{"paper":{"title":"The Betti side of the double shuffle theory. I. The harmonic coproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.QA"],"primary_cat":"math.AG","authors_text":"Benjamin Enriquez, Hidekazu Furusho","submitted_at":"2018-03-27T15:51:18Z","abstract_excerpt":"This paper is the first in a series which aims at: (a) giving a proof that the associator relations between multizeta values imply the double shuffle and regularization (DSR) ones, alternative to that of the second-named author's 2010 paper; (b) enhancing Racinet's construction of a torsor structure over the Q-scheme of DSR relations to an explicit bitorsor structure. In this paper, we revisit Racinet's original DSR formalism, whose main character is an algebra coproduct, called the harmonic coproduct, and we introduce a variant which is a module coproduct; we explain the `de Rham' nature of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10151","kind":"arxiv","version":5},"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/1803.10151/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"}