":"50d83b4bb07b01ce2646b5ace60bdca95deced4a3b71eb4f24aae23550a81180","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-11T20:21:40Z","title_canon_sha256":"faa6c2649a4be93cdf983cb3bd957fde712a2e598ab1a6232b82fce58f12dcda"},"schema_version":"1.0","source":{"id":"1105.2307","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2307","created_at":"2026-05-18T04:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2307v2","created_at":"2026-05-18T04:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2307","created_at":"2026-05-18T04:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"7GDEP3XMXGBZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7GDEP3XMXGBZJJHG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7GDEP3XM","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:3c378c97a49ccd2bce8533fecd51a9132ce5d8fc4bbc9daa348543a994164387","target":"graph","created_at":"2026-05-18T04:16:20Z","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 develop a notion of entropy, using hyperbolic time, for laminations by hyperbolic Riemann surfaces. When the lamination is compact and transversally smooth, we show that the entropy is finite and the Poincare metric on leaves is transversally Holder continuous. A notion of metric entropy is also introduced for harmonic measures.","authors_text":"Nessim Sibony, Tien-Cuong Dinh, Viet-Anh Nguyen","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-11T20:21:40Z","title":"Entropy for hyperbolic Riemann surface laminations I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2307","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":"sha256:6ebd0714ceaa14165efec59d7c5294f0eb3e0b027a7d135f3120337f8092679f","target":"record","created_at":"2026-05-18T04:16:20Z","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":"50d83b4bb07b01ce2646b5ace60bdca95deced4a3b71eb4f24aae23550a81180","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-11T20:21:40Z","title_canon_sha256":"faa6c2649a4be93cdf983cb3bd957fde712a2e598ab1a6232b82fce58f12dcda"},"schema_version":"1.0","source":{"id":"1105.2307","kind":"arxiv","version":2}},"canonical_sha256":"f98647eeecb98394a4e6205e9f88545e1fdfd7d9e103a0eb479b72d2425124be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f98647eeecb98394a4e6205e9f88545e1fdfd7d9e103a0eb479b72d2425124be","first_computed_at":"2026-05-18T04:16:20.512700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:20.512700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EL5didID1uaF0J7mihN0pU/A+AdzYHA9/74Wli8ES3R6T6KGlwcZ6KihLihuIQ5XDWywxO+piC9fuQ3XYIpvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:20.513266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2307","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ebd0714ceaa14165efec59d7c5294f0eb3e0b027a7d135f3120337f8092679f","sha256:3c378c97a49ccd2bce8533fecd51a9132ce5d8fc4bbc9daa348543a994164387"],"state_sha256":"1f9c0a32844553d7f7f0d123f45d67dedd687de07fd35d661dedb5d2c6bbaa1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6TYHsv7kRGKA1Wo1TbOD9Pl7DxTLNJyAOvcl1So08GpHD7CXKb3gyOZbJmL4Tt+il7x92cp6nlXbbMNmaFMlCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:54:12.268476Z","bundle_sha256":"3b2033f31e96b6f8e1164a53d460d4dc0b24468bbc22c442f1486aa5f45c0f2a"}}