{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6XBHJ42SFEZCI5YCI36OXDMDWW","short_pith_number":"pith:6XBHJ42S","canonical_record":{"source":{"id":"1312.3103","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-11T10:07:23Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"21044e5f79d6c4012f467c7fc5c016eebcfa8ff2fc871440c348bdc4646f30e0","abstract_canon_sha256":"2730f0f7cd106b4ae293d85ddc8afcbbd91fdba86f018b5540fbf8f4a19cd46c"},"schema_version":"1.0"},"canonical_sha256":"f5c274f352293224770246fceb8d83b5b6a250bdb37664bf5f251d4f717b4e06","source":{"kind":"arxiv","id":"1312.3103","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3103","created_at":"2026-05-18T00:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3103v4","created_at":"2026-05-18T00:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3103","created_at":"2026-05-18T00:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"6XBHJ42SFEZC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6XBHJ42SFEZCI5YC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6XBHJ42S","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6XBHJ42SFEZCI5YCI36OXDMDWW","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3103","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-11T10:07:23Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"21044e5f79d6c4012f467c7fc5c016eebcfa8ff2fc871440c348bdc4646f30e0","abstract_canon_sha256":"2730f0f7cd106b4ae293d85ddc8afcbbd91fdba86f018b5540fbf8f4a19cd46c"},"schema_version":"1.0"},"canonical_sha256":"f5c274f352293224770246fceb8d83b5b6a250bdb37664bf5f251d4f717b4e06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:04.280235Z","signature_b64":"WFSIyqMQrtI/5FaOqIIUSwOC+5bl+RzDdb0+6s3olGsT3K3nbh31zZdab9GYocQsAwwJcFQF+mvqSmCxztzcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5c274f352293224770246fceb8d83b5b6a250bdb37664bf5f251d4f717b4e06","last_reissued_at":"2026-05-18T00:36:04.279584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:04.279584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3103","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WE8T2+6cAi+KKxplDkwwLr9N9GzpM2zQW+aOBHcSScgvllp4lFfUZQAj/cC0cKEZOVsjcDh/r7h4VxSJmWy5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:55:19.825831Z"},"content_sha256":"5db73c77f6817f9617c6805d9da3493f067f980685db70850bf4681fb6a5ebe7","schema_version":"1.0","event_id":"sha256:5db73c77f6817f9617c6805d9da3493f067f980685db70850bf4681fb6a5ebe7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6XBHJ42SFEZCI5YCI36OXDMDWW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groupe de Brauer non ramifi\\'e alg\\'ebrique des espaces homog\\`enes (The unramified algebraic Brauer group of homogeneous spaces)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Giancarlo Lucchini Arteche","submitted_at":"2013-12-11T10:07:23Z","abstract_excerpt":"Using a reduction of the Galois cohomology of a linear algebraic group $G$ to that of a certain finite subquotient, we give different formulas allowing the calculation of the unramified algebraic Brauer group of a homogeneous space $V=G\\backslash G'$ with $G'$ semisimple and simply connected, both over a finite field and over an arbitrary field of characteristic $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3103","kind":"arxiv","version":4},"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":"2026-05-18T00:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNDOjuuRJR3sO3uAgpG5+wHzEO3YUaZy03dQPVwSFyUjDxLKSu28tySsy38olOEAJnwWW7+jGIPGym+2WvIaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:55:19.826180Z"},"content_sha256":"2e390c97ce8b8dae74dfd696e87769ddcc8d20f9596e4e215ea13ecb07de317b","schema_version":"1.0","event_id":"sha256:2e390c97ce8b8dae74dfd696e87769ddcc8d20f9596e4e215ea13ecb07de317b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XBHJ42SFEZCI5YCI36OXDMDWW/bundle.json","state_url":"https://pith.science/pith/6XBHJ42SFEZCI5YCI36OXDMDWW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XBHJ42SFEZCI5YCI36OXDMDWW/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":"2026-06-22T21:55:19Z","links":{"resolver":"https://pith.science/pith/6XBHJ42SFEZCI5YCI36OXDMDWW","bundle":"https://pith.science/pith/6XBHJ42SFEZCI5YCI36OXDMDWW/bundle.json","state":"https://pith.science/pith/6XBHJ42SFEZCI5YCI36OXDMDWW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XBHJ42SFEZCI5YCI36OXDMDWW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6XBHJ42SFEZCI5YCI36OXDMDWW","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":"2730f0f7cd106b4ae293d85ddc8afcbbd91fdba86f018b5540fbf8f4a19cd46c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-11T10:07:23Z","title_canon_sha256":"21044e5f79d6c4012f467c7fc5c016eebcfa8ff2fc871440c348bdc4646f30e0"},"schema_version":"1.0","source":{"id":"1312.3103","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3103","created_at":"2026-05-18T00:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3103v4","created_at":"2026-05-18T00:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3103","created_at":"2026-05-18T00:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"6XBHJ42SFEZC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6XBHJ42SFEZCI5YC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6XBHJ42S","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:2e390c97ce8b8dae74dfd696e87769ddcc8d20f9596e4e215ea13ecb07de317b","target":"graph","created_at":"2026-05-18T00:36:04Z","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":"Using a reduction of the Galois cohomology of a linear algebraic group $G$ to that of a certain finite subquotient, we give different formulas allowing the calculation of the unramified algebraic Brauer group of a homogeneous space $V=G\\backslash G'$ with $G'$ semisimple and simply connected, both over a finite field and over an arbitrary field of characteristic $0$.","authors_text":"Giancarlo Lucchini Arteche","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-11T10:07:23Z","title":"Groupe de Brauer non ramifi\\'e alg\\'ebrique des espaces homog\\`enes (The unramified algebraic Brauer group of homogeneous spaces)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3103","kind":"arxiv","version":4},"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":"sha256:5db73c77f6817f9617c6805d9da3493f067f980685db70850bf4681fb6a5ebe7","target":"record","created_at":"2026-05-18T00:36:04Z","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":"2730f0f7cd106b4ae293d85ddc8afcbbd91fdba86f018b5540fbf8f4a19cd46c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-11T10:07:23Z","title_canon_sha256":"21044e5f79d6c4012f467c7fc5c016eebcfa8ff2fc871440c348bdc4646f30e0"},"schema_version":"1.0","source":{"id":"1312.3103","kind":"arxiv","version":4}},"canonical_sha256":"f5c274f352293224770246fceb8d83b5b6a250bdb37664bf5f251d4f717b4e06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5c274f352293224770246fceb8d83b5b6a250bdb37664bf5f251d4f717b4e06","first_computed_at":"2026-05-18T00:36:04.279584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:04.279584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFSIyqMQrtI/5FaOqIIUSwOC+5bl+RzDdb0+6s3olGsT3K3nbh31zZdab9GYocQsAwwJcFQF+mvqSmCxztzcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:04.280235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3103","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5db73c77f6817f9617c6805d9da3493f067f980685db70850bf4681fb6a5ebe7","sha256:2e390c97ce8b8dae74dfd696e87769ddcc8d20f9596e4e215ea13ecb07de317b"],"state_sha256":"f4231b4408b803c3f2865bd46d5e50a91adffb054c8e93bad0e0197983ef815b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q4uPr5FLKngYk/NMt/7bCGoZJRXntF2zyashZ35xGnqZW4pNpzxDCCbC/W7JFbYcYQyb6iHkOKx/Dztj1uLdDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:55:19.828130Z","bundle_sha256":"e529293c32baa0697d9fe25641ec7b65a994e115f3007d4a3bde3dc9cd0352ed"}}