{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:6BL6QMEVK3CEX5LWJT4C37DH4Z","short_pith_number":"pith:6BL6QMEV","schema_version":"1.0","canonical_sha256":"f057e8309556c44bf5764cf82dfc67e65be74f37d5512b8cf18ca8744eb09720","source":{"kind":"arxiv","id":"0903.3225","version":1},"attestation_state":"computed","paper":{"title":"Compatibility of Gauss maps with metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"B. S. Kruglikov, J. Eschenburg, R. Tribuzy, V. S. Matveev","submitted_at":"2009-03-18T19:19:11Z","abstract_excerpt":"We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold $M^m$ into the sphere $S^m$ to be the Gauss map of an isometric immersion $u:M^m \\to R^n$, $n=m+1$. We briefly discuss the case of general $n$ as well"},"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":"0903.3225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-03-18T19:19:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"408fce7c17ceafbe017cddf1e9d146a151ba87479c8cccfc36abea2aa7d35508","abstract_canon_sha256":"0e3a91a9683343614641da1ae92efadbe79830b77aa0a9d52f8e633554c4b212"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:05.255219Z","signature_b64":"3EUuSewc1hZ37mDkxahK5OPBdaTEskPdDIzkH51PIbN0UMPDSphUY5NgocP9u2SmLoMmjxpQB07wKeHAFd9gAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f057e8309556c44bf5764cf82dfc67e65be74f37d5512b8cf18ca8744eb09720","last_reissued_at":"2026-05-18T03:36:05.254775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:05.254775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compatibility of Gauss maps with metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"B. S. Kruglikov, J. Eschenburg, R. Tribuzy, V. S. Matveev","submitted_at":"2009-03-18T19:19:11Z","abstract_excerpt":"We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold $M^m$ into the sphere $S^m$ to be the Gauss map of an isometric immersion $u:M^m \\to R^n$, $n=m+1$. We briefly discuss the case of general $n$ as well"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3225","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":"0903.3225","created_at":"2026-05-18T03:36:05.254848+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.3225v1","created_at":"2026-05-18T03:36:05.254848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3225","created_at":"2026-05-18T03:36:05.254848+00:00"},{"alias_kind":"pith_short_12","alias_value":"6BL6QMEVK3CE","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"6BL6QMEVK3CEX5LW","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"6BL6QMEV","created_at":"2026-05-18T12:25:58.837520+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/6BL6QMEVK3CEX5LWJT4C37DH4Z","json":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z.json","graph_json":"https://pith.science/api/pith-number/6BL6QMEVK3CEX5LWJT4C37DH4Z/graph.json","events_json":"https://pith.science/api/pith-number/6BL6QMEVK3CEX5LWJT4C37DH4Z/events.json","paper":"https://pith.science/paper/6BL6QMEV"},"agent_actions":{"view_html":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z","download_json":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z.json","view_paper":"https://pith.science/paper/6BL6QMEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.3225&json=true","fetch_graph":"https://pith.science/api/pith-number/6BL6QMEVK3CEX5LWJT4C37DH4Z/graph.json","fetch_events":"https://pith.science/api/pith-number/6BL6QMEVK3CEX5LWJT4C37DH4Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z/action/storage_attestation","attest_author":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z/action/author_attestation","sign_citation":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z/action/citation_signature","submit_replication":"https://pith.science/pith/6BL6QMEVK3CEX5LWJT4C37DH4Z/action/replication_record"}},"created_at":"2026-05-18T03:36:05.254848+00:00","updated_at":"2026-05-18T03:36:05.254848+00:00"}