{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LK6BUQLQ7BAPKZU3MV3WALUQH3","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":"799b582e32a2938bd02003ec03493da78d6dcfeed918b5a9cf2e2d3845029380","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-25T13:21:32Z","title_canon_sha256":"d1634cb49f3680eaadc27e1cfd3eb95bbb65bbf8d061c63688271d08406b7d41"},"schema_version":"1.0","source":{"id":"1406.6563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6563","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6563v2","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6563","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"LK6BUQLQ7BAP","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LK6BUQLQ7BAPKZU3","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LK6BUQLQ","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:fcea308d678a216cbff057f46d5c66d4b0c2c319bfdff5244123a52ca1e6b6b5","target":"graph","created_at":"2026-05-18T00:40:52Z","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":"A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for $\\Z^n$. Our theory also includes the bundles considered by Mathai and Rosenberg in their work on non-commutative T-duals, in which they allow twisted group algebras on one side of the duality.","authors_text":"Ansgar Schneider, Siegfried Echterhoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-25T13:21:32Z","title":"Non-Commutative T-Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6563","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":"sha256:16ec304195dbd440610df3bea7565c02fba16925c7dd333e0e36fb673568dd40","target":"record","created_at":"2026-05-18T00:40:52Z","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":"799b582e32a2938bd02003ec03493da78d6dcfeed918b5a9cf2e2d3845029380","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-25T13:21:32Z","title_canon_sha256":"d1634cb49f3680eaadc27e1cfd3eb95bbb65bbf8d061c63688271d08406b7d41"},"schema_version":"1.0","source":{"id":"1406.6563","kind":"arxiv","version":2}},"canonical_sha256":"5abc1a4170f840f5669b6577602e903ee159a85b4e46a87aa52b7dfb2feb4d38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5abc1a4170f840f5669b6577602e903ee159a85b4e46a87aa52b7dfb2feb4d38","first_computed_at":"2026-05-18T00:40:52.103261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:52.103261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nU1C/lGd58hybvBqWUDE94Tc9qNkHUCUyiZLG305rPyEE04qMH7WbBzWyJkohM1iIDZUwWrMcQzTa989eHY6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:52.103932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16ec304195dbd440610df3bea7565c02fba16925c7dd333e0e36fb673568dd40","sha256:fcea308d678a216cbff057f46d5c66d4b0c2c319bfdff5244123a52ca1e6b6b5"],"state_sha256":"1ca01ed5068c4c07816520f555cdd24ca0547308e24ec40729f48de3d11687ce"}