{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZE5AYVC3XFVDBPPMQQ4B2AD2RV","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":"23596fd55ebf5ea4cc5f5480b706c14e18366d128029465d6b503efc33e97cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-04T06:29:10Z","title_canon_sha256":"e765817eeedd0aa37f108ccf5776427f9e09a527ebe534e1ffcfb2813c310320"},"schema_version":"1.0","source":{"id":"1403.0698","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0698","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0698v4","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0698","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"ZE5AYVC3XFVD","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZE5AYVC3XFVDBPPM","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZE5AYVC3","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:ba70ad5f95d450e1117e4350c54011032d7488769245866da60174b4ccb3da49","target":"graph","created_at":"2026-05-18T01:23:29Z","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":"With each antiholomorphic involution $\\sigma $ of a connected complex semisimple Lie group $G$ we associate an automorphism $\\epsilon_\\sigma$ of the Dynkin diagram. The definition of $\\epsilon_\\sigma$ is given in terms of the Satake diagram of $\\sigma $. Let $H \\subset G$ be a self-normalizing spherical subgroup. If $\\epsilon_\\sigma ={\\rm id}$ then we prove the uniqueness and existence of a $\\sigma $-equivariant real structure on $G/H$ and on the wonderful completion of $G/H$.","authors_text":"Dmitri Akhiezer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-04T06:29:10Z","title":"Satake diagrams and real structures on spherical varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0698","kind":"arxiv","version":4},"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":"sha256:4a02e507a340a8f89a47cc3af03275b260d032d1780330bb0c76f589b26a69de","target":"record","created_at":"2026-05-18T01:23:29Z","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":"23596fd55ebf5ea4cc5f5480b706c14e18366d128029465d6b503efc33e97cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-04T06:29:10Z","title_canon_sha256":"e765817eeedd0aa37f108ccf5776427f9e09a527ebe534e1ffcfb2813c310320"},"schema_version":"1.0","source":{"id":"1403.0698","kind":"arxiv","version":4}},"canonical_sha256":"c93a0c545bb96a30bdec84381d007a8d468aa3300e13435148df317b72a4f67a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c93a0c545bb96a30bdec84381d007a8d468aa3300e13435148df317b72a4f67a","first_computed_at":"2026-05-18T01:23:29.885126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:29.885126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C0TVJbNYYX6VrjpXCI7/dRbTEZbO/f3pryboENwjIdwjRpn+z8IC0y2Az8e2jY5jA4ifncKN0smhFhSY2n6ZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:29.885818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0698","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a02e507a340a8f89a47cc3af03275b260d032d1780330bb0c76f589b26a69de","sha256:ba70ad5f95d450e1117e4350c54011032d7488769245866da60174b4ccb3da49"],"state_sha256":"f3e827180fabfa47724718290e9f6a7717673d5cdab50dd5b421fcf62177742b"}