{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CIU5DOPAV32OBZHJHB4HGP56E3","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":"3e4d3f3527e6de222ee058b83be8f1377ce5b927c56fff353928171e20ddfa99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-15T08:47:46Z","title_canon_sha256":"2e7d1439e5930583c3c63590c502b3c969ccc8e0060dafbe94cbb8e493013787"},"schema_version":"1.0","source":{"id":"1403.3770","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3770","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3770v2","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3770","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"CIU5DOPAV32O","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CIU5DOPAV32OBZHJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CIU5DOPA","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:7cd59470a146196c21351ff9945f324fc59a076eb5f2b38800497b5942e2d081","target":"graph","created_at":"2026-05-18T02:45:40Z","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 show that in locally-ringed connected topoi the primes dividing the period and index of a Brauer class coincide. The result applies in particular to Brauer classes on connected schemes, algebraic stacks, topological spaces and to the projective representation theory of profinite groups.","authors_text":"Benjamin Antieau, Ben Williams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-15T08:47:46Z","title":"The prime divisors of the period and index of a Brauer class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3770","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":"sha256:04593c20cc3f39ef9f326ccd61f587002cf9d8792fe2f87ff39a677c6ce075ff","target":"record","created_at":"2026-05-18T02:45:40Z","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":"3e4d3f3527e6de222ee058b83be8f1377ce5b927c56fff353928171e20ddfa99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-15T08:47:46Z","title_canon_sha256":"2e7d1439e5930583c3c63590c502b3c969ccc8e0060dafbe94cbb8e493013787"},"schema_version":"1.0","source":{"id":"1403.3770","kind":"arxiv","version":2}},"canonical_sha256":"1229d1b9e0aef4e0e4e93878733fbe26e9cbe30e1127aaffec507070a3a7902f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1229d1b9e0aef4e0e4e93878733fbe26e9cbe30e1127aaffec507070a3a7902f","first_computed_at":"2026-05-18T02:45:40.880410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:40.880410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MBEe//VK/2n3J6Xmtek9EVoxCjqQlL5bDNbqSzT4dIjCJqYl9hWqg4Y0/aDKulytbAD2wFOgN/7aYa1g2AssAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:40.881135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3770","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04593c20cc3f39ef9f326ccd61f587002cf9d8792fe2f87ff39a677c6ce075ff","sha256:7cd59470a146196c21351ff9945f324fc59a076eb5f2b38800497b5942e2d081"],"state_sha256":"c7894e6ee75421c98e23289a29985f041e624616e1c1953d589ad2d7195c3d66"}