{"paper":{"title":"Cluster algebras and tilings for the m=4 amplituhedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.CO","authors_text":"Chaim Even-Zohar, Lauren Williams, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Tsviqa Lakrec","submitted_at":"2023-10-26T18:38:34Z","abstract_excerpt":"The amplituhedron $A_{n,k,m}(Z)$ is the image of the positive Grassmannian $Gr_{k,n}^{\\geq 0}$ under the map ${Z}: Gr_{k,n}^{\\geq 0} \\to Gr_{k,k+m}$ induced by a positive linear map $Z:\\mathbb{R}^n \\to \\mathbb{R}^{k+m}$. Motivated by a question of Hodges, Arkani-Hamed and Trnka introduced the amplituhedron as a geometric object whose tilings conjecturally encode the BCFW recursion for computing scattering amplitudes. More specifically, the expectation was that one can compute scattering amplitudes in ${N}=4$ SYM by tiling the $m=4$ amplituhedron $A_{n,k,4}(Z)$ - that is, decomposing the amplit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17727","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/2310.17727/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"}