{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4PBDKCWRJSBOXU46QAM3JOQ3OH","short_pith_number":"pith:4PBDKCWR","canonical_record":{"source":{"id":"1603.00969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-03T04:26:42Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"0d4f8d65975bc4450e499d0d21ada674fc7605b310a0bcf78e84aae3009fd3b4","abstract_canon_sha256":"2dd5e71945a6dd9915ae84fb1899df9f969540fd0406c0c53f943cb3f908ad88"},"schema_version":"1.0"},"canonical_sha256":"e3c2350ad14c82ebd39e8019b4ba1b71dc9c4bc38bc3e3f2831790a69a042467","source":{"kind":"arxiv","id":"1603.00969","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00969","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00969v2","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00969","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"4PBDKCWRJSBO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4PBDKCWRJSBOXU46","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4PBDKCWR","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4PBDKCWRJSBOXU46QAM3JOQ3OH","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-03T04:26:42Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"0d4f8d65975bc4450e499d0d21ada674fc7605b310a0bcf78e84aae3009fd3b4","abstract_canon_sha256":"2dd5e71945a6dd9915ae84fb1899df9f969540fd0406c0c53f943cb3f908ad88"},"schema_version":"1.0"},"canonical_sha256":"e3c2350ad14c82ebd39e8019b4ba1b71dc9c4bc38bc3e3f2831790a69a042467","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:10.554909Z","signature_b64":"fOUPXZ6mI+Yn/B5jr1K+OjxVBaV5v0+qL/o0hQB5tY5OjAugzYOTWgGXuoKg+M+fjlxgrOcCjpioYXhNOWOeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3c2350ad14c82ebd39e8019b4ba1b71dc9c4bc38bc3e3f2831790a69a042467","last_reissued_at":"2026-05-18T00:24:10.554382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:10.554382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00969","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxRxBvho03ljg7YX4+KZjUEHrM+m+yXgJd1w6Y3JDYCmJSNmi3pSun3V0cQTMauPdmhos81JTuy6XwbxcbUfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:24:49.488918Z"},"content_sha256":"e63a09e3d308f617886fb2591b6e348d8711b31e7012f10225dd2a812f2bf131","schema_version":"1.0","event_id":"sha256:e63a09e3d308f617886fb2591b6e348d8711b31e7012f10225dd2a812f2bf131"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4PBDKCWRJSBOXU46QAM3JOQ3OH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group dualities, T-dualities, and twisted K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"hep-th","authors_text":"Jonathan Rosenberg, Varghese Mathai","submitted_at":"2016-03-03T04:26:42Z","abstract_excerpt":"This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on $H^3$ induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00969","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W/r0ynj3sX2o4T2QjOiDduhEcKKKHgg5Q0RYrslDpCSDw20ixf6lzDkWs8Lr6MjWbyI9EKlPSavLzEhkc8l/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:24:49.489265Z"},"content_sha256":"7fcca8229526290c30a5bfd7c1064e4a690064c2235f539886174b7566b38842","schema_version":"1.0","event_id":"sha256:7fcca8229526290c30a5bfd7c1064e4a690064c2235f539886174b7566b38842"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH/bundle.json","state_url":"https://pith.science/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T15:24:49Z","links":{"resolver":"https://pith.science/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH","bundle":"https://pith.science/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH/bundle.json","state":"https://pith.science/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PBDKCWRJSBOXU46QAM3JOQ3OH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4PBDKCWRJSBOXU46QAM3JOQ3OH","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":"2dd5e71945a6dd9915ae84fb1899df9f969540fd0406c0c53f943cb3f908ad88","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-03T04:26:42Z","title_canon_sha256":"0d4f8d65975bc4450e499d0d21ada674fc7605b310a0bcf78e84aae3009fd3b4"},"schema_version":"1.0","source":{"id":"1603.00969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00969","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00969v2","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00969","created_at":"2026-05-18T00:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"4PBDKCWRJSBO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4PBDKCWRJSBOXU46","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4PBDKCWR","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:7fcca8229526290c30a5bfd7c1064e4a690064c2235f539886174b7566b38842","target":"graph","created_at":"2026-05-18T00:24:10Z","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":"This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on $H^3$ induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the","authors_text":"Jonathan Rosenberg, Varghese Mathai","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-03T04:26:42Z","title":"Group dualities, T-dualities, and twisted K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00969","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:e63a09e3d308f617886fb2591b6e348d8711b31e7012f10225dd2a812f2bf131","target":"record","created_at":"2026-05-18T00:24:10Z","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":"2dd5e71945a6dd9915ae84fb1899df9f969540fd0406c0c53f943cb3f908ad88","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-03T04:26:42Z","title_canon_sha256":"0d4f8d65975bc4450e499d0d21ada674fc7605b310a0bcf78e84aae3009fd3b4"},"schema_version":"1.0","source":{"id":"1603.00969","kind":"arxiv","version":2}},"canonical_sha256":"e3c2350ad14c82ebd39e8019b4ba1b71dc9c4bc38bc3e3f2831790a69a042467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3c2350ad14c82ebd39e8019b4ba1b71dc9c4bc38bc3e3f2831790a69a042467","first_computed_at":"2026-05-18T00:24:10.554382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:10.554382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fOUPXZ6mI+Yn/B5jr1K+OjxVBaV5v0+qL/o0hQB5tY5OjAugzYOTWgGXuoKg+M+fjlxgrOcCjpioYXhNOWOeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:10.554909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e63a09e3d308f617886fb2591b6e348d8711b31e7012f10225dd2a812f2bf131","sha256:7fcca8229526290c30a5bfd7c1064e4a690064c2235f539886174b7566b38842"],"state_sha256":"18a16ceefa0829babca44a87b7c69688811f3510af9470501c20a0502602f3a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9nJMgOOO7KaOBuwvR0wat8u6Sr80f5bSiSofC9tJ/GymXyXzgDoePkpnKUreKQOvndrzUGl1PGvCjvA5YO2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:24:49.491219Z","bundle_sha256":"259a01fe809a2ee7a6b5bc13d806389d537c050b887f39af1d71db9c1418b692"}}