{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SVLLDTIFJNM2GQK6HDJFKD4DGS","short_pith_number":"pith:SVLLDTIF","canonical_record":{"source":{"id":"1604.00924","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-04T15:59:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ce00c22972bfa9721d4cba102e09dc4783a76872bebcad6bc73e09ccd8d2df7b","abstract_canon_sha256":"1bd6cd1a8f1c96f5f8dac3c0238af5bd5068f59bdbdaed9fd29d026ed0cc58d5"},"schema_version":"1.0"},"canonical_sha256":"9556b1cd054b59a3415e38d2550f833491a64cf9f629bd47e1534c0dcf73ae81","source":{"kind":"arxiv","id":"1604.00924","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00924","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00924v2","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00924","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"SVLLDTIFJNM2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SVLLDTIFJNM2GQK6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SVLLDTIF","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SVLLDTIFJNM2GQK6HDJFKD4DGS","target":"record","payload":{"canonical_record":{"source":{"id":"1604.00924","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-04T15:59:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ce00c22972bfa9721d4cba102e09dc4783a76872bebcad6bc73e09ccd8d2df7b","abstract_canon_sha256":"1bd6cd1a8f1c96f5f8dac3c0238af5bd5068f59bdbdaed9fd29d026ed0cc58d5"},"schema_version":"1.0"},"canonical_sha256":"9556b1cd054b59a3415e38d2550f833491a64cf9f629bd47e1534c0dcf73ae81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:59.485469Z","signature_b64":"lm69jQwNu3hkdtxQiZyNpmTAjxv1XXPq8n6HCGRWTte/Y3X9h7EPTJuE/R8eL2wLSDjw2TXXWkFOzeRJC9NkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9556b1cd054b59a3415e38d2550f833491a64cf9f629bd47e1534c0dcf73ae81","last_reissued_at":"2026-05-17T23:58:59.484949Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:59.484949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.00924","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":"2026-05-17T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jr8xtDa4r19LJq+coRH471jSq5qs+l4z9mrmHaJWzncP8CiKAV2JafJp3v2MtFQZS61F1j7Op7Djp4hgnzWWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:40:01.240833Z"},"content_sha256":"8c37927bd991279f91635674b38fdc371909742aee427f6c8392f80f9e2511e5","schema_version":"1.0","event_id":"sha256:8c37927bd991279f91635674b38fdc371909742aee427f6c8392f80f9e2511e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SVLLDTIFJNM2GQK6HDJFKD4DGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orbit Closures and Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Benjamin Martin, Haralampos Geranios, Michael Bate","submitted_at":"2016-04-04T15:59:32Z","abstract_excerpt":"Let G be a reductive linear algebraic group, H a reductive subgroup of G and X an affine G-variety. Let Y denote the set of fixed points of H in X, and N(H) the normalizer of H in G. In this paper we study the natural map from the quotient of Y by N(H) to the quotient of X by G induced by the inclusion of Y in X. We show that, given G and H, this map is a finite morphism for all G-varieties X if and only if H is G-completely reducible (in the sense defined by J-P. Serre); this was proved in characteristic zero by Luna in the 1970s. We discuss some applications and give a criterion for the map "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00924","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":"2026-05-17T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMEcCCnmpzkW1xEqaiWXx7jpXHxSHz+8QwYbUXUvyq447bli/51/BD+NQM27NV8gTrv8UM/+TyjslNWb2l9gBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:40:01.241284Z"},"content_sha256":"25fabaf1ecaea7d84f2dba29d264ffc153ae7305f5875cab56e8c76e4b687be5","schema_version":"1.0","event_id":"sha256:25fabaf1ecaea7d84f2dba29d264ffc153ae7305f5875cab56e8c76e4b687be5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS/bundle.json","state_url":"https://pith.science/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS/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":"2026-06-01T03:40:01Z","links":{"resolver":"https://pith.science/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS","bundle":"https://pith.science/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS/bundle.json","state":"https://pith.science/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVLLDTIFJNM2GQK6HDJFKD4DGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SVLLDTIFJNM2GQK6HDJFKD4DGS","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":"1bd6cd1a8f1c96f5f8dac3c0238af5bd5068f59bdbdaed9fd29d026ed0cc58d5","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-04T15:59:32Z","title_canon_sha256":"ce00c22972bfa9721d4cba102e09dc4783a76872bebcad6bc73e09ccd8d2df7b"},"schema_version":"1.0","source":{"id":"1604.00924","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00924","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00924v2","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00924","created_at":"2026-05-17T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"SVLLDTIFJNM2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SVLLDTIFJNM2GQK6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SVLLDTIF","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:25fabaf1ecaea7d84f2dba29d264ffc153ae7305f5875cab56e8c76e4b687be5","target":"graph","created_at":"2026-05-17T23:58:59Z","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 reductive linear algebraic group, H a reductive subgroup of G and X an affine G-variety. Let Y denote the set of fixed points of H in X, and N(H) the normalizer of H in G. In this paper we study the natural map from the quotient of Y by N(H) to the quotient of X by G induced by the inclusion of Y in X. We show that, given G and H, this map is a finite morphism for all G-varieties X if and only if H is G-completely reducible (in the sense defined by J-P. Serre); this was proved in characteristic zero by Luna in the 1970s. We discuss some applications and give a criterion for the map ","authors_text":"Benjamin Martin, Haralampos Geranios, Michael Bate","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-04T15:59:32Z","title":"Orbit Closures and Invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00924","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":"sha256:8c37927bd991279f91635674b38fdc371909742aee427f6c8392f80f9e2511e5","target":"record","created_at":"2026-05-17T23:58:59Z","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":"1bd6cd1a8f1c96f5f8dac3c0238af5bd5068f59bdbdaed9fd29d026ed0cc58d5","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-04T15:59:32Z","title_canon_sha256":"ce00c22972bfa9721d4cba102e09dc4783a76872bebcad6bc73e09ccd8d2df7b"},"schema_version":"1.0","source":{"id":"1604.00924","kind":"arxiv","version":2}},"canonical_sha256":"9556b1cd054b59a3415e38d2550f833491a64cf9f629bd47e1534c0dcf73ae81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9556b1cd054b59a3415e38d2550f833491a64cf9f629bd47e1534c0dcf73ae81","first_computed_at":"2026-05-17T23:58:59.484949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:59.484949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lm69jQwNu3hkdtxQiZyNpmTAjxv1XXPq8n6HCGRWTte/Y3X9h7EPTJuE/R8eL2wLSDjw2TXXWkFOzeRJC9NkCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:59.485469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00924","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c37927bd991279f91635674b38fdc371909742aee427f6c8392f80f9e2511e5","sha256:25fabaf1ecaea7d84f2dba29d264ffc153ae7305f5875cab56e8c76e4b687be5"],"state_sha256":"b620d407f83ec48f0ee4ada300e8c88de99383edbb13f0728005b0aba0b93fc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rxvyTBmqV65H5RtzPFAGFzAdeKbpkOBV9kcAmqGXinWADSup8cQreUYzQTKR455mdKeMv82ouJX/YCflLE96AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:40:01.243563Z","bundle_sha256":"d864b135a750c78be54792c1fdb69a2b8f0605f451283ba0128d2cc92e67537e"}}