{"paper":{"title":"On tight Euclidean $6$-designs: an experimental result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Djoko Suprijanto","submitted_at":"2010-12-09T09:04:06Z","abstract_excerpt":"A finite set $X \\seq \\RR^n$ with a weight function $w : X \\longrightarrow \\RR_{>0}$ is called \\emph{Euclidean $t$-design} in $\\RR^n$ (supported by $p$ concentric spheres) if the following condition holds: \\[ \\sum_{i=1}^p \\frac{w(X_i)}{|S_i|}\\int_{S_i} f(\\boldsymbol x)d\\sigma_i(\\boldsymbol x) =\\sum_{\\boldsymbol x \\in X}w(\\boldsymbol x) f(\\boldsymbol x), \\] for any polynomial $f(\\boldsymbol x) \\in \\mbox{Pol}(\\RR^n)$ of degree at most $t$. Here $S_i \\seq \\RR^n$ is a sphere of radius $r_i \\geq 0,$ $X_i=X \\cap S_i,$ and $\\sigma_i(\\boldsymbol x)$ is an $O(n)$-invariant measure on $S_i$ such that $|S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1946","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}