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This finishes the proof of Pyber's base size conjecture. An ingredient of the proof is that for the distinguishing number $d(G)$ (in the sense of Albertson and Collins) of a transitive permutation group $G$ of degree $n > 1$ we have the estimates $\\sqrt[n]{|G|} < d(G) \\leq 48 \\sqrt[n]{|G|}$."},"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":"1611.09487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-29T05:19:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"dad11fced97b6dd93636013b6458f7d19f050e740cc7116954aa2fed1f551ae1","abstract_canon_sha256":"bcd4f8d02dc37f11549cd1f0b10eeffd9a51cfe05ad1bd58ec63dfb92afbad91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:19.124180Z","signature_b64":"v4jc9GlQVdIR+glBhXnz2u6VSPAcmouAqvNX/J5ij9gRcgUvZqFIEzen2/OTBWhIdEbBQkE8fuPTVL0q7mbQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"711a12bd530c53e81962c5aa905761362460851d8e0c6a58cdf43f1bba478113","last_reissued_at":"2026-05-17T23:52:19.123341Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:19.123341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A proof of Pyber's base size conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Attila Mar\\'oti, H\\\"ulya Duyan, Zolt\\'an Halasi","submitted_at":"2016-11-29T05:19:10Z","abstract_excerpt":"Building on earlier papers of several authors, we establish that there exists a universal constant $c > 0$ such that the minimal base size $b(G)$ of a primitive permutation group $G$ of degree $n$ satisfies $\\log |G| / \\log n \\leq b(G) < 45 (\\log |G| / \\log n) + c$. 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