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A group $G$ is called a CI-group if $Cay(G,S)\\cong Cay(G,T)$ for some inverse closed subsets $S$ and $T$ of $G\\setminus \\{1\\}$, then $S^\\alpha=T$ for some automorphism $\\alpha$ of $G$. A finite group $G$ is called a BI-group if $Cay(G,S)\\cong Cay(G,T)$ for some inverse closed subsets $S$ and $T$ of $G\\setminus \\{1\\}$, then $M_\\nu^S=M_\\nu^T$ for all positive integers $"},"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":"1710.04446","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-12T11:03:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8d2e39cf9ccb8881efcf911ad8e095b32004d3a1ec918c87562ad8b7f5064ed2","abstract_canon_sha256":"0aab90d992b7de6090ab46a52e7bb2feb6799e38a4204b7de215964c6761b875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:01.027234Z","signature_b64":"af8E/LWaULHfDiQwOba/aznG9EIdHoCp+J9fUsdARdihzN/lwPlvjPhuEEfvFIVzI9OePF2byPk+aKYK/kDIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"006a1f691df2e93802a6359c2a383b060aa2647e7c01f59c2d1d4ffc5723ab1b","last_reissued_at":"2026-05-18T00:33:01.026623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:01.026623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-abelian finite groups whose character sums are invariant but are not Cayley isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"A. 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