{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KZVV6KKQMUOXIBMEZZ4G26BBZL","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":"f4c0a87391c2fc8e3c17dc0ecd77b5e826aa8cf879796722f5a5ea52a368ce99","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-07-19T12:12:46Z","title_canon_sha256":"18387cc0135b26b70631c251db5ddcc3080ef538b54569d054b0fe59a22d2490"},"schema_version":"1.0","source":{"id":"1907.08477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08477","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08477v1","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08477","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"KZVV6KKQMUOX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KZVV6KKQMUOXIBME","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KZVV6KKQ","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:762a149b86306cc657b514a86f54594dcdc32755a4e9cae0d344930500aa13db","target":"graph","created_at":"2026-05-17T23:40:09Z","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 show that, there exists a constant $a$ such that, for every subgroup $H$ of a finite group $G$, the number of maximal subgroups of $G$ containing $H$ is bounded above by $a|G:H|^{3/2}$. In particular, a transitive permutation group of degree $n$ has at most $an^{3/2}$ maximal systems of imprimitivity. When $G$ is soluble, generalizing a classic result of Tim Wall, we prove a much stroger bound, that is, the number of maximal subgroups of $G$ containing $H$ is at most $|G:H|-1$.","authors_text":"Andrea Lucchini, Mariapia Moscatiello, Pablo Spiga","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-07-19T12:12:46Z","title":"A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08477","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":"sha256:3b2c7ac8b4ec435898e4769442fd318db975d8cda32f304ea25ad8f50058aa4a","target":"record","created_at":"2026-05-17T23:40:09Z","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":"f4c0a87391c2fc8e3c17dc0ecd77b5e826aa8cf879796722f5a5ea52a368ce99","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-07-19T12:12:46Z","title_canon_sha256":"18387cc0135b26b70631c251db5ddcc3080ef538b54569d054b0fe59a22d2490"},"schema_version":"1.0","source":{"id":"1907.08477","kind":"arxiv","version":1}},"canonical_sha256":"566b5f2950651d740584ce786d7821cadd97cd9c8d846ad6fab239002888bc32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"566b5f2950651d740584ce786d7821cadd97cd9c8d846ad6fab239002888bc32","first_computed_at":"2026-05-17T23:40:09.726780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:09.726780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p66r9E1dzSqgTLkKIjCwKfBkZPCInnioWtEnlTrVu1sMn5o5PxfmahIgD0HV8Q7Cf7GOqrE5q5I26/QyferaCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:09.727505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b2c7ac8b4ec435898e4769442fd318db975d8cda32f304ea25ad8f50058aa4a","sha256:762a149b86306cc657b514a86f54594dcdc32755a4e9cae0d344930500aa13db"],"state_sha256":"9c38539e4ef568b4830d704cf3c7b68bffbe9f5f4646780e5bd21affb4fb56c4"}