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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0907.2557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-15T11:14:37Z","cross_cats_sorted":["cs.MS","hep-ph","hep-th","math.AG","math.MP","math.NT"],"title_canon_sha256":"7b989a2dfc47282f9d7511e4d33dd85327188781e9af94f5d503b41f4cf395e9","abstract_canon_sha256":"32cb2e77b22b0fffc258d5108a1db994a7b378b5c6a2f0075a03b86a4821a8ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:19:59.305604Z","signature_b64":"Ktzayiv+uA7fmhjS+I7vmTExKJI0MUfuMdqv1mhmTna9voZc0n0FTmnFFPr5plbnC2L39nPJ/aq8rtuFXEL2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7893b069cff7d72e61eaefc3c6f853480a21c0820732492d1dfdafbc0baf7259","last_reissued_at":"2026-07-04T17:19:59.305221Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:19:59.305221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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