{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZB3Z4LURR77SYSICYFUC4JWG3G","short_pith_number":"pith:ZB3Z4LUR","canonical_record":{"source":{"id":"0908.3998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-08-27T12:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"cfd73a300f0defdd8047958e7c56fb4c1433b95ae72fba522f4d260978e35228","abstract_canon_sha256":"8b61ae113d6ae2b06c4b65e9a61226cc8556d5b894bdf6da13f39515387db64b"},"schema_version":"1.0"},"canonical_sha256":"c8779e2e918fff2c4902c1682e26c6d99fc6878beba94932a6f9facc3dd57635","source":{"kind":"arxiv","id":"0908.3998","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3998","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3998v1","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3998","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZB3Z4LURR77S","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZB3Z4LURR77SYSIC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZB3Z4LUR","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZB3Z4LURR77SYSICYFUC4JWG3G","target":"record","payload":{"canonical_record":{"source":{"id":"0908.3998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-08-27T12:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"cfd73a300f0defdd8047958e7c56fb4c1433b95ae72fba522f4d260978e35228","abstract_canon_sha256":"8b61ae113d6ae2b06c4b65e9a61226cc8556d5b894bdf6da13f39515387db64b"},"schema_version":"1.0"},"canonical_sha256":"c8779e2e918fff2c4902c1682e26c6d99fc6878beba94932a6f9facc3dd57635","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:13.237897Z","signature_b64":"FvRTvp9VLJWtMMmTMV8wFDKIXnBsACPS3jvye8ifyahUMBsWdqrxwcUxuRyM5v35UzVaiIzLgIh8sjUtL60RAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8779e2e918fff2c4902c1682e26c6d99fc6878beba94932a6f9facc3dd57635","last_reissued_at":"2026-05-18T04:31:13.237393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:13.237393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.3998","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elnONAMtsDSsVPW4mENZYkFyiv3ARAxNbnokumJF0VCZJZx4ib/CL02xh5hdkkUDUT2/DDFZCuySYzdSEi0rBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:01:40.109995Z"},"content_sha256":"346139ed19e86b6c10ac770fe56b27ec23cec7eb23ae4c77a1fcb2db6a1c05a3","schema_version":"1.0","event_id":"sha256:346139ed19e86b6c10ac770fe56b27ec23cec7eb23ae4c77a1fcb2db6a1c05a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZB3Z4LURR77SYSICYFUC4JWG3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical gradient manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Christian Miebach, Henrik Stoetzel","submitted_at":"2009-08-27T12:27:52Z","abstract_excerpt":"We study the action of a real-reductive group $G=K\\exp(\\lie{p})$ on real-analytic submanifold $X$ of a K\\\"ahler manifold $Z$. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^\\mbb{C}$ such that the action of a maximal Hamiltonian subgroup is Hamiltonian. The moment map $\\mu$ induces a gradient map $\\mu_\\lie{p}\\colon X\\to\\lie{p}$. We show that $\\mu_\\lie{p}$ almost separates the $K$--orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion's characterization of spherical K\\\"ahler manifolds with moment m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3998","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hB9NAc33dkhsb9xlHNbE/K08n0VYBYDkQFnoRoMFr9KJyn/UcofE2Nz7wwfu9idrXO/p9IwXcXT2mAsvCsUeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:01:40.110357Z"},"content_sha256":"a38045122a86180d2700e190ee00ee415c6b3aa36b3ee8ab179d47a77e049fac","schema_version":"1.0","event_id":"sha256:a38045122a86180d2700e190ee00ee415c6b3aa36b3ee8ab179d47a77e049fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZB3Z4LURR77SYSICYFUC4JWG3G/bundle.json","state_url":"https://pith.science/pith/ZB3Z4LURR77SYSICYFUC4JWG3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZB3Z4LURR77SYSICYFUC4JWG3G/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T01:01:40Z","links":{"resolver":"https://pith.science/pith/ZB3Z4LURR77SYSICYFUC4JWG3G","bundle":"https://pith.science/pith/ZB3Z4LURR77SYSICYFUC4JWG3G/bundle.json","state":"https://pith.science/pith/ZB3Z4LURR77SYSICYFUC4JWG3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZB3Z4LURR77SYSICYFUC4JWG3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZB3Z4LURR77SYSICYFUC4JWG3G","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":"8b61ae113d6ae2b06c4b65e9a61226cc8556d5b894bdf6da13f39515387db64b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-08-27T12:27:52Z","title_canon_sha256":"cfd73a300f0defdd8047958e7c56fb4c1433b95ae72fba522f4d260978e35228"},"schema_version":"1.0","source":{"id":"0908.3998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3998","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3998v1","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3998","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZB3Z4LURR77S","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZB3Z4LURR77SYSIC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZB3Z4LUR","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:a38045122a86180d2700e190ee00ee415c6b3aa36b3ee8ab179d47a77e049fac","target":"graph","created_at":"2026-05-18T04:31:13Z","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 study the action of a real-reductive group $G=K\\exp(\\lie{p})$ on real-analytic submanifold $X$ of a K\\\"ahler manifold $Z$. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^\\mbb{C}$ such that the action of a maximal Hamiltonian subgroup is Hamiltonian. The moment map $\\mu$ induces a gradient map $\\mu_\\lie{p}\\colon X\\to\\lie{p}$. We show that $\\mu_\\lie{p}$ almost separates the $K$--orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion's characterization of spherical K\\\"ahler manifolds with moment m","authors_text":"Christian Miebach, Henrik Stoetzel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-08-27T12:27:52Z","title":"Spherical gradient manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3998","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":"sha256:346139ed19e86b6c10ac770fe56b27ec23cec7eb23ae4c77a1fcb2db6a1c05a3","target":"record","created_at":"2026-05-18T04:31:13Z","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":"8b61ae113d6ae2b06c4b65e9a61226cc8556d5b894bdf6da13f39515387db64b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-08-27T12:27:52Z","title_canon_sha256":"cfd73a300f0defdd8047958e7c56fb4c1433b95ae72fba522f4d260978e35228"},"schema_version":"1.0","source":{"id":"0908.3998","kind":"arxiv","version":1}},"canonical_sha256":"c8779e2e918fff2c4902c1682e26c6d99fc6878beba94932a6f9facc3dd57635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8779e2e918fff2c4902c1682e26c6d99fc6878beba94932a6f9facc3dd57635","first_computed_at":"2026-05-18T04:31:13.237393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:13.237393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FvRTvp9VLJWtMMmTMV8wFDKIXnBsACPS3jvye8ifyahUMBsWdqrxwcUxuRyM5v35UzVaiIzLgIh8sjUtL60RAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:13.237897Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.3998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:346139ed19e86b6c10ac770fe56b27ec23cec7eb23ae4c77a1fcb2db6a1c05a3","sha256:a38045122a86180d2700e190ee00ee415c6b3aa36b3ee8ab179d47a77e049fac"],"state_sha256":"845f1c059ba86c1abe92f5f2266b17f54f1f4b8ccd7b14d6827988ccf44fb137"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrhoh/huKa+wYu1KsCRSyiiR1FLz9xVQIgBXR51c10kaCvF5mbD6SAczMMBAbpDRaRDwFkD8ZQQaG2jw9ZUuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:01:40.112332Z","bundle_sha256":"b88512abaa3798cd8662fab1d12351eb1d222a25fd58ef660c5210e31ffb2f87"}}