{"paper":{"title":"\\zeta({{2}^m, 1, {2}^m, 3}^n, {2}^m) / \\pi^{4n + 2m(2n+1)} is rational","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Steven Charlton","submitted_at":"2013-06-28T10:06:52Z","abstract_excerpt":"The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lison\\v{e}k states that inserting all cyclic shifts of some fixed blocks of 2's into the multiple zeta value {\\zeta}(1,3,...,1,3) gives an explicit rational multiple of a power of {\\pi}. In this paper we use motivic multiple zeta values to establish a non-explicit symmetric insertion result: inserting all possible permutations of some fixed blocks of 2's into {\\zeta}(1,3,...,1,3) gives some rational multiple of a power of {\\pi}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6775","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"}