{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6BSPLDGWODMYC5VCPBHCZMHNY6","short_pith_number":"pith:6BSPLDGW","canonical_record":{"source":{"id":"1206.1840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-08T19:05:39Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c16606ea5a00d409b1874736490280d900c3d2f93c0cb1f14c9fa3d14128db3d","abstract_canon_sha256":"40bf66ac316ee9bb2106c2988c5f34b63d94e6da9874c419442d75f9c3f8263c"},"schema_version":"1.0"},"canonical_sha256":"f064f58cd670d98176a2784e2cb0edc7a7221aada901ce942b0383e43ef09be0","source":{"kind":"arxiv","id":"1206.1840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1840","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1840v1","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1840","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"6BSPLDGWODMY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6BSPLDGWODMYC5VC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6BSPLDGW","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6BSPLDGWODMYC5VCPBHCZMHNY6","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-08T19:05:39Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c16606ea5a00d409b1874736490280d900c3d2f93c0cb1f14c9fa3d14128db3d","abstract_canon_sha256":"40bf66ac316ee9bb2106c2988c5f34b63d94e6da9874c419442d75f9c3f8263c"},"schema_version":"1.0"},"canonical_sha256":"f064f58cd670d98176a2784e2cb0edc7a7221aada901ce942b0383e43ef09be0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:55.250267Z","signature_b64":"3pfnN/DM9nyIMltQGpOsHpaepsG7NNGq8JzkglFTWaz58f8i0bZdw1T6hBZr0IfvtKLWH75XBoRyW7NnuqlSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f064f58cd670d98176a2784e2cb0edc7a7221aada901ce942b0383e43ef09be0","last_reissued_at":"2026-05-18T03:53:55.249548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:55.249548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1840","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":"2026-05-18T03:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVmLEf7Yt+Lr8/kl/snfkqWVPLwdEhwlzW3AgH11qofkSZVTZWRet7peqTs+FuBiGEV5I136Ug57c0XD6tPEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:17:22.118899Z"},"content_sha256":"5682c0bfe8154c0e5d02811701be5d6d1207070f474700c72ff34194808c7431","schema_version":"1.0","event_id":"sha256:5682c0bfe8154c0e5d02811701be5d6d1207070f474700c72ff34194808c7431"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6BSPLDGWODMYC5VCPBHCZMHNY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular Representations and Indicators for Bismash Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Andrea Jedwab, Susan Montgomery","submitted_at":"2012-06-08T19:05:39Z","abstract_excerpt":"We introduce Brauer characters for representations of the bismash products of groups in characteristic p > 0, p not 2 and study their properties analogous to the classical case of finite groups. We then use our results to extend to bismash products a theorem of Thompson on lifting Frobenius-Schur indicators from characteristic p to characteristic 0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1840","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":"2026-05-18T03:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xFzx//cVKIHssFiwLf4Qu+G3/szNMeI6YyuqWkS3TxHNwXdQj7cP6tGS+5pSyyhKlxGvm9QQh38Ys8MJ0T6gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:17:22.119249Z"},"content_sha256":"dd25994c88de7e3b20ac743ae371ae2252fac9c527ccc46e5cbf2c6b7efd5fc9","schema_version":"1.0","event_id":"sha256:dd25994c88de7e3b20ac743ae371ae2252fac9c527ccc46e5cbf2c6b7efd5fc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BSPLDGWODMYC5VCPBHCZMHNY6/bundle.json","state_url":"https://pith.science/pith/6BSPLDGWODMYC5VCPBHCZMHNY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BSPLDGWODMYC5VCPBHCZMHNY6/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":"2026-06-01T22:17:22Z","links":{"resolver":"https://pith.science/pith/6BSPLDGWODMYC5VCPBHCZMHNY6","bundle":"https://pith.science/pith/6BSPLDGWODMYC5VCPBHCZMHNY6/bundle.json","state":"https://pith.science/pith/6BSPLDGWODMYC5VCPBHCZMHNY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BSPLDGWODMYC5VCPBHCZMHNY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6BSPLDGWODMYC5VCPBHCZMHNY6","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":"40bf66ac316ee9bb2106c2988c5f34b63d94e6da9874c419442d75f9c3f8263c","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-08T19:05:39Z","title_canon_sha256":"c16606ea5a00d409b1874736490280d900c3d2f93c0cb1f14c9fa3d14128db3d"},"schema_version":"1.0","source":{"id":"1206.1840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1840","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1840v1","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1840","created_at":"2026-05-18T03:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"6BSPLDGWODMY","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6BSPLDGWODMYC5VC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6BSPLDGW","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:dd25994c88de7e3b20ac743ae371ae2252fac9c527ccc46e5cbf2c6b7efd5fc9","target":"graph","created_at":"2026-05-18T03:53:55Z","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":"We introduce Brauer characters for representations of the bismash products of groups in characteristic p > 0, p not 2 and study their properties analogous to the classical case of finite groups. We then use our results to extend to bismash products a theorem of Thompson on lifting Frobenius-Schur indicators from characteristic p to characteristic 0","authors_text":"Andrea Jedwab, Susan Montgomery","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-08T19:05:39Z","title":"Modular Representations and Indicators for Bismash Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1840","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":"sha256:5682c0bfe8154c0e5d02811701be5d6d1207070f474700c72ff34194808c7431","target":"record","created_at":"2026-05-18T03:53:55Z","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":"40bf66ac316ee9bb2106c2988c5f34b63d94e6da9874c419442d75f9c3f8263c","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-08T19:05:39Z","title_canon_sha256":"c16606ea5a00d409b1874736490280d900c3d2f93c0cb1f14c9fa3d14128db3d"},"schema_version":"1.0","source":{"id":"1206.1840","kind":"arxiv","version":1}},"canonical_sha256":"f064f58cd670d98176a2784e2cb0edc7a7221aada901ce942b0383e43ef09be0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f064f58cd670d98176a2784e2cb0edc7a7221aada901ce942b0383e43ef09be0","first_computed_at":"2026-05-18T03:53:55.249548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:55.249548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3pfnN/DM9nyIMltQGpOsHpaepsG7NNGq8JzkglFTWaz58f8i0bZdw1T6hBZr0IfvtKLWH75XBoRyW7NnuqlSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:55.250267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5682c0bfe8154c0e5d02811701be5d6d1207070f474700c72ff34194808c7431","sha256:dd25994c88de7e3b20ac743ae371ae2252fac9c527ccc46e5cbf2c6b7efd5fc9"],"state_sha256":"0206e3c8acf18ad962e039d9b7e8467dc43af6f697a05b944de5de2410da20bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bI/J2uISHtfTkStkdgiAp3s6teFP4OVCmUkSELATQTQ02RjdYMaGhBaNCMcA/jk4Nb0fnP3dzbprQMJM5kzyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:17:22.121239Z","bundle_sha256":"d69ad169155f16069d022b33a2a00473a002e725ba7fd78f996877dc739abd8f"}}