{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CEADV252PNRNAQ3UHC6ULEBT2L","short_pith_number":"pith:CEADV252","canonical_record":{"source":{"id":"1401.7854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-30T14:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"53fd6fd2d5f898e624f11226c7d103d15239b2972c8f575209c9a8d8ca41d753","abstract_canon_sha256":"a75a908c771aa770c010fde56714882a1471692c52e46a74878323e0568b1704"},"schema_version":"1.0"},"canonical_sha256":"11003aebba7b62d0437438bd459033d2ce2d0a56d7647f9fc52ea941639b4e92","source":{"kind":"arxiv","id":"1401.7854","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7854","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7854v2","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7854","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"CEADV252PNRN","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CEADV252PNRNAQ3U","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CEADV252","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CEADV252PNRNAQ3UHC6ULEBT2L","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-30T14:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"53fd6fd2d5f898e624f11226c7d103d15239b2972c8f575209c9a8d8ca41d753","abstract_canon_sha256":"a75a908c771aa770c010fde56714882a1471692c52e46a74878323e0568b1704"},"schema_version":"1.0"},"canonical_sha256":"11003aebba7b62d0437438bd459033d2ce2d0a56d7647f9fc52ea941639b4e92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:39.439307Z","signature_b64":"3gxpMTxKeq7282HNOb2JuG0IK4ABA+CmSTRSqgz8diW914uI+sSBibyVVdoGw3Lp/uag9NtqIDHytNB8nZqRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11003aebba7b62d0437438bd459033d2ce2d0a56d7647f9fc52ea941639b4e92","last_reissued_at":"2026-05-18T02:42:39.438615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:39.438615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7854","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":"2026-05-18T02:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RjmPcIXH58FNvDTp4eXaMWxsufAXHJ6yncfwT/2wnIX+Cye1Eff1cmvpULRn4jjoSK+l3QtSAgTHXlD8kav3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:36:55.129459Z"},"content_sha256":"e0097cea759d991c06535ed6b05479fb3b6ada6de920f9c3f9b3a1c5d8c717ed","schema_version":"1.0","event_id":"sha256:e0097cea759d991c06535ed6b05479fb3b6ada6de920f9c3f9b3a1c5d8c717ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CEADV252PNRNAQ3UHC6ULEBT2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Describing units of integral group rings up to commensurability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ann Kiefer, Florian Eisele, Inneke Van Gelder","submitted_at":"2014-01-30T14:19:42Z","abstract_excerpt":"We restrict the type of $2 \\times 2$-matrices which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring $\\mathbb Z G$ for all finite groups $G$ that do not have a non-commutative Frobenius complement as a quotient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7854","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":"2026-05-18T02:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43U7YzsKiIZu/emND+fxCMx8EIDGJwyHP04CyNRu7LIPccAuhPop9wkkM85W6jdTuV+t+YaZcUYYkIZW7DO/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:36:55.129812Z"},"content_sha256":"20cc153b7c7ef5aeea04ace742299e1e36aadc2210b5418d21146e2f60c936a8","schema_version":"1.0","event_id":"sha256:20cc153b7c7ef5aeea04ace742299e1e36aadc2210b5418d21146e2f60c936a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CEADV252PNRNAQ3UHC6ULEBT2L/bundle.json","state_url":"https://pith.science/pith/CEADV252PNRNAQ3UHC6ULEBT2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CEADV252PNRNAQ3UHC6ULEBT2L/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":"2026-06-04T21:36:55Z","links":{"resolver":"https://pith.science/pith/CEADV252PNRNAQ3UHC6ULEBT2L","bundle":"https://pith.science/pith/CEADV252PNRNAQ3UHC6ULEBT2L/bundle.json","state":"https://pith.science/pith/CEADV252PNRNAQ3UHC6ULEBT2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CEADV252PNRNAQ3UHC6ULEBT2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CEADV252PNRNAQ3UHC6ULEBT2L","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":"a75a908c771aa770c010fde56714882a1471692c52e46a74878323e0568b1704","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-30T14:19:42Z","title_canon_sha256":"53fd6fd2d5f898e624f11226c7d103d15239b2972c8f575209c9a8d8ca41d753"},"schema_version":"1.0","source":{"id":"1401.7854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7854","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7854v2","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7854","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"CEADV252PNRN","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CEADV252PNRNAQ3U","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CEADV252","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:20cc153b7c7ef5aeea04ace742299e1e36aadc2210b5418d21146e2f60c936a8","target":"graph","created_at":"2026-05-18T02:42:39Z","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 restrict the type of $2 \\times 2$-matrices which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring $\\mathbb Z G$ for all finite groups $G$ that do not have a non-commutative Frobenius complement as a quotient.","authors_text":"Ann Kiefer, Florian Eisele, Inneke Van Gelder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-30T14:19:42Z","title":"Describing units of integral group rings up to commensurability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7854","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:e0097cea759d991c06535ed6b05479fb3b6ada6de920f9c3f9b3a1c5d8c717ed","target":"record","created_at":"2026-05-18T02:42:39Z","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":"a75a908c771aa770c010fde56714882a1471692c52e46a74878323e0568b1704","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-30T14:19:42Z","title_canon_sha256":"53fd6fd2d5f898e624f11226c7d103d15239b2972c8f575209c9a8d8ca41d753"},"schema_version":"1.0","source":{"id":"1401.7854","kind":"arxiv","version":2}},"canonical_sha256":"11003aebba7b62d0437438bd459033d2ce2d0a56d7647f9fc52ea941639b4e92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11003aebba7b62d0437438bd459033d2ce2d0a56d7647f9fc52ea941639b4e92","first_computed_at":"2026-05-18T02:42:39.438615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.438615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3gxpMTxKeq7282HNOb2JuG0IK4ABA+CmSTRSqgz8diW914uI+sSBibyVVdoGw3Lp/uag9NtqIDHytNB8nZqRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.439307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0097cea759d991c06535ed6b05479fb3b6ada6de920f9c3f9b3a1c5d8c717ed","sha256:20cc153b7c7ef5aeea04ace742299e1e36aadc2210b5418d21146e2f60c936a8"],"state_sha256":"0cca69768efae8d085ffe363b7fa4d1188d22f6c2f552bb39257ec5a2b941f53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2+6ADgmWm733mW6l1lWqIz7j5RPbvYPv1aoDr32kTXRdZ8ITDcq8Bk7+lfmWaqsm6HnU1iV1zzTOERvL7VORDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:36:55.131993Z","bundle_sha256":"c394b7601e1261165ea5e7bf006696e73a1b93a26efc8a615efe9c3520cd6b3d"}}