{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:IUGLSCK3F4G4ISHV4NSHUX7RHT","short_pith_number":"pith:IUGLSCK3","schema_version":"1.0","canonical_sha256":"450cb9095b2f0dc448f5e3647a5ff13cf8443de14e2d4ad2fd8d2a6bf2f773b0","source":{"kind":"arxiv","id":"0704.3422","version":2},"attestation_state":"computed","paper":{"title":"Orthogonal complex structures on domains in R^4","license":"","headline":"","cross_cats":["math.AG","math.AP"],"primary_cat":"math.DG","authors_text":"Jeff Viaclovsky, Simon Salamon","submitted_at":"2007-04-25T18:44:41Z","abstract_excerpt":"An orthogonal complex structure on a domain in R^4 is a complex structure which is integrable and is compatible with the Euclidean metric. This gives rise to a first order system of partial differential equations which is conformally invariant. We prove two Liouville-type uniqueness theorems for solutions of this system, and use these to give an alternative proof of the classification of compact locally conformally flat Hermitian surfaces first proved by Pontecorvo. We also give a classification of non-degenerate quadrics in CP^3 under the action of the conformal group. Using this classificati"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0704.3422","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-04-25T18:44:41Z","cross_cats_sorted":["math.AG","math.AP"],"title_canon_sha256":"5bc3ed98df9452310a7a55a3ecb1b21954ca282fc4dc662580abc250640c0132","abstract_canon_sha256":"4b8fddd09cc3328451ebff0fe0601aa27f5140292b7e4ff14ac986c92abbcfd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:48:26.187819Z","signature_b64":"Rw8eKGBQMdx4WC9GrRrBA/2nSptJOFhS5o5zqQKwKFKrbTzZWardJdB7uVfiyEicgRgexo8hQAHrvW6J3Jk3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"450cb9095b2f0dc448f5e3647a5ff13cf8443de14e2d4ad2fd8d2a6bf2f773b0","last_reissued_at":"2026-07-04T15:48:26.187303Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:48:26.187303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthogonal complex structures on domains in R^4","license":"","headline":"","cross_cats":["math.AG","math.AP"],"primary_cat":"math.DG","authors_text":"Jeff Viaclovsky, Simon Salamon","submitted_at":"2007-04-25T18:44:41Z","abstract_excerpt":"An orthogonal complex structure on a domain in R^4 is a complex structure which is integrable and is compatible with the Euclidean metric. This gives rise to a first order system of partial differential equations which is conformally invariant. We prove two Liouville-type uniqueness theorems for solutions of this system, and use these to give an alternative proof of the classification of compact locally conformally flat Hermitian surfaces first proved by Pontecorvo. We also give a classification of non-degenerate quadrics in CP^3 under the action of the conformal group. Using this classificati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3422","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0704.3422/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0704.3422","created_at":"2026-07-04T15:48:26.187375+00:00"},{"alias_kind":"arxiv_version","alias_value":"0704.3422v2","created_at":"2026-07-04T15:48:26.187375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3422","created_at":"2026-07-04T15:48:26.187375+00:00"},{"alias_kind":"pith_short_12","alias_value":"IUGLSCK3F4G4","created_at":"2026-07-04T15:48:26.187375+00:00"},{"alias_kind":"pith_short_16","alias_value":"IUGLSCK3F4G4ISHV","created_at":"2026-07-04T15:48:26.187375+00:00"},{"alias_kind":"pith_short_8","alias_value":"IUGLSCK3","created_at":"2026-07-04T15:48:26.187375+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT","json":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT.json","graph_json":"https://pith.science/api/pith-number/IUGLSCK3F4G4ISHV4NSHUX7RHT/graph.json","events_json":"https://pith.science/api/pith-number/IUGLSCK3F4G4ISHV4NSHUX7RHT/events.json","paper":"https://pith.science/paper/IUGLSCK3"},"agent_actions":{"view_html":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT","download_json":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT.json","view_paper":"https://pith.science/paper/IUGLSCK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0704.3422&json=true","fetch_graph":"https://pith.science/api/pith-number/IUGLSCK3F4G4ISHV4NSHUX7RHT/graph.json","fetch_events":"https://pith.science/api/pith-number/IUGLSCK3F4G4ISHV4NSHUX7RHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT/action/storage_attestation","attest_author":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT/action/author_attestation","sign_citation":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT/action/citation_signature","submit_replication":"https://pith.science/pith/IUGLSCK3F4G4ISHV4NSHUX7RHT/action/replication_record"}},"created_at":"2026-07-04T15:48:26.187375+00:00","updated_at":"2026-07-04T15:48:26.187375+00:00"}