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We study such matrices through the centraliser algebras of monomial representations of finite groups. Using an exhaustive search over the linear characters of Schur covers, we classify, up to monomial equivalence, the complex generalised weighing matrices admitting a primitive group of rank at most five and degree at most $80$ acting by strong automorphisms, for coeffici"},"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":"2607.16069","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-17T15:52:10Z","cross_cats_sorted":[],"title_canon_sha256":"8cc46e69aee0955e329e9002572afb892f8cbd6b306bb9ab206b6a9aa2bbfb41","abstract_canon_sha256":"be1712aefa0bf85effaada25e8aa37a77f14f973d6fa53294c5ce40bf8b70608"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T02:19:29.355279Z","signature_b64":"ZS3vyx3Wg8eV2plcB0jioG3G+TR4WAES3uWAf/0DsPgVVr+NcxaLP6eELciPkY0VU4GSNcuPWVATtTgeVHnnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59c8b8187d4f92e5f67738577edd6ee7d0d6e7b8da2e261c08c97d11f09f0b11","last_reissued_at":"2026-07-20T02:19:29.354419Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T02:19:29.354419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex generalised weighing matrices in centraliser algebras of monomial representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrea \\v{S}vob, Padraig \\'O Cath\\'ain, Ronan Egan","submitted_at":"2026-07-17T15:52:10Z","abstract_excerpt":"An $n \\times n$ matrix $W$ with exactly $w$ non-zero entries taken from the set of $k^{\\rm th}$ complex roots of unity in each row and column satisfying $WW^{\\ast} = wI_n$ is a complex generalised weighing matrix $CGW(n,w;k)$. 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