{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E6RFY7SBSTW6NSNWISI7XOCW3V","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":"7e29854cf03592034cb8dd859efaee101b1ba0baa3614337afd16d5cfbc80e5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-27T11:46:13Z","title_canon_sha256":"d4749bd210bf2c92cf8751bb654302f70282d0f670434f5f6a9f2e87b6e19bbd"},"schema_version":"1.0","source":{"id":"1802.09836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09836","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09836v2","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09836","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"E6RFY7SBSTW6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E6RFY7SBSTW6NSNW","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E6RFY7SB","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:fea3effbae19613433c758045f566191b0564de193a54ed67d0b38821deda16c","target":"graph","created_at":"2026-05-17T23:46:30Z","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":"We give a spinorial representation of a submanifold of any dimension and co-dimension in a symmetric space $G/H,$ where $G$ is a complex semi-simple Lie group and $H$ is a compact real form of $G.$ This in particular includes $SL_n(\\mathbb{C})/SU(n),$ and extends the previously known spinorial representation of a surface in $\\mathbb{H}^3$ if $n=2.$ We also recover the Bryant representation of a surface with constant mean curvature 1 in $\\mathbb{H}^3$ and its generalization for a surface with holomorphic right Gauss map in $SL_n(\\mathbb{C})/SU(n).$ As a new application, we obtain a fundamental ","authors_text":"Pierre Bayard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-27T11:46:13Z","title":"Spinorial representation of submanifolds in $SL_n(\\mathbb{C})/SU(n)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09836","kind":"arxiv","version":2},"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:d5c53441e37670b5a824763e6b27f5b43562f8c512e64aea98a89268e7b78e6b","target":"record","created_at":"2026-05-17T23:46:30Z","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":"7e29854cf03592034cb8dd859efaee101b1ba0baa3614337afd16d5cfbc80e5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-27T11:46:13Z","title_canon_sha256":"d4749bd210bf2c92cf8751bb654302f70282d0f670434f5f6a9f2e87b6e19bbd"},"schema_version":"1.0","source":{"id":"1802.09836","kind":"arxiv","version":2}},"canonical_sha256":"27a25c7e4194ede6c9b64491fbb856dd421c30e5c2068f40641c26606cd80ddd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27a25c7e4194ede6c9b64491fbb856dd421c30e5c2068f40641c26606cd80ddd","first_computed_at":"2026-05-17T23:46:30.751440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:30.751440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0koeIwUdZXISpmNxTiaNrwQfnFI7gUtt3MPfPLJFHm5W+lsw3j34VVhQM3MFmSqZvU4dku4C5cVLMQIbAkOrCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:30.752054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5c53441e37670b5a824763e6b27f5b43562f8c512e64aea98a89268e7b78e6b","sha256:fea3effbae19613433c758045f566191b0564de193a54ed67d0b38821deda16c"],"state_sha256":"2fa82ef1d6824d5bd2d4154bd530aab29ea6cd3e3a9de1de9242e61fc2f5b413"}