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We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ relations, where $\\delta_n$ i"},"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":"1104.2029","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-04-11T19:35:56Z","cross_cats_sorted":["math.CO","math.GR","math.QA","math.RT"],"title_canon_sha256":"b3d14b02af00935d37cef93a86194464877482520d8abdc3ce58ca9d273fdd7c","abstract_canon_sha256":"367b569c62d70a193c28bd48ae13a6a11d6080e2799799a59f56238b7d76e95f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.333088Z","signature_b64":"GflPNVrdLB2rfpnsCA+qGtg1XTnOYdDoieItxF2OcaBLAR7oJTFmOeGH1T2WNrEcBBwaqN7uMibPfS5hL19LBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5527b39f07e8f0ae1cc6a85798705a602d467005afd7b2974d91df7e1dbe8f79","last_reissued_at":"2026-05-18T03:27:23.332468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.332468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite dimensional semigroup quadratic algebras with minimal number of relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Natalia Iyudu, Stanislav Shkarin","submitted_at":"2011-04-11T19:35:56Z","abstract_excerpt":"A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. 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