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Also we define rack system on the set $V \\times G$, where $V$ is a vector space of dimension $n$ over $\\Bbbk$, $G$ is a subgroup of $GL_n(\\Bbbk)$.Finally, we find connection between skew braces and dimono"},"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":"2312.15052","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2023-12-22T20:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"f21469854d688fa211b19d15aa3cf4ec0806c0809e071fd7e622f54f040926d6","abstract_canon_sha256":"df0636417d3967971a3f733eaa5f6f5a5c0a1db85ba9b3fc84c6325cb75383ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:27:30.316832Z","signature_b64":"DxDoo5oNXRRObPRqHt8j4xe3627afk76wndUHTMlwtR7qqYrTIFV3I8JQ/G3m2XzzSTj0R4cMW+t6OWpgqIZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c0aa995cccbce5315b4dc50fba9fd150d3cb00650d78687e93fb85550f3b934","last_reissued_at":"2026-07-05T07:27:30.316278Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:27:30.316278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-groups","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Tatyana A. 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