{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LSVQA4XEV2PCCHKECP2VAILNKK","short_pith_number":"pith:LSVQA4XE","canonical_record":{"source":{"id":"1711.10281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-11-28T13:26:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2a1301e2e72cc94d3e7222253814f9bbe3395dbc9e843f1475cf29952a89f9c0","abstract_canon_sha256":"e549db60620635141cb74797326e10aaaf0b71f5eb0fc40daa1c78122de350fa"},"schema_version":"1.0"},"canonical_sha256":"5cab0072e4ae9e211d4413f550216d5299bf99ea90bb7b543ad5849416972483","source":{"kind":"arxiv","id":"1711.10281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10281","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10281v1","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10281","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"LSVQA4XEV2PC","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LSVQA4XEV2PCCHKE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LSVQA4XE","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LSVQA4XEV2PCCHKECP2VAILNKK","target":"record","payload":{"canonical_record":{"source":{"id":"1711.10281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-11-28T13:26:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2a1301e2e72cc94d3e7222253814f9bbe3395dbc9e843f1475cf29952a89f9c0","abstract_canon_sha256":"e549db60620635141cb74797326e10aaaf0b71f5eb0fc40daa1c78122de350fa"},"schema_version":"1.0"},"canonical_sha256":"5cab0072e4ae9e211d4413f550216d5299bf99ea90bb7b543ad5849416972483","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:22.744106Z","signature_b64":"roPVmQXyARCLFlCzpXoMHrb6ACToA1JMi98jaO94vlVYgjrr13AuCZCg/8lgc3cOYtEOimb1h7uE184Rz65ICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cab0072e4ae9e211d4413f550216d5299bf99ea90bb7b543ad5849416972483","last_reissued_at":"2026-05-18T00:29:22.743568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:22.743568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.10281","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZXj8GfMCrll945jcdXBc5nYIw1EK7K8eTQZc1pWmGpuj/HJNCI2KsOd6/5Er0QYifXVSICR2kQAnyFrEplZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:58:26.097149Z"},"content_sha256":"dd7c83a887521ddebbd7a83040a8585e5c1f51191f2fce83f47b7e3385f7c21c","schema_version":"1.0","event_id":"sha256:dd7c83a887521ddebbd7a83040a8585e5c1f51191f2fce83f47b7e3385f7c21c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LSVQA4XEV2PCCHKECP2VAILNKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincar\\'e duality and Langlands duality for extended affine Weyl groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.KT","authors_text":"Graham A. Niblo, Nick Wright, Roger Plymen","submitted_at":"2017-11-28T13:26:40Z","abstract_excerpt":"In this paper we construct an equivariant Poincar\\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine Weyl groups at the level of $K$-theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10281","kind":"arxiv","version":1},"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":"2026-05-18T00:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lz768B+ZeXXASr1HzG5ogWUoSzH/uphZnRkFhI6dQKW3f9B2+VGkXGtWDgIswVFyXMwBksJDNWawj/narqfJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:58:26.097759Z"},"content_sha256":"396311d94c44d36ba674445ddf3a79ce9d19cbdd2dd55eed5138965c5c8b0eaf","schema_version":"1.0","event_id":"sha256:396311d94c44d36ba674445ddf3a79ce9d19cbdd2dd55eed5138965c5c8b0eaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LSVQA4XEV2PCCHKECP2VAILNKK/bundle.json","state_url":"https://pith.science/pith/LSVQA4XEV2PCCHKECP2VAILNKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LSVQA4XEV2PCCHKECP2VAILNKK/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":"2026-05-30T04:58:26Z","links":{"resolver":"https://pith.science/pith/LSVQA4XEV2PCCHKECP2VAILNKK","bundle":"https://pith.science/pith/LSVQA4XEV2PCCHKECP2VAILNKK/bundle.json","state":"https://pith.science/pith/LSVQA4XEV2PCCHKECP2VAILNKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LSVQA4XEV2PCCHKECP2VAILNKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LSVQA4XEV2PCCHKECP2VAILNKK","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":"e549db60620635141cb74797326e10aaaf0b71f5eb0fc40daa1c78122de350fa","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-11-28T13:26:40Z","title_canon_sha256":"2a1301e2e72cc94d3e7222253814f9bbe3395dbc9e843f1475cf29952a89f9c0"},"schema_version":"1.0","source":{"id":"1711.10281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10281","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10281v1","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10281","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"LSVQA4XEV2PC","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LSVQA4XEV2PCCHKE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LSVQA4XE","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:396311d94c44d36ba674445ddf3a79ce9d19cbdd2dd55eed5138965c5c8b0eaf","target":"graph","created_at":"2026-05-18T00:29:22Z","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":"In this paper we construct an equivariant Poincar\\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine Weyl groups at the level of $K$-theory.","authors_text":"Graham A. Niblo, Nick Wright, Roger Plymen","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-11-28T13:26:40Z","title":"Poincar\\'e duality and Langlands duality for extended affine Weyl groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10281","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:dd7c83a887521ddebbd7a83040a8585e5c1f51191f2fce83f47b7e3385f7c21c","target":"record","created_at":"2026-05-18T00:29:22Z","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":"e549db60620635141cb74797326e10aaaf0b71f5eb0fc40daa1c78122de350fa","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-11-28T13:26:40Z","title_canon_sha256":"2a1301e2e72cc94d3e7222253814f9bbe3395dbc9e843f1475cf29952a89f9c0"},"schema_version":"1.0","source":{"id":"1711.10281","kind":"arxiv","version":1}},"canonical_sha256":"5cab0072e4ae9e211d4413f550216d5299bf99ea90bb7b543ad5849416972483","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cab0072e4ae9e211d4413f550216d5299bf99ea90bb7b543ad5849416972483","first_computed_at":"2026-05-18T00:29:22.743568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:22.743568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"roPVmQXyARCLFlCzpXoMHrb6ACToA1JMi98jaO94vlVYgjrr13AuCZCg/8lgc3cOYtEOimb1h7uE184Rz65ICA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:22.744106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd7c83a887521ddebbd7a83040a8585e5c1f51191f2fce83f47b7e3385f7c21c","sha256:396311d94c44d36ba674445ddf3a79ce9d19cbdd2dd55eed5138965c5c8b0eaf"],"state_sha256":"013c97a30c74d4489deeb4dc8e2f50f32348122f59d7b93f04654cf054db931a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZacB0PTS+8q7db2GkfXdbuo1u2lj97dX25b2QPD7eLTcVNIdB2N6bHNXq4KI0bjGlngvc5fjQBEZhdpJU4UAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:58:26.100898Z","bundle_sha256":"662e4edcacbba831e92930fdaad55d5e71a137f5c26b03cf8633b8853b473117"}}