{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:SXAPUUNDAIOPH3PX5PNQN32EPD","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":"9f162449e1ba6b83a0d1db3ac88e8a133160b8fb6f7f35f81c5f292a2b9dd69e","cross_cats_sorted":["hep-th","math-ph","math.KT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-01-27T07:36:52Z","title_canon_sha256":"e0a90cb3613d27c921caf53952f0649ef7747432d34d2552fdc6d02c8cf5ecc4"},"schema_version":"1.0","source":{"id":"math/0501487","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501487","created_at":"2026-07-05T06:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501487v6","created_at":"2026-07-05T06:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501487","created_at":"2026-07-05T06:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"SXAPUUNDAIOP","created_at":"2026-07-05T06:18:33Z"},{"alias_kind":"pith_short_16","alias_value":"SXAPUUNDAIOPH3PX","created_at":"2026-07-05T06:18:33Z"},{"alias_kind":"pith_short_8","alias_value":"SXAPUUND","created_at":"2026-07-05T06:18:33Z"}],"graph_snapshots":[{"event_id":"sha256:ba766e8ed7c8cb788dded45a43bc71995d097b1ae92b8bba6377c7773f470118","target":"graph","created_at":"2026-07-05T06:18:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0501487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In string theory, the concept of T-duality between two principal T^n-bundles E_1 and E_2 over the same base space B, together with cohomology classes h_1\\in H^3(E_1) and h_2\\in H^3(E_2), has been introduced. One of the main virtues of T-duality is that h_1-twisted K-theory of E_1 is isomorphic to h_2-twisted K-theory of E_2. In this paper, a new, very topological concept of T-duality is introduced. We construct a classifying space for pairs as above with additional \"dualizing data\", with a forgetful map to the classifying space for pairs (also constructed in the paper). On the first classifyin","authors_text":"Philipp Rumpf (Muenster), Thomas Schick (Goettingen), Ulrich Bunke (Goettingen)","cross_cats":["hep-th","math-ph","math.KT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-01-27T07:36:52Z","title":"The topology of T-duality for T^n-bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501487","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:bbe4fca7da8a14c42e8630ca51f23136be8dc8d457f33ef25e7b9aed73691fc8","target":"record","created_at":"2026-07-05T06:18:33Z","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":"9f162449e1ba6b83a0d1db3ac88e8a133160b8fb6f7f35f81c5f292a2b9dd69e","cross_cats_sorted":["hep-th","math-ph","math.KT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2005-01-27T07:36:52Z","title_canon_sha256":"e0a90cb3613d27c921caf53952f0649ef7747432d34d2552fdc6d02c8cf5ecc4"},"schema_version":"1.0","source":{"id":"math/0501487","kind":"arxiv","version":6}},"canonical_sha256":"95c0fa51a3021cf3edf7ebdb06ef4478ef34f69a5474f7b85db0ff7e1de4b6e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95c0fa51a3021cf3edf7ebdb06ef4478ef34f69a5474f7b85db0ff7e1de4b6e1","first_computed_at":"2026-07-05T06:18:33.452848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:18:33.452848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8qit3ml2scHNUOe559OiLXJo5qvCT+Tg049oPz8Dy6GfpvH3RG7f9aK4uHp9x4W2sWD2qooGeixXbwFddlUgCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:18:33.453392Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501487","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbe4fca7da8a14c42e8630ca51f23136be8dc8d457f33ef25e7b9aed73691fc8","sha256:ba766e8ed7c8cb788dded45a43bc71995d097b1ae92b8bba6377c7773f470118"],"state_sha256":"1f927ba9a6ac4de52ced0b20f363ba548f7a091fed138689e255e87d73afd558"}