{"paper":{"title":"The Hasse principle for random homogeneous polynomials in thin sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Daniel Flores, Kiseok Yeon","submitted_at":"2025-06-02T03:56:37Z","abstract_excerpt":"Let $d$ and $n$ be natural numbers. Let $\\nu_{d,n}: \\mathbb{R}^n\\rightarrow \\mathbb{R}^{N}$ denote the Veronese embedding with $N=N_{n,d}:=\\binom{n+d-1}{d}$, defined by listing all the monomials of degree $d$ in $n$ variables using the lexicographical ordering. Let $\\langle \\boldsymbol{a}, \\nu_{d,n}(\\boldsymbol{x})\\rangle\\in \\mathbb{Z}[\\boldsymbol{x}]$ be a homogeneous polynomial in $n$ variables of degree $d$ with integer coefficients $\\boldsymbol{a}$, where $\\langle\\cdot,\\cdot\\rangle$ denotes the inner product. For a non-singular form $P\\in \\mathbb{Z}[\\boldsymbol{x}]$ of degree $k\\ (\\leq d)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01291","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/2506.01291/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"}