{"paper":{"title":"An inverse theorem for Freiman multi-homomorphisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"L. Mili\\'cevi\\'c, W. T. Gowers","submitted_at":"2020-02-26T17:53:14Z","abstract_excerpt":"Let $G_1, \\dots, G_k$ and $H$ be vector spaces over a finite field $\\mathbb{F}_p$ of prime order. Let $A \\subset G_1 \\times\\dots\\times G_k$ be a set of size $\\delta |G_1| \\cdots |G_k|$. Let a map $\\phi \\colon A \\to H$ be a multi-homomorphism, meaning that for each direction $d \\in [k]$, and each element $(x_1, \\dots, x_{d-1}, x_{d+1}, \\dots, x_k)$ of $G_1\\times\\dots\\times G_{d-1}\\times G_{d+1}\\times \\dots\\times G_k$, the map that sends each $y_d$ such that $(x_1, \\dots,$ $x_{d-1},$ $y_d,$ $x_{d+1}, \\dots,$ $x_k) \\in A$ to $\\phi(x_1, \\dots,$ $x_{d-1},$ $y_d,$ $x_{d+1}, \\dots,$ $x_k)$ is a Freim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.11667","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.11667/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"}