{"paper":{"title":"A dual linear programming bound for sphere packing in dimension 36","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"Rifat Jumagulov","submitted_at":"2026-07-13T09:37:13Z","abstract_excerpt":"We construct an explicit dual-feasible point for the Cohn-Elkies linear program in dimension 36, built from the space of weight-18 modular forms for $\\Gamma_0(24)$ following the method of Cohn and Triantafillou. The certificate shows that the two-point linear programming bound on the sphere packing density in dimension 36 exceeds the density of the best packing currently known -- the Kschischang-Pasupathy packing, of center density $2^{18}/3^{10}$ -- by a factor of at least 32.91. In particular, no Cohn-Elkies auxiliary function can certify the best known packing in dimension 36 as optimal. To"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11319","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.11319/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"}