{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YTFFEHZ2HEQJKVHZ7DGDFIFVPJ","short_pith_number":"pith:YTFFEHZ2","canonical_record":{"source":{"id":"1204.4747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-20T20:58:27Z","cross_cats_sorted":[],"title_canon_sha256":"56b5bb2924e05d88dcd748013bcb3657aed7dbc6496f871dd32041947425a4f9","abstract_canon_sha256":"781319ab9bd1e2efd101775e08c0fd28e855c11fa0135d4cf725946d4e9e3bb8"},"schema_version":"1.0"},"canonical_sha256":"c4ca521f3a39209554f9f8cc32a0b57a655b36500756748ab096bcb3bf46923f","source":{"kind":"arxiv","id":"1204.4747","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4747","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4747v1","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4747","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"YTFFEHZ2HEQJ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YTFFEHZ2HEQJKVHZ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YTFFEHZ2","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YTFFEHZ2HEQJKVHZ7DGDFIFVPJ","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-20T20:58:27Z","cross_cats_sorted":[],"title_canon_sha256":"56b5bb2924e05d88dcd748013bcb3657aed7dbc6496f871dd32041947425a4f9","abstract_canon_sha256":"781319ab9bd1e2efd101775e08c0fd28e855c11fa0135d4cf725946d4e9e3bb8"},"schema_version":"1.0"},"canonical_sha256":"c4ca521f3a39209554f9f8cc32a0b57a655b36500756748ab096bcb3bf46923f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:15.425547Z","signature_b64":"AwwM7Trnszf6WZ0RvwsGW0/D+k9EriD5qFOmzQL+eaw7KvGQOS3uhmEkEAOTh7PJfZ+33rpq2IlKZKSh7qLUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4ca521f3a39209554f9f8cc32a0b57a655b36500756748ab096bcb3bf46923f","last_reissued_at":"2026-05-18T03:57:15.425104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:15.425104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4747","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":"2026-05-18T03:57:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QfKu8OcGXM+IDRz3X4UmNO/ObfOoXZ7r2LoYy0zgPbDLGmjNJRnlODZ2dxhiTn/yxovtPJV0fVKnfg1dKamLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:14:12.351219Z"},"content_sha256":"d82fcc2ddc764ffabcad2f26ca679188c140d9b97aaa8e13e9564d161e446547","schema_version":"1.0","event_id":"sha256:d82fcc2ddc764ffabcad2f26ca679188c140d9b97aaa8e13e9564d161e446547"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YTFFEHZ2HEQJKVHZ7DGDFIFVPJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isoclinism and stable cohomology of wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian B\\\"ohning, Fedor Bogomolov","submitted_at":"2012-04-20T20:58:27Z","abstract_excerpt":"Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups, see Theorem 4.4. Moreover, we show that the stable cohomology of the n-fold wreath product of cyclic groups ZZ/p is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4747","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":"2026-05-18T03:57:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vj7iDjrmuOzxZswvwA/2Ap8uIMl2W600t+WQ668N1dbuDKL48jB8xM/gQlfKPpehIFLaDC3EHR3nlCqfHLN/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:14:12.351953Z"},"content_sha256":"3dc90831c469cf97170fafb772ae65d60ab2f4042859c6a05788c24c9048076f","schema_version":"1.0","event_id":"sha256:3dc90831c469cf97170fafb772ae65d60ab2f4042859c6a05788c24c9048076f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ/bundle.json","state_url":"https://pith.science/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ/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":"2026-05-31T07:14:12Z","links":{"resolver":"https://pith.science/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ","bundle":"https://pith.science/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ/bundle.json","state":"https://pith.science/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTFFEHZ2HEQJKVHZ7DGDFIFVPJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YTFFEHZ2HEQJKVHZ7DGDFIFVPJ","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":"781319ab9bd1e2efd101775e08c0fd28e855c11fa0135d4cf725946d4e9e3bb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-20T20:58:27Z","title_canon_sha256":"56b5bb2924e05d88dcd748013bcb3657aed7dbc6496f871dd32041947425a4f9"},"schema_version":"1.0","source":{"id":"1204.4747","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4747","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4747v1","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4747","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"YTFFEHZ2HEQJ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YTFFEHZ2HEQJKVHZ","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YTFFEHZ2","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:3dc90831c469cf97170fafb772ae65d60ab2f4042859c6a05788c24c9048076f","target":"graph","created_at":"2026-05-18T03:57:15Z","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":"Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups, see Theorem 4.4. Moreover, we show that the stable cohomology of the n-fold wreath product of cyclic groups ZZ/p is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given.","authors_text":"Christian B\\\"ohning, Fedor Bogomolov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-20T20:58:27Z","title":"Isoclinism and stable cohomology of wreath products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4747","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:d82fcc2ddc764ffabcad2f26ca679188c140d9b97aaa8e13e9564d161e446547","target":"record","created_at":"2026-05-18T03:57:15Z","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":"781319ab9bd1e2efd101775e08c0fd28e855c11fa0135d4cf725946d4e9e3bb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-20T20:58:27Z","title_canon_sha256":"56b5bb2924e05d88dcd748013bcb3657aed7dbc6496f871dd32041947425a4f9"},"schema_version":"1.0","source":{"id":"1204.4747","kind":"arxiv","version":1}},"canonical_sha256":"c4ca521f3a39209554f9f8cc32a0b57a655b36500756748ab096bcb3bf46923f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4ca521f3a39209554f9f8cc32a0b57a655b36500756748ab096bcb3bf46923f","first_computed_at":"2026-05-18T03:57:15.425104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:15.425104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AwwM7Trnszf6WZ0RvwsGW0/D+k9EriD5qFOmzQL+eaw7KvGQOS3uhmEkEAOTh7PJfZ+33rpq2IlKZKSh7qLUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:15.425547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4747","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d82fcc2ddc764ffabcad2f26ca679188c140d9b97aaa8e13e9564d161e446547","sha256:3dc90831c469cf97170fafb772ae65d60ab2f4042859c6a05788c24c9048076f"],"state_sha256":"282e0af3dc83f7f615cdf2c39b55267a575d6fd5c6c9c94df17a7279b1cf852d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xIZRYwaKd0u1ZZskAET1jTJAGn/UIg4v2/qVrVwV1+3H+puwLqGCpbBtKPXo6aa2SdWs2ZwOInUQmEgZMT2JBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:14:12.355523Z","bundle_sha256":"9ad259eb17a9107669f2ef5e980df0d1d93163bfdd6543a411a91c57c7889fbe"}}