{"paper":{"title":"The Multiple Zeta Value Data Mine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","hep-ph","hep-th","math.AG","math.MP","math.NT"],"primary_cat":"math-ph","authors_text":"D.J. Broadhurst, J.A.M. Vermaseren, J. Bl\\\"umlein","submitted_at":"2009-07-15T11:14:37Z","abstract_excerpt":"We provide a data mine of proven results for multiple zeta values (MZVs) of the form $\\zeta(s_1,s_2,...,s_k)=\\sum_{n_1>n_2>...>n_k>0}^\\infty \\{1/(n_1^{s_1} >... n_k^{s_k})\\}$ with weight $w=\\sum_{i=1}^k s_i$ and depth $k$ and for Euler sums of the form $\\sum_{n_1>n_2>...>n_k>0}^\\infty t\\{(\\epsilon_1^{n_1} >...\\epsilon_1 ^{n_k})/ (n_1^{s_1} ... n_k^{s_k}) \\}$ with signs $\\epsilon_i=\\pm1$. Notably, we achieve explicit proven reductions of all MZVs with weights $w\\le22$, and all Euler sums with weights $w\\le12$, to bases whose dimensions, bigraded by weight and depth, have sizes in precise agreem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2557","kind":"arxiv","version":2},"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/0907.2557/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"}