{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:47FJEVZQR5AKQKENXZIS4XYULK","short_pith_number":"pith:47FJEVZQ","canonical_record":{"source":{"id":"1009.1934","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-10T05:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"e5eac87d137c979fba8bfbed6bf283eddda481aac2f9749617a0630e5d1ab060","abstract_canon_sha256":"c5c342f68f07f9d77a24638a1aff36a8cac2ae6caf11f98dcc725f6c70fa5f86"},"schema_version":"1.0"},"canonical_sha256":"e7ca9257308f40a8288dbe512e5f145a8a074f5a3b833496d3e6083f82d6cb3b","source":{"kind":"arxiv","id":"1009.1934","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1934","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1934v3","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1934","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"47FJEVZQR5AK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"47FJEVZQR5AKQKEN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"47FJEVZQ","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:47FJEVZQR5AKQKENXZIS4XYULK","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1934","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-10T05:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"e5eac87d137c979fba8bfbed6bf283eddda481aac2f9749617a0630e5d1ab060","abstract_canon_sha256":"c5c342f68f07f9d77a24638a1aff36a8cac2ae6caf11f98dcc725f6c70fa5f86"},"schema_version":"1.0"},"canonical_sha256":"e7ca9257308f40a8288dbe512e5f145a8a074f5a3b833496d3e6083f82d6cb3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:03.718224Z","signature_b64":"pyUvm4K/JHUtAbMgd8AgkDE00FHCJGJh60wbdFQCT6G0USy5p4maGSjH2YjAvknDNAcHCvseopeXbdTmjecyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ca9257308f40a8288dbe512e5f145a8a074f5a3b833496d3e6083f82d6cb3b","last_reissued_at":"2026-05-18T04:30:03.717781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:03.717781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1934","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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K4EVLkHHM+V9ggupECEqbp2Q8NsZfCZrBgH0a+bsaSvoRIntzznUXxl8oq530bdXRp0Ep+n87TFFWz7zIbsvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:54:46.781008Z"},"content_sha256":"62647448e1116f12a80d1602ee9c5e63345e0db52bdd76a41312f24b649ab0c4","schema_version":"1.0","event_id":"sha256:62647448e1116f12a80d1602ee9c5e63345e0db52bdd76a41312f24b649ab0c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:47FJEVZQR5AKQKENXZIS4XYULK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Survey of Oka theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Finnur Larusson, Franc Forstneric","submitted_at":"2010-09-10T05:18:24Z","abstract_excerpt":"Oka theory has its roots in the classical Oka principle in complex analysis. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989. Following a brief review of Stein manifolds, we discuss the recently introduced category of Oka manifolds and Oka maps. We consider geometric sufficient conditions for being Oka, the most important of which is ellipticity, introduced by Gromov. We explain how Oka manifolds and maps naturally fit into an abstract homotopy-theoretic framework. We describe recent applications and some key open p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1934","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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nu433Zl+hSSgaI0+4buCCB7XLtWekB1pcUjjmalpK47nKMoMU2mQtgWmMAtoJ9h1VApWGSbLaqh81Se7UHdFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:54:46.781733Z"},"content_sha256":"b4f476c7e29ca5eef27e15733838aaa5bbcf99e27a3f3a6a21182fa4df94eeed","schema_version":"1.0","event_id":"sha256:b4f476c7e29ca5eef27e15733838aaa5bbcf99e27a3f3a6a21182fa4df94eeed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47FJEVZQR5AKQKENXZIS4XYULK/bundle.json","state_url":"https://pith.science/pith/47FJEVZQR5AKQKENXZIS4XYULK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47FJEVZQR5AKQKENXZIS4XYULK/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":"2026-06-12T06:54:46Z","links":{"resolver":"https://pith.science/pith/47FJEVZQR5AKQKENXZIS4XYULK","bundle":"https://pith.science/pith/47FJEVZQR5AKQKENXZIS4XYULK/bundle.json","state":"https://pith.science/pith/47FJEVZQR5AKQKENXZIS4XYULK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47FJEVZQR5AKQKENXZIS4XYULK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:47FJEVZQR5AKQKENXZIS4XYULK","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":"c5c342f68f07f9d77a24638a1aff36a8cac2ae6caf11f98dcc725f6c70fa5f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-10T05:18:24Z","title_canon_sha256":"e5eac87d137c979fba8bfbed6bf283eddda481aac2f9749617a0630e5d1ab060"},"schema_version":"1.0","source":{"id":"1009.1934","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1934","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1934v3","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1934","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"47FJEVZQR5AK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"47FJEVZQR5AKQKEN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"47FJEVZQ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:b4f476c7e29ca5eef27e15733838aaa5bbcf99e27a3f3a6a21182fa4df94eeed","target":"graph","created_at":"2026-05-18T04:30:03Z","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":"Oka theory has its roots in the classical Oka principle in complex analysis. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989. Following a brief review of Stein manifolds, we discuss the recently introduced category of Oka manifolds and Oka maps. We consider geometric sufficient conditions for being Oka, the most important of which is ellipticity, introduced by Gromov. We explain how Oka manifolds and maps naturally fit into an abstract homotopy-theoretic framework. We describe recent applications and some key open p","authors_text":"Finnur Larusson, Franc Forstneric","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-10T05:18:24Z","title":"Survey of Oka theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1934","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":"sha256:62647448e1116f12a80d1602ee9c5e63345e0db52bdd76a41312f24b649ab0c4","target":"record","created_at":"2026-05-18T04:30:03Z","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":"c5c342f68f07f9d77a24638a1aff36a8cac2ae6caf11f98dcc725f6c70fa5f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-09-10T05:18:24Z","title_canon_sha256":"e5eac87d137c979fba8bfbed6bf283eddda481aac2f9749617a0630e5d1ab060"},"schema_version":"1.0","source":{"id":"1009.1934","kind":"arxiv","version":3}},"canonical_sha256":"e7ca9257308f40a8288dbe512e5f145a8a074f5a3b833496d3e6083f82d6cb3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ca9257308f40a8288dbe512e5f145a8a074f5a3b833496d3e6083f82d6cb3b","first_computed_at":"2026-05-18T04:30:03.717781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.717781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pyUvm4K/JHUtAbMgd8AgkDE00FHCJGJh60wbdFQCT6G0USy5p4maGSjH2YjAvknDNAcHCvseopeXbdTmjecyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.718224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1934","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62647448e1116f12a80d1602ee9c5e63345e0db52bdd76a41312f24b649ab0c4","sha256:b4f476c7e29ca5eef27e15733838aaa5bbcf99e27a3f3a6a21182fa4df94eeed"],"state_sha256":"ed3fe46bc02c630e737014ec25bc83880a85366ee7fbb1f38f8494240549397e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtE6uWBRqmdWkSFxgGiil4HsJezy6b81tmtYStKauKpakXfGTe2cbXdZPgDVLckP+B10UDM59Vs1ZZNiWNseDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:54:46.785308Z","bundle_sha256":"02741d0a8c9367de9a464cd6c6a305437687b31e120e86524f747eb93feff582"}}