{"paper":{"title":"The Jamneshan-Tao conjecture for finite abelian groups of bounded rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Jamneshan-Tao conjecture holds for all finite abelian groups generated by at most R elements.","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Bal\\'azs Szegedy, Diego Gonz\\'alez-S\\'anchez, Pablo Candela","submitted_at":"2026-01-13T18:48:08Z","abstract_excerpt":"We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer $R$ (i.e. finite abelian groups generated by at most $R$ elements), by proving an inverse theorem for 1-bounded functions of non-trivial Gowers norm on such groups, concluding that such a function must correlate non-trivially with a nilsequence of bounded complexity."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer R by proving an inverse theorem for 1-bounded functions of non-trivial Gowers norm on such groups, concluding that such a function must correlate non-trivially with a nilsequence of bounded complexity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The inverse theorem holds when the finite abelian group is generated by at most R elements; the argument relies on this bounded-rank restriction to control nilsequence complexity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Jamneshan-Tao conjecture holds for finite abelian groups of rank at most R via an inverse theorem linking non-trivial Gowers norms to bounded-complexity nilsequences.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Jamneshan-Tao conjecture holds for all finite abelian groups generated by at most R elements.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f05df0a39457126d47273283b5d6fbef63e28b5621df5fe68d42b56d9f56efdf"},"source":{"id":"2601.08810","kind":"arxiv","version":2},"verdict":{"id":"93247d98-4a8d-4e62-856a-189fdf4eb90d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T14:28:21.819539Z","strongest_claim":"We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer R by proving an inverse theorem for 1-bounded functions of non-trivial Gowers norm on such groups, concluding that such a function must correlate non-trivially with a nilsequence of bounded complexity.","one_line_summary":"The Jamneshan-Tao conjecture holds for finite abelian groups of rank at most R via an inverse theorem linking non-trivial Gowers norms to bounded-complexity nilsequences.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The inverse theorem holds when the finite abelian group is generated by at most R elements; the argument relies on this bounded-rank restriction to control nilsequence complexity.","pith_extraction_headline":"The Jamneshan-Tao conjecture holds for all finite abelian groups generated by at most R elements."},"references":{"count":29,"sample":[{"doi":"","year":2010,"title":"V . Bergelson, T. Tao and T. Ziegler,An inverse theorem for the uniformity seminorms associated with the action ofF ∞ p , Geom. Funct. Anal.19(2010), no. 6, 1539–1596. 1","work_id":"2bbdc014-faf5-4ff7-9f99-cb7c0ef371cf","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Antol ´ın Camarena, B","work_id":"e5f74c93-fc5f-42d6-b83a-d9c3e9a98725","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Candela,Notes on nilspaces: algebraic aspects, Discrete Anal., 2017, Paper No","work_id":"d6fd6036-4e87-48da-9edc-2d3827581011","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Candela,Notes on compact nilspaces, Discrete Anal., 2017, Paper No","work_id":"4a689b04-38f4-4c08-846b-e1996a273c35","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"P. Candela, D. Gonz ´alez-S´anchez, B. SzegedyOn nilspace systems and their morphisms, Ergodic Theory Dynam. Systems40(2020), no. 11, 3015–3029. 6","work_id":"738350ed-0a79-48cd-b9be-cf1422fdf1f1","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":29,"snapshot_sha256":"e5aa90b7faa898d0a05574cb2086c0477908ba32143f945efe4199157fa5aa6b","internal_anchors":2},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}