{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CABZQMA5ODFMECIAW4T5DCIFGP","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":"fa978aedede9fa3aa35efac342cdb42b7b88ee039487e972dcd9e3f760bd3a8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-28T22:16:43Z","title_canon_sha256":"9e0817eacf3744b0bae09f2eb6a12ef9d38a516c0ec6a3e2b1a87f5ba633b1d9"},"schema_version":"1.0","source":{"id":"1711.11435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11435","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11435v1","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11435","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"CABZQMA5ODFM","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CABZQMA5ODFMECIA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CABZQMA5","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:1f622b41eca4af5567a0a1992e1d881cb55d883863c7af3ff3a8bbc5c979f057","target":"graph","created_at":"2026-05-18T00:29:11Z","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 define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold admits a virtual immersion with skew symmetric second fundamental form, if and only if it is a symmetric space, and in this case the virtual immersion is essentially unique.","authors_text":"Marco Radeschi, Ricardo A. E. Mendes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-28T22:16:43Z","title":"Virtual immersions, and a characterization of symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11435","kind":"arxiv","version":1},"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:e28c945c2c5fd2d5ebbbd668dad1c48c82c12d562940223749452717b60ac856","target":"record","created_at":"2026-05-18T00:29:11Z","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":"fa978aedede9fa3aa35efac342cdb42b7b88ee039487e972dcd9e3f760bd3a8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-28T22:16:43Z","title_canon_sha256":"9e0817eacf3744b0bae09f2eb6a12ef9d38a516c0ec6a3e2b1a87f5ba633b1d9"},"schema_version":"1.0","source":{"id":"1711.11435","kind":"arxiv","version":1}},"canonical_sha256":"100398301d70cac20900b727d1890533e65a9a8b348c1a91eb2a6f4b4bc86ae0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"100398301d70cac20900b727d1890533e65a9a8b348c1a91eb2a6f4b4bc86ae0","first_computed_at":"2026-05-18T00:29:11.619353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:11.619353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y04VaT8Q8hLUWOa204sQ6dcDTuV9owjtJYRlOzybB5EOvLtXaGNQPdIQd7jaKx288CUU5UKYv61hC0YEjUgXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:11.620017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e28c945c2c5fd2d5ebbbd668dad1c48c82c12d562940223749452717b60ac856","sha256:1f622b41eca4af5567a0a1992e1d881cb55d883863c7af3ff3a8bbc5c979f057"],"state_sha256":"d88e4cd64637379a50a75186397513bf4a8966ce8d8e7f7cf4538a3f4efa30da"}