{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GCGWIR3FH5DC7RWCEPS2D466LF","short_pith_number":"pith:GCGWIR3F","schema_version":"1.0","canonical_sha256":"308d6447653f462fc6c223e5a1f3de59792928792e2d0075651b799f8779f1b2","source":{"kind":"arxiv","id":"1301.6325","version":2},"attestation_state":"computed","paper":{"title":"A loop group method for Demoulin surfaces in the 3-dimensional real projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shimpei Kobayashi","submitted_at":"2013-01-27T07:04:16Z","abstract_excerpt":"For a surface in the 3-dimensional real projective space, we define a Gauss map, which is a quadric in $\\mathbb R^{4}$ and called the first-order Gauss map. It will be shown that the surface is a Demoulin surface if and only if the first-order Gauss map is conformal, and the surface is a projective minimal coincidence surface or a Demoulin surface if and only if the first-order Gauss map is harmonic. Moreover for a Demoulin surface, it will be shown that the first-order Gauss map can be obtained by the natural projection of the Lorentz primitive map into a 6-symmetric space. We also characteri"},"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":"1301.6325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-27T07:04:16Z","cross_cats_sorted":[],"title_canon_sha256":"cdbcba8d5edac067607aa21e8ffe72ab36caf44aeb59d2b43d5291a30d05c850","abstract_canon_sha256":"4dc56ffe94c8e3381187bc640faedf81264e8345b484801d5f4306df30d7cdd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:17.147183Z","signature_b64":"87jolS5VbDUHmiUIHh4bJQ4VbldCMeiqiZGyNgh7N4QhWODd/QXZBOGW7ZQCOd+zZCCk/tN74F+T0IGwKDTgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308d6447653f462fc6c223e5a1f3de59792928792e2d0075651b799f8779f1b2","last_reissued_at":"2026-05-18T03:28:17.146505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:17.146505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A loop group method for Demoulin surfaces in the 3-dimensional real projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shimpei Kobayashi","submitted_at":"2013-01-27T07:04:16Z","abstract_excerpt":"For a surface in the 3-dimensional real projective space, we define a Gauss map, which is a quadric in $\\mathbb R^{4}$ and called the first-order Gauss map. It will be shown that the surface is a Demoulin surface if and only if the first-order Gauss map is conformal, and the surface is a projective minimal coincidence surface or a Demoulin surface if and only if the first-order Gauss map is harmonic. Moreover for a Demoulin surface, it will be shown that the first-order Gauss map can be obtained by the natural projection of the Lorentz primitive map into a 6-symmetric space. We also characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6325","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.6325","created_at":"2026-05-18T03:28:17.146621+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6325v2","created_at":"2026-05-18T03:28:17.146621+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6325","created_at":"2026-05-18T03:28:17.146621+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCGWIR3FH5DC","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCGWIR3FH5DC7RWC","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCGWIR3F","created_at":"2026-05-18T12:27:45.050594+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/GCGWIR3FH5DC7RWCEPS2D466LF","json":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF.json","graph_json":"https://pith.science/api/pith-number/GCGWIR3FH5DC7RWCEPS2D466LF/graph.json","events_json":"https://pith.science/api/pith-number/GCGWIR3FH5DC7RWCEPS2D466LF/events.json","paper":"https://pith.science/paper/GCGWIR3F"},"agent_actions":{"view_html":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF","download_json":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF.json","view_paper":"https://pith.science/paper/GCGWIR3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6325&json=true","fetch_graph":"https://pith.science/api/pith-number/GCGWIR3FH5DC7RWCEPS2D466LF/graph.json","fetch_events":"https://pith.science/api/pith-number/GCGWIR3FH5DC7RWCEPS2D466LF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF/action/storage_attestation","attest_author":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF/action/author_attestation","sign_citation":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF/action/citation_signature","submit_replication":"https://pith.science/pith/GCGWIR3FH5DC7RWCEPS2D466LF/action/replication_record"}},"created_at":"2026-05-18T03:28:17.146621+00:00","updated_at":"2026-05-18T03:28:17.146621+00:00"}