{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:V4OLINDFCW36VGQJTEKYIN3HCU","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":"3fb199a8ae57dd5a450c7c2cf824570479d8cbe3583ed5fb8cf403c12e0439c3","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2004-12-22T13:00:29Z","title_canon_sha256":"ab67f7f8584fc1873a1fd23ecfd73d7f66941790aeebfcb630c00b04df317604"},"schema_version":"1.0","source":{"id":"math/0412451","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412451","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412451v3","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412451","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"V4OLINDFCW36","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"V4OLINDFCW36VGQJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"V4OLINDF","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:5a4788900fde46bce1a715bd847306a22340ee222d97a935121b48ace11aaa91","target":"graph","created_at":"2026-05-18T04:08:04Z","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":"We study C*-algebra endomorphims which are special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts. We assign to such endomorphisms a geometrical invariant, representing a cohomological obstruction for them to be special in the usual sense. Moreover, we construct the crossed product of a C*-algebra by the action of the dual of a (nonabelian, noncompact) group of vector bundle automorphisms. These crossed products supply a class of examples for such generalized special endomorphisms.","authors_text":"Ezio Vasselli","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2004-12-22T13:00:29Z","title":"Crossed products by endomorphisms, vector bundles and group duality, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412451","kind":"arxiv","version":3},"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:eeee8a4e6a52cb3cd5fabd98f9464b9b188f23d78d0ad2df61d738830f0940cd","target":"record","created_at":"2026-05-18T04:08:04Z","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":"3fb199a8ae57dd5a450c7c2cf824570479d8cbe3583ed5fb8cf403c12e0439c3","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2004-12-22T13:00:29Z","title_canon_sha256":"ab67f7f8584fc1873a1fd23ecfd73d7f66941790aeebfcb630c00b04df317604"},"schema_version":"1.0","source":{"id":"math/0412451","kind":"arxiv","version":3}},"canonical_sha256":"af1cb4346515b7ea9a09991584376715169a4139c2e0b2dca4d59eac467bb698","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af1cb4346515b7ea9a09991584376715169a4139c2e0b2dca4d59eac467bb698","first_computed_at":"2026-05-18T04:08:04.335626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:04.335626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tuZeK/Wk4aFVoJSYfTbyvjL8ZpAY+F+JBeswA+uXyadrmHK47GYkNS9mUYMuWI5ycvq6o2UHafHVTd21tVSjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:04.336198Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412451","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeee8a4e6a52cb3cd5fabd98f9464b9b188f23d78d0ad2df61d738830f0940cd","sha256:5a4788900fde46bce1a715bd847306a22340ee222d97a935121b48ace11aaa91"],"state_sha256":"e074037c1654daf5afdc7e88501b0b36a8648ac6a0b53be5e0b58519a649122a"}