{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:3NXCGGWEFW4DPTBRMW532URUVN","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":"f778902017d3d1c84a58d59112d52fc0a0fa196f1f35432c6a357e11980f6f7d","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-06-27T13:18:14Z","title_canon_sha256":"84ee8e367b825ead50fb6119a91eb41a876e63b493a7ecff3a76751795e82175"},"schema_version":"1.0","source":{"id":"0706.4019","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.4019","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"0706.4019v3","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.4019","created_at":"2026-05-18T04:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"3NXCGGWEFW4D","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3NXCGGWEFW4DPTBR","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3NXCGGWE","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:5b2fd1f9baf8c64d933fd6f39f74b981980d32ccb68d19fd4f0d9eb88f55873f","target":"graph","created_at":"2026-05-18T04:42:02Z","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":"Let G be a finite group. We show that the Bass Nil-groups $NK_n(RG)$, $n \\in Z$, are generated from the p-subgroups of G by induction maps, certain twisting maps depending on elements in the centralizers of the p-subgroups, and the Verschiebung homomorphisms. As a consequence, the groups $NK_n(RG)$ are generated by induction from elementary subgroups. For $NK_0(ZG)$ we get an improved estimate of the torsion exponent.","authors_text":"Ian Hambleton, Wolfgang Lueck","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-06-27T13:18:14Z","title":"Induction and computation of Bass Nil Groups for finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4019","kind":"arxiv","version":3},"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":"sha256:302e3211481533403779ed1132c68b0e23051943130584856db0618d2a38299d","target":"record","created_at":"2026-05-18T04:42:02Z","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":"f778902017d3d1c84a58d59112d52fc0a0fa196f1f35432c6a357e11980f6f7d","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2007-06-27T13:18:14Z","title_canon_sha256":"84ee8e367b825ead50fb6119a91eb41a876e63b493a7ecff3a76751795e82175"},"schema_version":"1.0","source":{"id":"0706.4019","kind":"arxiv","version":3}},"canonical_sha256":"db6e231ac42db837cc3165bbbd5234ab6f5fc82906616029d88bed3275e59a72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db6e231ac42db837cc3165bbbd5234ab6f5fc82906616029d88bed3275e59a72","first_computed_at":"2026-05-18T04:42:02.843991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:02.843991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HFe5G9pQkpcW1OQuvXioqJNpcWEkr7j6dBvjxSyrkUqEiH3krNPsq1uuJu+JC1kVUk5q6tgobsgSOYbJZ0PnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:02.844577Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.4019","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:302e3211481533403779ed1132c68b0e23051943130584856db0618d2a38299d","sha256:5b2fd1f9baf8c64d933fd6f39f74b981980d32ccb68d19fd4f0d9eb88f55873f"],"state_sha256":"a778e4382f94f62214de822c458454e5368e49dfb86ea8d6e30d648a19a34902"}