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We show that key elements of $H$ needed to construct such an isomorphism $\\varphi$, such as those whose image under $\\varphi$ is an $n$-cycle or $(n-1)$-cycle, can be recognised with high probability by the lengths of just four of their cycles in $\\Lambda$."},"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":"1205.6586","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-05-30T08:48:56Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"efb572090d62e9ee3a21ceb143f86f67f0bd368733ea1c5b7a534b0cdb855997","abstract_canon_sha256":"bd676d2cad7b236d723da77642910d946b202acb5d4f95b9b10812be98c17767"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:01.707380Z","signature_b64":"JnPZa8wfD1xM4YrEj21x0ZP0mgEDxKdqdA6B9hktxc/ZSmxgqpb03mFILXCjVuI5050y5Yp7mdQMkQo0LaBQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c8c3294cf94f76fd03b891ea951b1067a0be3a797a436e8f559e4bb420fd5f0","last_reissued_at":"2026-05-18T02:17:01.706831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:01.706831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identifying long cycles in finite alternating and symmetric groups acting on subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.GR","authors_text":"Alice C. 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