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The Chebotarev invariant $C(G)$ of $G$ is the expected value of the random variable $n$ that is minimal subject to the requirement that $n$ randomly chosen elements of $G$ invariably generate $G$. Confirming a conjecture of Kowalski and Zywina, we prove that there exists an absolute constant $\\beta$ such that $C(G) \\leq \\beta\\sqrt{|G|}$ for all finite groups $G.$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.05859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-19T08:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"ad1bdf63b6e90efec9084a2c17782d14aad651b414a2edfdeb66577a08f9e243","abstract_canon_sha256":"2406802b0430bd8d6029e055e534229559b7e70edaa2343655762dea7398a1c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:51.947457Z","signature_b64":"YjeSDUMnGyOs/kpPnVy9vaeKka0AW349IpJDExAv2Jlh1KJLaBjiPmI+yxI/psHtYc1V0IpMKYpbpg+39vnjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d616161c6763c72f8f5ea76e6553fcdb4625ac5ea8a20617f108619cc3b438d4","last_reissued_at":"2026-05-18T01:20:51.946631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:51.946631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Chebotarev invariant of a finite group: a conjecture of Kowalski and Zywina","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini","submitted_at":"2015-09-19T08:12:16Z","abstract_excerpt":"A subset $\\{g_1, \\ldots , g_d\\}$ of a finite group $G$ invariably generates $G$ if $\\{g_1^{x_1}, \\ldots , g_d^{x_d}\\}$ generates $G$ for every choice of $x_i \\in G$. 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