{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MVEHGWOEWIR3GVHFVRQNNFUIMI","short_pith_number":"pith:MVEHGWOE","canonical_record":{"source":{"id":"1510.03767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-13T16:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"77e3f2494389f00b098c51b645e9bbb2e8b4cc6278ffd77dde6b43cbca556d02","abstract_canon_sha256":"dc5e0804905c143de8804e9c50ca6114f039d60f7cb16b9b950f6ae1728f399b"},"schema_version":"1.0"},"canonical_sha256":"65487359c4b223b354e5ac60d69688622be4f89c0044e9c5fd911afd21dc5649","source":{"kind":"arxiv","id":"1510.03767","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03767","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03767v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03767","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"MVEHGWOEWIR3","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVEHGWOEWIR3GVHF","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVEHGWOE","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MVEHGWOEWIR3GVHFVRQNNFUIMI","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-13T16:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"77e3f2494389f00b098c51b645e9bbb2e8b4cc6278ffd77dde6b43cbca556d02","abstract_canon_sha256":"dc5e0804905c143de8804e9c50ca6114f039d60f7cb16b9b950f6ae1728f399b"},"schema_version":"1.0"},"canonical_sha256":"65487359c4b223b354e5ac60d69688622be4f89c0044e9c5fd911afd21dc5649","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:16.216335Z","signature_b64":"FB4LMaG2JRxb/pxo6kyZLKLw3FTXaMzbA4YDkEJVtVIbzKUJOhnpSHLAWSMT1DPMVoFPDPgATR9EPvIk79UsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65487359c4b223b354e5ac60d69688622be4f89c0044e9c5fd911afd21dc5649","last_reissued_at":"2026-05-18T01:30:16.215781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:16.215781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03767","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":"2026-05-18T01:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AoMUXTWUf12qljZRUANEUI0qbRKYdg9DOlsLSBYrIdIp5L14nvXEM9XsmEri32J/iGF564tDRTt3xw3eg/qRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:06:31.840759Z"},"content_sha256":"7f0d5a88d82a9d94f1b6df6ba8357cc12297886eba554c228eb5be28bdc727d0","schema_version":"1.0","event_id":"sha256:7f0d5a88d82a9d94f1b6df6ba8357cc12297886eba554c228eb5be28bdc727d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MVEHGWOEWIR3GVHFVRQNNFUIMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prime decomposition for the index of a Brauer class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Antieau, Ben Williams","submitted_at":"2015-10-13T16:41:45Z","abstract_excerpt":"We prove that the index of a Brauer class satisfies prime decomposition over a general base scheme. This contrasts with our previous result that there is no general prime decomposition of Azumaya algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03767","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":"2026-05-18T01:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5NBznZnyAU8qJg/xx4VUsU2OY3so4nA11ot0ZzrBq4HUSE0DGAqQ01LN4cQm1JGgNZmhlb5OZbvW2WPkhGBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:06:31.841283Z"},"content_sha256":"e8c396c6b053b3e777d8f25b1bacee94017404206d3b661670f41a830b562b2a","schema_version":"1.0","event_id":"sha256:e8c396c6b053b3e777d8f25b1bacee94017404206d3b661670f41a830b562b2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI/bundle.json","state_url":"https://pith.science/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI/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":"2026-06-07T09:06:31Z","links":{"resolver":"https://pith.science/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI","bundle":"https://pith.science/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI/bundle.json","state":"https://pith.science/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVEHGWOEWIR3GVHFVRQNNFUIMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MVEHGWOEWIR3GVHFVRQNNFUIMI","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":"dc5e0804905c143de8804e9c50ca6114f039d60f7cb16b9b950f6ae1728f399b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-13T16:41:45Z","title_canon_sha256":"77e3f2494389f00b098c51b645e9bbb2e8b4cc6278ffd77dde6b43cbca556d02"},"schema_version":"1.0","source":{"id":"1510.03767","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03767","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03767v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03767","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"MVEHGWOEWIR3","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MVEHGWOEWIR3GVHF","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MVEHGWOE","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:e8c396c6b053b3e777d8f25b1bacee94017404206d3b661670f41a830b562b2a","target":"graph","created_at":"2026-05-18T01:30:16Z","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 prove that the index of a Brauer class satisfies prime decomposition over a general base scheme. This contrasts with our previous result that there is no general prime decomposition of Azumaya algebras.","authors_text":"Benjamin Antieau, Ben Williams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-13T16:41:45Z","title":"Prime decomposition for the index of a Brauer class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03767","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":"sha256:7f0d5a88d82a9d94f1b6df6ba8357cc12297886eba554c228eb5be28bdc727d0","target":"record","created_at":"2026-05-18T01:30:16Z","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":"dc5e0804905c143de8804e9c50ca6114f039d60f7cb16b9b950f6ae1728f399b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-13T16:41:45Z","title_canon_sha256":"77e3f2494389f00b098c51b645e9bbb2e8b4cc6278ffd77dde6b43cbca556d02"},"schema_version":"1.0","source":{"id":"1510.03767","kind":"arxiv","version":1}},"canonical_sha256":"65487359c4b223b354e5ac60d69688622be4f89c0044e9c5fd911afd21dc5649","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65487359c4b223b354e5ac60d69688622be4f89c0044e9c5fd911afd21dc5649","first_computed_at":"2026-05-18T01:30:16.215781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:16.215781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FB4LMaG2JRxb/pxo6kyZLKLw3FTXaMzbA4YDkEJVtVIbzKUJOhnpSHLAWSMT1DPMVoFPDPgATR9EPvIk79UsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:16.216335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03767","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f0d5a88d82a9d94f1b6df6ba8357cc12297886eba554c228eb5be28bdc727d0","sha256:e8c396c6b053b3e777d8f25b1bacee94017404206d3b661670f41a830b562b2a"],"state_sha256":"eeb41d755357052370a4b517444d5ce00099668a04c13d38179c0e90e9a50680"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6z5UBsWXM/Dy2/XMTf/L8lL7d+F+cap9emqMJqHnBTEYb5z/NETHgtE0dhhEpQKrX/gJ3YXextRy/UhOuaj/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:06:31.844102Z","bundle_sha256":"57b0c93615238de04f7ac84191af14786eee2495599c173f447b685d49e96419"}}