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Also, we obtain that for $1\\ll |\\Gamma| \\le p^{6/7-\\varepsilon}$ and any $\\xi\\neq 0$ there is no a set $B$ such that $\\xi \\Gamma+1=B/B$."},"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":"1702.01197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-03T22:54:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"aa3066ee6a318e83a6483b335301d6760faa0674dd7e471ba53b1deb8f06efed","abstract_canon_sha256":"b82b9304d2ff62403abe8f58faab989fd176bfa0e726429082849863192df8c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:24.231141Z","signature_b64":"aeR+VMQ3sOj2jvcg8/R+5cy/Wu7Tcno5QfL7N+z3bmfSvUl6jbQJnGRFLHzd5I5leOv8jEyFh6M37zJAtzd4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf2a113f85aa8ddf2cef2e0ea09e1728f0b8fe32d1fbd8812c6a06638cb0771","last_reissued_at":"2026-05-18T00:51:24.230502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:24.230502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Any small multiplicative sugroup is not a sumset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Ilya D. 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