{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:X7W5UT3C5RJR26XV45VRT5CZH7","short_pith_number":"pith:X7W5UT3C","canonical_record":{"source":{"id":"1811.07450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T01:39:31Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"80b28d5a55c71b2f4484e80ffed720872659fae6d565be92dba42a64e34912ec","abstract_canon_sha256":"f7eb352f94880492a663ec270094fed0a24218b7839b3d6956c8f2c8a6def9e2"},"schema_version":"1.0"},"canonical_sha256":"bfedda4f62ec531d7af5e76b19f4593ff2f42fe6b56609e2323788a5f226a338","source":{"kind":"arxiv","id":"1811.07450","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07450","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07450v2","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07450","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"X7W5UT3C5RJR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X7W5UT3C5RJR26XV","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X7W5UT3C","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:X7W5UT3C5RJR26XV45VRT5CZH7","target":"record","payload":{"canonical_record":{"source":{"id":"1811.07450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T01:39:31Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"80b28d5a55c71b2f4484e80ffed720872659fae6d565be92dba42a64e34912ec","abstract_canon_sha256":"f7eb352f94880492a663ec270094fed0a24218b7839b3d6956c8f2c8a6def9e2"},"schema_version":"1.0"},"canonical_sha256":"bfedda4f62ec531d7af5e76b19f4593ff2f42fe6b56609e2323788a5f226a338","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:06.393631Z","signature_b64":"4BNEdzsNgvSzq9rrfbJ8WszR9Pf+5nShqqDdWwjlyJr4VNeiFFM/vnlDUQd0ImKynXGVlJoFPIKd9v/4bTIpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfedda4f62ec531d7af5e76b19f4593ff2f42fe6b56609e2323788a5f226a338","last_reissued_at":"2026-05-17T23:48:06.393219Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:06.393219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.07450","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":"2026-05-17T23:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mnWBq5/KY+7EZvCxsMyJ9CDTjbB+9jX04csVFQPMSPsreVEr/glOtAgDtXTEK4rbc2szi9Oqm4f80ROPbwA1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:34.976731Z"},"content_sha256":"d104c1b1158aa92fcc97953a9ca91a4b0ff072b991eb1395d5193c800f9bdb4c","schema_version":"1.0","event_id":"sha256:d104c1b1158aa92fcc97953a9ca91a4b0ff072b991eb1395d5193c800f9bdb4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:X7W5UT3C5RJR26XV45VRT5CZH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unique Ergodicity for foliations on compact K\\\"ahler surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Nessim Sibony, Tien-Cuong Dinh, Viet-Anh Nguyen","submitted_at":"2018-11-19T01:39:31Z","abstract_excerpt":"Let \\Fc be a holomorphic foliation by Riemann surfaces on a compact K\\\"ahler surface X. Assume it is generic in the sense that all the singularities are hyperbolic and that the foliation admits no directed positive closed (1,1)-current. Then there exists a unique (up to a multiplicative constant) positive \\ddc-closed (1,1)-current directed by \\Fc. This is a very strong ergodic property of \\Fc. Our proof uses an extension of the theory of densities to a class of non-\\ddc-closed currents. A complete description of the cone of directed positive \\ddc-closed (1,1)-currents is also given when \\Fc ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07450","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":"2026-05-17T23:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8u7UvbLtAcu6gOBR2zeIbqWU8Srb8guj0hQP9VLz0TlQxyPIPA+CySutIyRb35ZPRVqYIGlxK8KX3EF+PgsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:34.977076Z"},"content_sha256":"1e0b63811854566600d36d951fbaa0f04831f217a6d8ccdd7d371148c9f39f5f","schema_version":"1.0","event_id":"sha256:1e0b63811854566600d36d951fbaa0f04831f217a6d8ccdd7d371148c9f39f5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7W5UT3C5RJR26XV45VRT5CZH7/bundle.json","state_url":"https://pith.science/pith/X7W5UT3C5RJR26XV45VRT5CZH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7W5UT3C5RJR26XV45VRT5CZH7/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":"2026-06-01T19:40:34Z","links":{"resolver":"https://pith.science/pith/X7W5UT3C5RJR26XV45VRT5CZH7","bundle":"https://pith.science/pith/X7W5UT3C5RJR26XV45VRT5CZH7/bundle.json","state":"https://pith.science/pith/X7W5UT3C5RJR26XV45VRT5CZH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7W5UT3C5RJR26XV45VRT5CZH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:X7W5UT3C5RJR26XV45VRT5CZH7","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":"f7eb352f94880492a663ec270094fed0a24218b7839b3d6956c8f2c8a6def9e2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T01:39:31Z","title_canon_sha256":"80b28d5a55c71b2f4484e80ffed720872659fae6d565be92dba42a64e34912ec"},"schema_version":"1.0","source":{"id":"1811.07450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07450","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07450v2","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07450","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"X7W5UT3C5RJR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"X7W5UT3C5RJR26XV","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"X7W5UT3C","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:1e0b63811854566600d36d951fbaa0f04831f217a6d8ccdd7d371148c9f39f5f","target":"graph","created_at":"2026-05-17T23:48:06Z","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 \\Fc be a holomorphic foliation by Riemann surfaces on a compact K\\\"ahler surface X. Assume it is generic in the sense that all the singularities are hyperbolic and that the foliation admits no directed positive closed (1,1)-current. Then there exists a unique (up to a multiplicative constant) positive \\ddc-closed (1,1)-current directed by \\Fc. This is a very strong ergodic property of \\Fc. Our proof uses an extension of the theory of densities to a class of non-\\ddc-closed currents. A complete description of the cone of directed positive \\ddc-closed (1,1)-currents is also given when \\Fc ad","authors_text":"Nessim Sibony, Tien-Cuong Dinh, Viet-Anh Nguyen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T01:39:31Z","title":"Unique Ergodicity for foliations on compact K\\\"ahler surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07450","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:d104c1b1158aa92fcc97953a9ca91a4b0ff072b991eb1395d5193c800f9bdb4c","target":"record","created_at":"2026-05-17T23:48:06Z","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":"f7eb352f94880492a663ec270094fed0a24218b7839b3d6956c8f2c8a6def9e2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-19T01:39:31Z","title_canon_sha256":"80b28d5a55c71b2f4484e80ffed720872659fae6d565be92dba42a64e34912ec"},"schema_version":"1.0","source":{"id":"1811.07450","kind":"arxiv","version":2}},"canonical_sha256":"bfedda4f62ec531d7af5e76b19f4593ff2f42fe6b56609e2323788a5f226a338","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfedda4f62ec531d7af5e76b19f4593ff2f42fe6b56609e2323788a5f226a338","first_computed_at":"2026-05-17T23:48:06.393219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:06.393219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4BNEdzsNgvSzq9rrfbJ8WszR9Pf+5nShqqDdWwjlyJr4VNeiFFM/vnlDUQd0ImKynXGVlJoFPIKd9v/4bTIpCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:06.393631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d104c1b1158aa92fcc97953a9ca91a4b0ff072b991eb1395d5193c800f9bdb4c","sha256:1e0b63811854566600d36d951fbaa0f04831f217a6d8ccdd7d371148c9f39f5f"],"state_sha256":"92517ca5e97f07434f27949766fce7f2db29f9637b10f856e2c968443897f342"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFpoZV3grasLnd4ouY2DD0uwqh8gAxDWA+JtIVapw9hj0hAuUeti1wyXNl0x4tu5tJvRM0EUYlPDSAbPo6OpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:40:34.979117Z","bundle_sha256":"362f8ced5fc07be92ec28e45cf1818223be2f4293c7609cc54cc17062239517a"}}