{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:I3CQJIRL3LHLO6BBGFPHCNEKII","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":"434a265f09987e61197b44dc164132e4acc420219843dddd9d8e1c0cca1ad642","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-26T16:58:33Z","title_canon_sha256":"9cfc2d8171de2a08c13aec7781730032d0633afebacce2bc83c004af22e4e9f8"},"schema_version":"1.0","source":{"id":"1005.4878","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4878","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4878v6","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4878","created_at":"2026-05-18T02:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"I3CQJIRL3LHL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I3CQJIRL3LHLO6BB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I3CQJIRL","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:ed8dfe92fe31cdeec597d998087e6183f1359b55000a194a7d4f07f74441cd38","target":"graph","created_at":"2026-05-18T02:23:56Z","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 introduce the notion of Azumaya object in general homotopy-theoretic settings. We give a self-contained account of Azumaya objects and Brauer groups in bicategorical contexts, generalizing the Brauer group of a commutative ring. We go on to describe triangulated bicategories and prove a characterization theorem for Azumaya objects therein. This theory applies to give a homotopical Brauer group for derived categories of rings and ring spectra. We show that the homotopical Brauer group of an Eilenberg-Mac Lane spectrum is isomorphic to the homotopical Brauer group of its underlying commutativ","authors_text":"Niles Johnson","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-26T16:58:33Z","title":"Azumaya Objects in Triangulated Bicategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4878","kind":"arxiv","version":6},"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":"sha256:6ba4d878eaa749c4f101f9e235c1508365e87f0acfccb1f769425695165fd669","target":"record","created_at":"2026-05-18T02:23:56Z","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":"434a265f09987e61197b44dc164132e4acc420219843dddd9d8e1c0cca1ad642","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-26T16:58:33Z","title_canon_sha256":"9cfc2d8171de2a08c13aec7781730032d0633afebacce2bc83c004af22e4e9f8"},"schema_version":"1.0","source":{"id":"1005.4878","kind":"arxiv","version":6}},"canonical_sha256":"46c504a22bdaceb77821315e71348a421eba1a409184f6affebe17de533cc7e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46c504a22bdaceb77821315e71348a421eba1a409184f6affebe17de533cc7e8","first_computed_at":"2026-05-18T02:23:56.003890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:56.003890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COxrLjqT867X9qGHe/9uaG/vvekmCz3eBJ8/fEmowoo0P26cNH9+ycJ5X5Um/fhLPYKtSGxYhv+A90R+oQLDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:56.004505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4878","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba4d878eaa749c4f101f9e235c1508365e87f0acfccb1f769425695165fd669","sha256:ed8dfe92fe31cdeec597d998087e6183f1359b55000a194a7d4f07f74441cd38"],"state_sha256":"297a5be19872a5d55a32a9137666d15eaf6da6e44319bd293efeb81e11f2a372"}