{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QFRMO32AW4OWVIREP236P3COBY","short_pith_number":"pith:QFRMO32A","schema_version":"1.0","canonical_sha256":"8162c76f40b71d6aa2247eb7e7ec4e0e2cace3f21f4709184fee8f4875a5057d","source":{"kind":"arxiv","id":"1807.11133","version":1},"attestation_state":"computed","paper":{"title":"Cr-invariants for surfaces in 4-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jorge Luiz Deolindo Silva","submitted_at":"2018-07-30T01:13:07Z","abstract_excerpt":"We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas's work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of ortogonal projections of the surface. The cross-ratio invariants at $P_3(c)$-points are used to recover two moduli in the 4-jet of the projective parametrization of the surface and show the stable configurations of asymptotic curves."},"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":"1807.11133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-30T01:13:07Z","cross_cats_sorted":[],"title_canon_sha256":"0d55efc153a71f2d51c2abd58a93660596f3c033257c1569795521268be7c0ef","abstract_canon_sha256":"511d1a344edaf0203dc65fe9389d1815b15db297c077ca022f3a42521033dbd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.843682Z","signature_b64":"aRmKHYS5Gv8y7UGqLrTLE6XvoAV+DWhQla6mG/16ZZiWejNJf3iWCQfa1Am2Q2d0oUF2w9pbfDB6jfQbov21BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8162c76f40b71d6aa2247eb7e7ec4e0e2cace3f21f4709184fee8f4875a5057d","last_reissued_at":"2026-05-18T00:09:32.843277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.843277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cr-invariants for surfaces in 4-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jorge Luiz Deolindo Silva","submitted_at":"2018-07-30T01:13:07Z","abstract_excerpt":"We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas's work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of ortogonal projections of the surface. The cross-ratio invariants at $P_3(c)$-points are used to recover two moduli in the 4-jet of the projective parametrization of the surface and show the stable configurations of asymptotic curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11133","kind":"arxiv","version":1},"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":"1807.11133","created_at":"2026-05-18T00:09:32.843357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11133v1","created_at":"2026-05-18T00:09:32.843357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11133","created_at":"2026-05-18T00:09:32.843357+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFRMO32AW4OW","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFRMO32AW4OWVIRE","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFRMO32A","created_at":"2026-05-18T12:32:46.962924+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/QFRMO32AW4OWVIREP236P3COBY","json":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY.json","graph_json":"https://pith.science/api/pith-number/QFRMO32AW4OWVIREP236P3COBY/graph.json","events_json":"https://pith.science/api/pith-number/QFRMO32AW4OWVIREP236P3COBY/events.json","paper":"https://pith.science/paper/QFRMO32A"},"agent_actions":{"view_html":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY","download_json":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY.json","view_paper":"https://pith.science/paper/QFRMO32A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11133&json=true","fetch_graph":"https://pith.science/api/pith-number/QFRMO32AW4OWVIREP236P3COBY/graph.json","fetch_events":"https://pith.science/api/pith-number/QFRMO32AW4OWVIREP236P3COBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY/action/storage_attestation","attest_author":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY/action/author_attestation","sign_citation":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY/action/citation_signature","submit_replication":"https://pith.science/pith/QFRMO32AW4OWVIREP236P3COBY/action/replication_record"}},"created_at":"2026-05-18T00:09:32.843357+00:00","updated_at":"2026-05-18T00:09:32.843357+00:00"}