{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KTFL7IDTJZGIDMCI4277CUYA63","short_pith_number":"pith:KTFL7IDT","canonical_record":{"source":{"id":"1505.00754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T18:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"037de0c0072f822823c980978892bdaf408cba4d67deda84bc5c25647454c98b","abstract_canon_sha256":"3e7984fc88272ece3ec1a1df6923e4aaa7e9adab21769c053101d21fb5d2a63a"},"schema_version":"1.0"},"canonical_sha256":"54cabfa0734e4c81b048e6bff15300f6c882b451fc561d61458c34e84ac1a31e","source":{"kind":"arxiv","id":"1505.00754","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00754","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00754v1","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00754","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"KTFL7IDTJZGI","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KTFL7IDTJZGIDMCI","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KTFL7IDT","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KTFL7IDTJZGIDMCI4277CUYA63","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T18:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"037de0c0072f822823c980978892bdaf408cba4d67deda84bc5c25647454c98b","abstract_canon_sha256":"3e7984fc88272ece3ec1a1df6923e4aaa7e9adab21769c053101d21fb5d2a63a"},"schema_version":"1.0"},"canonical_sha256":"54cabfa0734e4c81b048e6bff15300f6c882b451fc561d61458c34e84ac1a31e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:01.914992Z","signature_b64":"gzG1y3tc5gca4CNAO8pj9MoF3zXzXHSro8tqzh5olhtWB+AbvcST/JBCeemWtfI4J4d1pUQRaO0qjdv0v+U8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54cabfa0734e4c81b048e6bff15300f6c882b451fc561d61458c34e84ac1a31e","last_reissued_at":"2026-05-18T02:17:01.914235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:01.914235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00754","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":"2026-05-18T02:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mN5pM7ZowvRvrheSIoekULy/8H4EKNuk5V1tgPJP12qw+naAhfzmKL0xJ8flyivsuBdZPtEdHNxODqowcOOMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:51:44.891222Z"},"content_sha256":"2a98f5857e1900d9c57a397a58002096759efe528e7bb891e600b66ad567f51c","schema_version":"1.0","event_id":"sha256:2a98f5857e1900d9c57a397a58002096759efe528e7bb891e600b66ad567f51c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KTFL7IDTJZGIDMCI4277CUYA63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Luna's fundamental lemma for diagonalizable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Abramovich, Michael Temkin","submitted_at":"2015-05-04T18:59:34Z","abstract_excerpt":"We study relatively affine actions of a diagonalizable group $G$ on locally noetherian schemes. In particular, we generalize Luna's fundamental lemma when applied to a diagonalizable group: we obtain criteria for a $G$-equivariant morphism $f: X'\\to X$ to be $strongly\\ equivariant$, namely the base change of the morphism $f/\\!/G$ of quotient schemes, and establish descent criteria for $f/\\!/G$ to be an open embedding, \\'etale, smooth, regular, syntomic, or lci."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00754","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":"2026-05-18T02:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54TI2AtDgDViiR/dv31iZY6PSyqbBrJAonvsFyvVby2VB70CKgxyvxgMT4fOkQWQ0yR5h/riTiXUJi/cRm7XDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:51:44.891825Z"},"content_sha256":"bb669274d2de0d6408c9c3135d7a8d00d5c36ba4141d54b9df2286b1e0d76056","schema_version":"1.0","event_id":"sha256:bb669274d2de0d6408c9c3135d7a8d00d5c36ba4141d54b9df2286b1e0d76056"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTFL7IDTJZGIDMCI4277CUYA63/bundle.json","state_url":"https://pith.science/pith/KTFL7IDTJZGIDMCI4277CUYA63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTFL7IDTJZGIDMCI4277CUYA63/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":"2026-05-27T11:51:44Z","links":{"resolver":"https://pith.science/pith/KTFL7IDTJZGIDMCI4277CUYA63","bundle":"https://pith.science/pith/KTFL7IDTJZGIDMCI4277CUYA63/bundle.json","state":"https://pith.science/pith/KTFL7IDTJZGIDMCI4277CUYA63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTFL7IDTJZGIDMCI4277CUYA63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KTFL7IDTJZGIDMCI4277CUYA63","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":"3e7984fc88272ece3ec1a1df6923e4aaa7e9adab21769c053101d21fb5d2a63a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T18:59:34Z","title_canon_sha256":"037de0c0072f822823c980978892bdaf408cba4d67deda84bc5c25647454c98b"},"schema_version":"1.0","source":{"id":"1505.00754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00754","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00754v1","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00754","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"KTFL7IDTJZGI","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KTFL7IDTJZGIDMCI","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KTFL7IDT","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:bb669274d2de0d6408c9c3135d7a8d00d5c36ba4141d54b9df2286b1e0d76056","target":"graph","created_at":"2026-05-18T02:17:01Z","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 relatively affine actions of a diagonalizable group $G$ on locally noetherian schemes. In particular, we generalize Luna's fundamental lemma when applied to a diagonalizable group: we obtain criteria for a $G$-equivariant morphism $f: X'\\to X$ to be $strongly\\ equivariant$, namely the base change of the morphism $f/\\!/G$ of quotient schemes, and establish descent criteria for $f/\\!/G$ to be an open embedding, \\'etale, smooth, regular, syntomic, or lci.","authors_text":"Dan Abramovich, Michael Temkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T18:59:34Z","title":"Luna's fundamental lemma for diagonalizable groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00754","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":"sha256:2a98f5857e1900d9c57a397a58002096759efe528e7bb891e600b66ad567f51c","target":"record","created_at":"2026-05-18T02:17:01Z","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":"3e7984fc88272ece3ec1a1df6923e4aaa7e9adab21769c053101d21fb5d2a63a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-04T18:59:34Z","title_canon_sha256":"037de0c0072f822823c980978892bdaf408cba4d67deda84bc5c25647454c98b"},"schema_version":"1.0","source":{"id":"1505.00754","kind":"arxiv","version":1}},"canonical_sha256":"54cabfa0734e4c81b048e6bff15300f6c882b451fc561d61458c34e84ac1a31e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54cabfa0734e4c81b048e6bff15300f6c882b451fc561d61458c34e84ac1a31e","first_computed_at":"2026-05-18T02:17:01.914235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:01.914235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gzG1y3tc5gca4CNAO8pj9MoF3zXzXHSro8tqzh5olhtWB+AbvcST/JBCeemWtfI4J4d1pUQRaO0qjdv0v+U8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:01.914992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a98f5857e1900d9c57a397a58002096759efe528e7bb891e600b66ad567f51c","sha256:bb669274d2de0d6408c9c3135d7a8d00d5c36ba4141d54b9df2286b1e0d76056"],"state_sha256":"670038f4adda3b2018805f3189b070c53ed7917a294549dff87ab6b301d45f8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Ikfw/GpIPSzIhDOJwLYdoR6b1tMHW6e8gVKwK7PWrRiIUcqjlNhC8EYtEYmp6+WCFS/QduMsqThr2z4WszwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:51:44.894858Z","bundle_sha256":"c84f1b0c54f91053c7369b95c0940872a7c3e28b4946a6c2311c46e3bf58b68e"}}