{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:KC7VKT5OUKXLISHVPCT5PMQCSW","short_pith_number":"pith:KC7VKT5O","canonical_record":{"source":{"id":"math/9905049","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-05-09T22:30:13Z","cross_cats_sorted":[],"title_canon_sha256":"87ee29eb7d03eb77306482b8000efbb9c609935ceb30ad435e20c1c861227f08","abstract_canon_sha256":"0c626853c330eabd2e34c9e845b3c4febe5241f1cc9ea75c66c89c4857aba649"},"schema_version":"1.0"},"canonical_sha256":"50bf554faea2aeb448f578a7d7b202958b8c1f81ec9fe9aa899222267c7f5dfb","source":{"kind":"arxiv","id":"math/9905049","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9905049","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/9905049v3","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9905049","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"KC7VKT5OUKXL","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"KC7VKT5OUKXLISHV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"KC7VKT5O","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:KC7VKT5OUKXLISHVPCT5PMQCSW","target":"record","payload":{"canonical_record":{"source":{"id":"math/9905049","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-05-09T22:30:13Z","cross_cats_sorted":[],"title_canon_sha256":"87ee29eb7d03eb77306482b8000efbb9c609935ceb30ad435e20c1c861227f08","abstract_canon_sha256":"0c626853c330eabd2e34c9e845b3c4febe5241f1cc9ea75c66c89c4857aba649"},"schema_version":"1.0"},"canonical_sha256":"50bf554faea2aeb448f578a7d7b202958b8c1f81ec9fe9aa899222267c7f5dfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:33.071952Z","signature_b64":"OkY6WHsEQXcsIyVHUCKiqzcfCkPXF7WHtM4zsT3ZFuvYakq/li2uQmGU597uRm2T4sjET6PrLixwE5bxWJzsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50bf554faea2aeb448f578a7d7b202958b8c1f81ec9fe9aa899222267c7f5dfb","last_reissued_at":"2026-05-18T01:05:33.071279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:33.071279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9905049","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yG3cugW/T/SLyKzTenee2OxhFtw/OFn2ENNoj7bEyPD6ZIrFKl3ahW5lBgTf5wHOlKRNzzrGMYBMGIuTQjuXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:14:20.556166Z"},"content_sha256":"670eb815e4341cfd1293b9c32655b385ed0d2747726a19f8f36b601a35148364","schema_version":"1.0","event_id":"sha256:670eb815e4341cfd1293b9c32655b385ed0d2747726a19f8f36b601a35148364"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:KC7VKT5OUKXLISHVPCT5PMQCSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brauer groups and quotient stacks","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Kresch, A. Vistoli, B. Hassett, D. Edidin","submitted_at":"1999-05-09T22:30:13Z","abstract_excerpt":"A natural question is to determine which algebraic stacks are qoutient stacks. In this paper we give some partial answers and relate it to the old question of whether, for a scheme X, the natural map from the Brauer goup (equivalence classes of Azumaya algebras) to the cohomological Brauer group (the torsion subgroup of $H^2(X,{\\mathbb G}_m)$ is surjective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905049","kind":"arxiv","version":3},"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":"2026-05-18T01:05:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EA/M5bPh7/B30jOA+ORPaSIQPfzSosgftx3GkDX7a3w42poK69TPyh/iBtnNyYSfbejrTZFBI5o6avAc6z/sBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:14:20.556534Z"},"content_sha256":"4f506118a1947851c2c61cb782cfc80ad6dbede55edd179cc2b5b79c291d860c","schema_version":"1.0","event_id":"sha256:4f506118a1947851c2c61cb782cfc80ad6dbede55edd179cc2b5b79c291d860c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KC7VKT5OUKXLISHVPCT5PMQCSW/bundle.json","state_url":"https://pith.science/pith/KC7VKT5OUKXLISHVPCT5PMQCSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KC7VKT5OUKXLISHVPCT5PMQCSW/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":"2026-06-05T15:14:20Z","links":{"resolver":"https://pith.science/pith/KC7VKT5OUKXLISHVPCT5PMQCSW","bundle":"https://pith.science/pith/KC7VKT5OUKXLISHVPCT5PMQCSW/bundle.json","state":"https://pith.science/pith/KC7VKT5OUKXLISHVPCT5PMQCSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KC7VKT5OUKXLISHVPCT5PMQCSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:KC7VKT5OUKXLISHVPCT5PMQCSW","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":"0c626853c330eabd2e34c9e845b3c4febe5241f1cc9ea75c66c89c4857aba649","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-05-09T22:30:13Z","title_canon_sha256":"87ee29eb7d03eb77306482b8000efbb9c609935ceb30ad435e20c1c861227f08"},"schema_version":"1.0","source":{"id":"math/9905049","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9905049","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/9905049v3","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9905049","created_at":"2026-05-18T01:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"KC7VKT5OUKXL","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"KC7VKT5OUKXLISHV","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"KC7VKT5O","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:4f506118a1947851c2c61cb782cfc80ad6dbede55edd179cc2b5b79c291d860c","target":"graph","created_at":"2026-05-18T01:05:33Z","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":"A natural question is to determine which algebraic stacks are qoutient stacks. In this paper we give some partial answers and relate it to the old question of whether, for a scheme X, the natural map from the Brauer goup (equivalence classes of Azumaya algebras) to the cohomological Brauer group (the torsion subgroup of $H^2(X,{\\mathbb G}_m)$ is surjective.","authors_text":"A. Kresch, A. Vistoli, B. Hassett, D. Edidin","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1999-05-09T22:30:13Z","title":"Brauer groups and quotient stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905049","kind":"arxiv","version":3},"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":"sha256:670eb815e4341cfd1293b9c32655b385ed0d2747726a19f8f36b601a35148364","target":"record","created_at":"2026-05-18T01:05:33Z","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":"0c626853c330eabd2e34c9e845b3c4febe5241f1cc9ea75c66c89c4857aba649","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"1999-05-09T22:30:13Z","title_canon_sha256":"87ee29eb7d03eb77306482b8000efbb9c609935ceb30ad435e20c1c861227f08"},"schema_version":"1.0","source":{"id":"math/9905049","kind":"arxiv","version":3}},"canonical_sha256":"50bf554faea2aeb448f578a7d7b202958b8c1f81ec9fe9aa899222267c7f5dfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50bf554faea2aeb448f578a7d7b202958b8c1f81ec9fe9aa899222267c7f5dfb","first_computed_at":"2026-05-18T01:05:33.071279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:33.071279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OkY6WHsEQXcsIyVHUCKiqzcfCkPXF7WHtM4zsT3ZFuvYakq/li2uQmGU597uRm2T4sjET6PrLixwE5bxWJzsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:33.071952Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9905049","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:670eb815e4341cfd1293b9c32655b385ed0d2747726a19f8f36b601a35148364","sha256:4f506118a1947851c2c61cb782cfc80ad6dbede55edd179cc2b5b79c291d860c"],"state_sha256":"696cfe97ca3ce2008f160601120618d7067e8e0d666e253c475483d12835a221"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TfFZsNayga+LwffGmbEwbo2+ykagVeZoPOdkj2ORf1rH3/78cdhXnOdU0suNRDlMtElL1l6VYZgKrSoD0DHAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:14:20.558497Z","bundle_sha256":"d5aa60683bb4867d45dd35034c8841def028f06464ec396904752d11b23d2935"}}