{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CILLDVQNAWYRTQGDZOOVCMZ7UJ","short_pith_number":"pith:CILLDVQN","canonical_record":{"source":{"id":"1211.0885","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-05T15:13:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ea292f0abc1d0b2f8ea0c7d05c171c9daf0f766bb8a5e3f05812f172601ea6ee","abstract_canon_sha256":"04a4b6c4e850e47cde5552fc9fb4cb2fd299ec5d3ef20d24c74b44fe87f9a986"},"schema_version":"1.0"},"canonical_sha256":"1216b1d60d05b119c0c3cb9d51333fa27e8111e3a512e5b09e8f31fecb51557e","source":{"kind":"arxiv","id":"1211.0885","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0885","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0885v2","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0885","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"CILLDVQNAWYR","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CILLDVQNAWYRTQGD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CILLDVQN","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CILLDVQNAWYRTQGDZOOVCMZ7UJ","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0885","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-05T15:13:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ea292f0abc1d0b2f8ea0c7d05c171c9daf0f766bb8a5e3f05812f172601ea6ee","abstract_canon_sha256":"04a4b6c4e850e47cde5552fc9fb4cb2fd299ec5d3ef20d24c74b44fe87f9a986"},"schema_version":"1.0"},"canonical_sha256":"1216b1d60d05b119c0c3cb9d51333fa27e8111e3a512e5b09e8f31fecb51557e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:47.397804Z","signature_b64":"QFyh3hpvNEkLmKIB1MIOsDkEknn7SKoI1gcsnbbPLOwWN88v49AduRPYAhsrO7vI3FswnSC5dAcOoTkgYAf2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1216b1d60d05b119c0c3cb9d51333fa27e8111e3a512e5b09e8f31fecb51557e","last_reissued_at":"2026-05-18T01:17:47.397225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:47.397225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0885","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9QJw9X77rQKqrlrpGAWOGGUPaMelbil9xMIFjB6zaoPitrHxLt1lt61L0aPM3/gCBN50SFmMKgNd11CMXlE9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:17:07.983297Z"},"content_sha256":"cc91bec1228a41e579007174111037dd83af0d9f82639aa39dca8d71e8e83790","schema_version":"1.0","event_id":"sha256:cc91bec1228a41e579007174111037dd83af0d9f82639aa39dca8d71e8e83790"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CILLDVQNAWYRTQGDZOOVCMZ7UJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed H-orbits in G-varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Michael Bate","submitted_at":"2012-11-05T15:13:26Z","abstract_excerpt":"Let G be a linear algebraic group, H a subgroup of G and X a G-variety. This paper explores the connection between G-orbits and H-orbits in X, concentrating in particular on the question of when we have the implications G.x closed in X implies H.x closed in X, and vice versa. Some of the general results found in this paper are then used in the special case where G and H are reductive and X is affine to extend two classical results of Luna from characteristic zero to arbitrary characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0885","kind":"arxiv","version":2},"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":"2026-05-18T01:17:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MiyCrlCB3uZs6ExSPVRp5rkezpKhMtJhZ7T0nX3OsTMIZ7B2mc/rsNK8g4X/ZrWae+6vxN+bQCGatS11fCwICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:17:07.983655Z"},"content_sha256":"028090c583e29a8edf77bb1550dbf8904ba09bdd097ed837a407303f1ba33ac8","schema_version":"1.0","event_id":"sha256:028090c583e29a8edf77bb1550dbf8904ba09bdd097ed837a407303f1ba33ac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ/bundle.json","state_url":"https://pith.science/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ/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":"2026-06-22T09:17:07Z","links":{"resolver":"https://pith.science/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ","bundle":"https://pith.science/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ/bundle.json","state":"https://pith.science/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CILLDVQNAWYRTQGDZOOVCMZ7UJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CILLDVQNAWYRTQGDZOOVCMZ7UJ","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":"04a4b6c4e850e47cde5552fc9fb4cb2fd299ec5d3ef20d24c74b44fe87f9a986","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-05T15:13:26Z","title_canon_sha256":"ea292f0abc1d0b2f8ea0c7d05c171c9daf0f766bb8a5e3f05812f172601ea6ee"},"schema_version":"1.0","source":{"id":"1211.0885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0885","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0885v2","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0885","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"CILLDVQNAWYR","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CILLDVQNAWYRTQGD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CILLDVQN","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:028090c583e29a8edf77bb1550dbf8904ba09bdd097ed837a407303f1ba33ac8","target":"graph","created_at":"2026-05-18T01:17:47Z","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":"Let G be a linear algebraic group, H a subgroup of G and X a G-variety. This paper explores the connection between G-orbits and H-orbits in X, concentrating in particular on the question of when we have the implications G.x closed in X implies H.x closed in X, and vice versa. Some of the general results found in this paper are then used in the special case where G and H are reductive and X is affine to extend two classical results of Luna from characteristic zero to arbitrary characteristic.","authors_text":"Michael Bate","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-05T15:13:26Z","title":"Closed H-orbits in G-varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0885","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:cc91bec1228a41e579007174111037dd83af0d9f82639aa39dca8d71e8e83790","target":"record","created_at":"2026-05-18T01:17:47Z","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":"04a4b6c4e850e47cde5552fc9fb4cb2fd299ec5d3ef20d24c74b44fe87f9a986","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-11-05T15:13:26Z","title_canon_sha256":"ea292f0abc1d0b2f8ea0c7d05c171c9daf0f766bb8a5e3f05812f172601ea6ee"},"schema_version":"1.0","source":{"id":"1211.0885","kind":"arxiv","version":2}},"canonical_sha256":"1216b1d60d05b119c0c3cb9d51333fa27e8111e3a512e5b09e8f31fecb51557e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1216b1d60d05b119c0c3cb9d51333fa27e8111e3a512e5b09e8f31fecb51557e","first_computed_at":"2026-05-18T01:17:47.397225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:47.397225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QFyh3hpvNEkLmKIB1MIOsDkEknn7SKoI1gcsnbbPLOwWN88v49AduRPYAhsrO7vI3FswnSC5dAcOoTkgYAf2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:47.397804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc91bec1228a41e579007174111037dd83af0d9f82639aa39dca8d71e8e83790","sha256:028090c583e29a8edf77bb1550dbf8904ba09bdd097ed837a407303f1ba33ac8"],"state_sha256":"27e83ccc1934055da1b6868aa2f8402fde8f4c5471530dda4d61a63ac7af7879"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qs5V1vrcU25yy/x2ZKPpA3989tU3pzV+AeM+5PyV2JxNB1gHO6Jg0Bkv6w39zSr8aaJeMCgD4VcYMviAupopAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:17:07.985534Z","bundle_sha256":"69be1b5c3210396eb6d3283561d85b959ad91fd2a96f2cf6627491c5e59c869a"}}