{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZYEULS6BF247GYBWDOKDBESRI2","short_pith_number":"pith:ZYEULS6B","canonical_record":{"source":{"id":"1103.2047","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-10T14:30:10Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"0bd90a6ba075dd8a06fc9820e144dfefe3c59b0bc3e39ebbfa9b028ca4afa5c6","abstract_canon_sha256":"cd0b8062d437bd974973326d6c089c2904fea34018d19db8703c9947101096fa"},"schema_version":"1.0"},"canonical_sha256":"ce0945cbc12eb9f360361b9430925146b0b7db189714c8c43ace3395b6319282","source":{"kind":"arxiv","id":"1103.2047","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2047","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2047v6","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2047","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZYEULS6BF247","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZYEULS6BF247GYBW","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZYEULS6B","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZYEULS6BF247GYBWDOKDBESRI2","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2047","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-10T14:30:10Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"0bd90a6ba075dd8a06fc9820e144dfefe3c59b0bc3e39ebbfa9b028ca4afa5c6","abstract_canon_sha256":"cd0b8062d437bd974973326d6c089c2904fea34018d19db8703c9947101096fa"},"schema_version":"1.0"},"canonical_sha256":"ce0945cbc12eb9f360361b9430925146b0b7db189714c8c43ace3395b6319282","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:41.406676Z","signature_b64":"Sp/wL/X095yxU9QSIPVUyjM2PUJFxZUM8eyxKYjobD1mQq6XF41nYF6Miv8eAgqDjdzD4kwpXdzC7OWqw824CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce0945cbc12eb9f360361b9430925146b0b7db189714c8c43ace3395b6319282","last_reissued_at":"2026-05-18T01:30:41.406017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:41.406017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2047","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHc2yPcX8YRbEJEeGhAvYCoxZu/AIgtQ+PJ9tSaE9VpJS3Lr4Tj9Arh4SYBynyfMeDCaoX3kdzJPO701XETzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:44:15.813996Z"},"content_sha256":"e9033444bd08f65831f630d2cb459c0dc5c4c86f42e4a5640ec1c52e8e7a7efa","schema_version":"1.0","event_id":"sha256:e9033444bd08f65831f630d2cb459c0dc5c4c86f42e4a5640ec1c52e8e7a7efa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZYEULS6BF247GYBWDOKDBESRI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brauer relations in finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alex Bartel, Tim Dokchitser","submitted_at":"2011-03-10T14:30:10Z","abstract_excerpt":"If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave-Bouc classification in the case of p-groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2047","kind":"arxiv","version":6},"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":"2026-05-18T01:30:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iA+WlDnSTrvT6W3lVVa4VbW6K1IXcLDeMTeGffuhaSbxP3wnWPl/PCdH6BKY9Nf7BVhD86HU2c22Z812Nle7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:44:15.814657Z"},"content_sha256":"8ba0fb42c470273464c494a3a98bf889f2e06320d16a9eb190db284f22bdc013","schema_version":"1.0","event_id":"sha256:8ba0fb42c470273464c494a3a98bf889f2e06320d16a9eb190db284f22bdc013"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYEULS6BF247GYBWDOKDBESRI2/bundle.json","state_url":"https://pith.science/pith/ZYEULS6BF247GYBWDOKDBESRI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYEULS6BF247GYBWDOKDBESRI2/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":"2026-06-11T11:44:15Z","links":{"resolver":"https://pith.science/pith/ZYEULS6BF247GYBWDOKDBESRI2","bundle":"https://pith.science/pith/ZYEULS6BF247GYBWDOKDBESRI2/bundle.json","state":"https://pith.science/pith/ZYEULS6BF247GYBWDOKDBESRI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYEULS6BF247GYBWDOKDBESRI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZYEULS6BF247GYBWDOKDBESRI2","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":"cd0b8062d437bd974973326d6c089c2904fea34018d19db8703c9947101096fa","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-10T14:30:10Z","title_canon_sha256":"0bd90a6ba075dd8a06fc9820e144dfefe3c59b0bc3e39ebbfa9b028ca4afa5c6"},"schema_version":"1.0","source":{"id":"1103.2047","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2047","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2047v6","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2047","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZYEULS6BF247","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZYEULS6BF247GYBW","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZYEULS6B","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:8ba0fb42c470273464c494a3a98bf889f2e06320d16a9eb190db284f22bdc013","target":"graph","created_at":"2026-05-18T01:30:41Z","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":"If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave-Bouc classification in the case of p-groups.","authors_text":"Alex Bartel, Tim Dokchitser","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-10T14:30:10Z","title":"Brauer relations in finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2047","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:e9033444bd08f65831f630d2cb459c0dc5c4c86f42e4a5640ec1c52e8e7a7efa","target":"record","created_at":"2026-05-18T01:30:41Z","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":"cd0b8062d437bd974973326d6c089c2904fea34018d19db8703c9947101096fa","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-10T14:30:10Z","title_canon_sha256":"0bd90a6ba075dd8a06fc9820e144dfefe3c59b0bc3e39ebbfa9b028ca4afa5c6"},"schema_version":"1.0","source":{"id":"1103.2047","kind":"arxiv","version":6}},"canonical_sha256":"ce0945cbc12eb9f360361b9430925146b0b7db189714c8c43ace3395b6319282","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce0945cbc12eb9f360361b9430925146b0b7db189714c8c43ace3395b6319282","first_computed_at":"2026-05-18T01:30:41.406017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:41.406017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sp/wL/X095yxU9QSIPVUyjM2PUJFxZUM8eyxKYjobD1mQq6XF41nYF6Miv8eAgqDjdzD4kwpXdzC7OWqw824CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:41.406676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2047","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9033444bd08f65831f630d2cb459c0dc5c4c86f42e4a5640ec1c52e8e7a7efa","sha256:8ba0fb42c470273464c494a3a98bf889f2e06320d16a9eb190db284f22bdc013"],"state_sha256":"0fd98a82be43207248e76b2b21aa1984b65d742c388a0171769e105c4568b23a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEuz0/AFa3Tfq8BhIah6oVKHV92hCyea264TRSE3ZJPPGZTRiV3bYaszbTyHFy9/ct4NAZU2Mgd6Pp1qCa9LAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:44:15.818143Z","bundle_sha256":"50e4b140ba3f0358dc87f6ddf222076c236bb51eecc815ea750a5afb087f5078"}}