{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4LGG5NE3X5QZI3SPXFRWEK3XGC","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":"172758e34fd167a3420132dd8079d60224b6395a23df2e3c2e257e9a0c43317a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-24T15:45:51Z","title_canon_sha256":"531d9823ce9fac3df911d884591601ed9525617241b0900a5a810df533df76f9"},"schema_version":"1.0","source":{"id":"1502.06840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06840","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06840v1","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06840","created_at":"2026-05-18T02:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"4LGG5NE3X5QZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4LGG5NE3X5QZI3SP","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4LGG5NE3","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:a8d772b0f3d0f9903764ba943d1d51872d515f4ede1f5b47792f22e69d50088f","target":"graph","created_at":"2026-05-18T02:26:24Z","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":"For a finite group $G$ we investigate the difference between the maximum size MaxDim$(G)$ of an \"independent\" family of maximal subgroups of $G$ and maximum size $m(G)$ of an irredundant sequence of generators of $G$. We prove that MaxDim$(G)=m(G)$ if the derived subgroup of $G$ is nilpotent. However MaxDim$(G)-m(G)$ can be arbitrarily large: for any odd prime $p,$ we construct a finite soluble group with Fitting length 2 satisfying $m(G)=3$ and MaxDim$(G)=p.$","authors_text":"Andrea Lucchini, Eloisa Detomi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-24T15:45:51Z","title":"Maximal subgroups of finite soluble groups in general position"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06840","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":"sha256:6d779207e506689dc89b03c494c9de5f57b2203ed23a83a25c20e68ffdeaad50","target":"record","created_at":"2026-05-18T02:26:24Z","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":"172758e34fd167a3420132dd8079d60224b6395a23df2e3c2e257e9a0c43317a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-24T15:45:51Z","title_canon_sha256":"531d9823ce9fac3df911d884591601ed9525617241b0900a5a810df533df76f9"},"schema_version":"1.0","source":{"id":"1502.06840","kind":"arxiv","version":1}},"canonical_sha256":"e2cc6eb49bbf61946e4fb963622b7730977b5d1c5ffac74804abc6ab37de1d6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2cc6eb49bbf61946e4fb963622b7730977b5d1c5ffac74804abc6ab37de1d6b","first_computed_at":"2026-05-18T02:26:24.496570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:24.496570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pWc27o0QeioosCUixjvZA8TDjsMhSuV5WdyATfXmHGFRw1rQvKQMkKHXny3HgVgsTE7UrE8w6i5ABdNB5dXoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:24.497158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d779207e506689dc89b03c494c9de5f57b2203ed23a83a25c20e68ffdeaad50","sha256:a8d772b0f3d0f9903764ba943d1d51872d515f4ede1f5b47792f22e69d50088f"],"state_sha256":"92004ef24f15ed2984ce8f10992cdea766f064cd364dbfa10390d56e98e3933a"}