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We prove that \\[|A| \\le |G|^2 \\cdot \\exp(-(\\log |G|)^{\\Omega(1)}).\\] As a consequence, we obtain polynomial (in the input length) lower bounds on the nondeterministic communication complexity of Exactly-N in the 3-player Number-on-Forehead model. We also obtain the first \"reasonable'' lower bounds on the coloring version of the $3$-dimensional corners problem, as well as on the nondete"},"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":"2504.07006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-04-09T16:26:06Z","cross_cats_sorted":["cs.CC","math.NT"],"title_canon_sha256":"3acd601e2e61649801b56278b647fca1ff9f7994edf7d420c736e992a8652c07","abstract_canon_sha256":"0c200360666e537a17867d44307be1cb948dbcdbb254884b7db72f1813ca344b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:30.532163Z","signature_b64":"I64u2SmUxXVxKGN6EdTyDteldOZI7H/6bfiHF5evHIt2Dv3ZyG8I6kUebf5bijt4C5LWZwxW63cuTAC7jhkYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"092c1e6fc6296d7ed08030b1fd562ca6719fad1ce9f009bd36d9dd32691c0018","last_reissued_at":"2026-07-05T11:36:30.531648Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:30.531648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasipolynomial bounds for the corners theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT"],"primary_cat":"math.CO","authors_text":"Anthony Ostuni, Mehtaab Sawhney, Michael Jaber, Shachar Lovett, Yang P. Liu","submitted_at":"2025-04-09T16:26:06Z","abstract_excerpt":"Let $G$ be a finite abelian group and $A$ be a subset of $G \\times G$ which is corner--free, meaning that there are no $x, y \\in G$ and $d \\in G \\setminus \\{0\\}$ such that $(x, y)$, $(x+d, y)$, $(x, y+d) \\in A$. We prove that \\[|A| \\le |G|^2 \\cdot \\exp(-(\\log |G|)^{\\Omega(1)}).\\] As a consequence, we obtain polynomial (in the input length) lower bounds on the nondeterministic communication complexity of Exactly-N in the 3-player Number-on-Forehead model. 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