{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:2RBP3ITEOFGH4UD6FMW6LPMBDW","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":"8c02288f1b370a847179ed15bd315bffcadda965fa1635726123557411f5cb39","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"funct-an","submitted_at":"1994-10-12T20:48:47Z","title_canon_sha256":"eaa222199a8b19b8fa18a1df288eab4b4e7111706761834d50dae4dea1f9cd8e"},"schema_version":"1.0","source":{"id":"funct-an/9410003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"funct-an/9410003","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"funct-an/9410003v1","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.funct-an/9410003","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"2RBP3ITEOFGH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"2RBP3ITEOFGH4UD6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"2RBP3ITE","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:345b0ae82253e8a67ebc5932c0c87e0ddc74f2b24889da27c6bd5f2fec67c4e9","target":"graph","created_at":"2026-05-18T01:06:48Z","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 characterize when the primitive ideal space of a crossed product $\\acg$ of a \\cs-algebra $A$ by a locally compact abelian group $G$ is a $\\sigma$-trivial $\\ghat G$-space for the dual $\\ghat G$-action.  Specifically, we show that $\\Prim(\\acg)$ is $\\sigma$-trivial if and only if the quasi-orbit space is Hausdorff, the map which assigns to each quasi-orbit $\\w$ a certain subgroup $\\ttg(\\alpha^\\w)$ of the Connes spectrum of the system $(A_\\w,G,\\alpha^\\w)$ is continuous, and there is a generalized Green twisting map for $(A,G,\\alpha)$.  Our proof requires a substantial generalization of a theore","authors_text":"Dana Williams, Siegfried Echterhoff","cross_cats":["math.OA"],"headline":"","license":"","primary_cat":"funct-an","submitted_at":"1994-10-12T20:48:47Z","title":"Crossed products whose primitive ideal spaces are generalized trivial $\\widehat G$-bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9410003","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:da0b7f14c1150d8337c390b4a214e4409ec77127b14ef14bac8af7bd1e4d837c","target":"record","created_at":"2026-05-18T01:06:48Z","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":"8c02288f1b370a847179ed15bd315bffcadda965fa1635726123557411f5cb39","cross_cats_sorted":["math.OA"],"license":"","primary_cat":"funct-an","submitted_at":"1994-10-12T20:48:47Z","title_canon_sha256":"eaa222199a8b19b8fa18a1df288eab4b4e7111706761834d50dae4dea1f9cd8e"},"schema_version":"1.0","source":{"id":"funct-an/9410003","kind":"arxiv","version":1}},"canonical_sha256":"d442fda264714c7e507e2b2de5bd811db7776fd9434ef374c633a1d05fa36681","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d442fda264714c7e507e2b2de5bd811db7776fd9434ef374c633a1d05fa36681","first_computed_at":"2026-05-18T01:06:48.329599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:48.329599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fSYxl2IhXzMlKYM19IDVgKz4muWUKjvCJrRof1k3igWL3Zs6NgKU3ncMUWiQ7XDxL08gKd0qVTAtAx80AHONDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:48.330235Z","signed_message":"canonical_sha256_bytes"},"source_id":"funct-an/9410003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da0b7f14c1150d8337c390b4a214e4409ec77127b14ef14bac8af7bd1e4d837c","sha256:345b0ae82253e8a67ebc5932c0c87e0ddc74f2b24889da27c6bd5f2fec67c4e9"],"state_sha256":"72b7dcf1fc7ebfb1c8d28b34472ceaaf21215a7d2c3c1e0529adedc64540b593"}