{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:537MMCKBIAKHTLDDE6MZLC6XBE","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":"77b347f9982b5d16a72e2350ae58c02029ed34637c623d69149da0da8c3265d9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-07T10:45:35Z","title_canon_sha256":"c743572212611c75c03ea7896c44209eb991abcfef7e7424ca539266b0e498b7"},"schema_version":"1.0","source":{"id":"1512.01972","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01972","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01972v2","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01972","created_at":"2026-05-18T00:48:28Z"},{"alias_kind":"pith_short_12","alias_value":"537MMCKBIAKH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"537MMCKBIAKHTLDD","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"537MMCKB","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:7d687a3591a4d6ab749e016e2c8ff11b2d1cc2afe533a32473b7c40a3cba7518","target":"graph","created_at":"2026-05-18T00:48:28Z","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":"The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is shown that sphericity of subgroup schemes is an open and closed condition over arbitrary base schemes generalizing a result by Knop and Roehrle. Moreover spherical embeddings are classified over arbitrary fields generalizing and simplifying results by Huruguen.","authors_text":"Torsten Wedhorn","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-07T10:45:35Z","title":"Spherical Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01972","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":"sha256:811d59bd42064464319e96b13239c00d15d304b58f8121d2c7ac3b6e44979dd2","target":"record","created_at":"2026-05-18T00:48:28Z","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":"77b347f9982b5d16a72e2350ae58c02029ed34637c623d69149da0da8c3265d9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-07T10:45:35Z","title_canon_sha256":"c743572212611c75c03ea7896c44209eb991abcfef7e7424ca539266b0e498b7"},"schema_version":"1.0","source":{"id":"1512.01972","kind":"arxiv","version":2}},"canonical_sha256":"eefec60941401479ac632799958bd709342fa3341572b1c1e54fca6932fa09bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eefec60941401479ac632799958bd709342fa3341572b1c1e54fca6932fa09bd","first_computed_at":"2026-05-18T00:48:28.551057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:28.551057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+UQ2lkx6zdLk/6tWH1N0gIlj2B76TM8/GYfWBl8BMxM/PuYJx0am8Mp2ZuiB//GljTEDcZZ08Dh7PvtilbscAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:28.551610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01972","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:811d59bd42064464319e96b13239c00d15d304b58f8121d2c7ac3b6e44979dd2","sha256:7d687a3591a4d6ab749e016e2c8ff11b2d1cc2afe533a32473b7c40a3cba7518"],"state_sha256":"ed83f1e2a3381a1b7c4f9273d77235c16471f0a683fb7d03762de6c98970c2d7"}