{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WL5HIAFJ37DCWWHR4BOTX46VZY","short_pith_number":"pith:WL5HIAFJ","canonical_record":{"source":{"id":"1311.1226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-05T21:25:01Z","cross_cats_sorted":[],"title_canon_sha256":"71d89f0f7a2f141dc177aab6235daf19d0863643455c39c9d32ee2762b34510d","abstract_canon_sha256":"2f08d31d5b18dbd492baa2a514ad0544b4dbd9ac6eb1d1c2d623118822e13bfb"},"schema_version":"1.0"},"canonical_sha256":"b2fa7400a9dfc62b58f1e05d3bf3d5ce1e6c34499ef625b61a1dcefa798cb650","source":{"kind":"arxiv","id":"1311.1226","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1226","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1226v2","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1226","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"WL5HIAFJ37DC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WL5HIAFJ37DCWWHR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WL5HIAFJ","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WL5HIAFJ37DCWWHR4BOTX46VZY","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-05T21:25:01Z","cross_cats_sorted":[],"title_canon_sha256":"71d89f0f7a2f141dc177aab6235daf19d0863643455c39c9d32ee2762b34510d","abstract_canon_sha256":"2f08d31d5b18dbd492baa2a514ad0544b4dbd9ac6eb1d1c2d623118822e13bfb"},"schema_version":"1.0"},"canonical_sha256":"b2fa7400a9dfc62b58f1e05d3bf3d5ce1e6c34499ef625b61a1dcefa798cb650","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:12.531120Z","signature_b64":"ZFzUShFuckANlgaCUVXpv2av/NoYV4c5fV8Mtd6Q83dE6vtL9mO2lbq6GhwIhYTi03x1hr8AQ8CowkMvS2meBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2fa7400a9dfc62b58f1e05d3bf3d5ce1e6c34499ef625b61a1dcefa798cb650","last_reissued_at":"2026-05-18T02:56:12.530725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:12.530725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1226","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eL8lloEu+4XF40ny1bHJEPx3z77DaO/AhZMfQwmxf9igxBdl6d5SStM+P1Op4Uf7rLuHkOT6h3MHskAhIqQfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:48:16.057973Z"},"content_sha256":"119ff3877e092dfd00ccac261acaf3da792b98adfb4980d1f3763cb103bad173","schema_version":"1.0","event_id":"sha256:119ff3877e092dfd00ccac261acaf3da792b98adfb4980d1f3763cb103bad173"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WL5HIAFJ37DCWWHR4BOTX46VZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally Monge-Ampere Foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Giorgio Patrizio, Morris Kalka","submitted_at":"2013-11-05T21:25:01Z","abstract_excerpt":"It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the fact that codimension one foliations of complex manifolds are necessarily locally Monge-Amp\\`ere foliations and that parabolic leaves cannot have hyperbolic behavior. The result holds true also for locally Monge-Amp\\`ere foliations with parabolic leaves of arbitrary codimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1226","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYwQ23uvdU2PAF2KxVt7MSN2FDSfr+AFnZ2dKqcIoYo+cFgxcjyr9HZFboc9sZYBVP7K2wDzjpzIb7IOvJxQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:48:16.058329Z"},"content_sha256":"491eb68b7dfdc54f0723e6a4531f35dab4609ec0d9126fb7c9a80ec3a86c8d1a","schema_version":"1.0","event_id":"sha256:491eb68b7dfdc54f0723e6a4531f35dab4609ec0d9126fb7c9a80ec3a86c8d1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WL5HIAFJ37DCWWHR4BOTX46VZY/bundle.json","state_url":"https://pith.science/pith/WL5HIAFJ37DCWWHR4BOTX46VZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WL5HIAFJ37DCWWHR4BOTX46VZY/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":"2026-06-21T21:48:16Z","links":{"resolver":"https://pith.science/pith/WL5HIAFJ37DCWWHR4BOTX46VZY","bundle":"https://pith.science/pith/WL5HIAFJ37DCWWHR4BOTX46VZY/bundle.json","state":"https://pith.science/pith/WL5HIAFJ37DCWWHR4BOTX46VZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WL5HIAFJ37DCWWHR4BOTX46VZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WL5HIAFJ37DCWWHR4BOTX46VZY","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":"2f08d31d5b18dbd492baa2a514ad0544b4dbd9ac6eb1d1c2d623118822e13bfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-05T21:25:01Z","title_canon_sha256":"71d89f0f7a2f141dc177aab6235daf19d0863643455c39c9d32ee2762b34510d"},"schema_version":"1.0","source":{"id":"1311.1226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1226","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1226v2","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1226","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"WL5HIAFJ37DC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WL5HIAFJ37DCWWHR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WL5HIAFJ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:491eb68b7dfdc54f0723e6a4531f35dab4609ec0d9126fb7c9a80ec3a86c8d1a","target":"graph","created_at":"2026-05-18T02:56:12Z","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":"It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the fact that codimension one foliations of complex manifolds are necessarily locally Monge-Amp\\`ere foliations and that parabolic leaves cannot have hyperbolic behavior. The result holds true also for locally Monge-Amp\\`ere foliations with parabolic leaves of arbitrary codimension.","authors_text":"Giorgio Patrizio, Morris Kalka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-05T21:25:01Z","title":"Locally Monge-Ampere Foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1226","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":"sha256:119ff3877e092dfd00ccac261acaf3da792b98adfb4980d1f3763cb103bad173","target":"record","created_at":"2026-05-18T02:56:12Z","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":"2f08d31d5b18dbd492baa2a514ad0544b4dbd9ac6eb1d1c2d623118822e13bfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-05T21:25:01Z","title_canon_sha256":"71d89f0f7a2f141dc177aab6235daf19d0863643455c39c9d32ee2762b34510d"},"schema_version":"1.0","source":{"id":"1311.1226","kind":"arxiv","version":2}},"canonical_sha256":"b2fa7400a9dfc62b58f1e05d3bf3d5ce1e6c34499ef625b61a1dcefa798cb650","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2fa7400a9dfc62b58f1e05d3bf3d5ce1e6c34499ef625b61a1dcefa798cb650","first_computed_at":"2026-05-18T02:56:12.530725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.530725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZFzUShFuckANlgaCUVXpv2av/NoYV4c5fV8Mtd6Q83dE6vtL9mO2lbq6GhwIhYTi03x1hr8AQ8CowkMvS2meBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.531120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:119ff3877e092dfd00ccac261acaf3da792b98adfb4980d1f3763cb103bad173","sha256:491eb68b7dfdc54f0723e6a4531f35dab4609ec0d9126fb7c9a80ec3a86c8d1a"],"state_sha256":"343a6fb624416bb6c4fc5d9ef3d53aea7d13c2f9469c36548d7545b0c86a0b6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EdNGt72iynz43jrxes2aD0mf9EcSwtf6AycOSkzUmCVzhoAz9OvRelupw8jp7nYAglJdnrMzcC6R+JS5rQFYAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:48:16.060226Z","bundle_sha256":"dfda6faa4b10835541e4a48897863f135e0820438c4aed18ac57fec495210fce"}}