{"paper":{"title":"Integral magneticity of the level-two K3 packet: CM theta lifts and a 2-isogeny trace contraction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alex Shvets","submitted_at":"2026-07-20T18:32:56Z","abstract_excerpt":"B\\\"onisch, Duhr, and Maggio introduced three meromorphic modular forms \\(C_4,C_{6a},C_{6b}\\) on \\(\\Gamma_0(2)\\), arising from a hypergeometric K3 family, and conjectured that they are magnetic of depths \\(1,2,2\\). Writing \\[ C_4=\\sum_{n\\ge1}c_4(n)q^n,\\qquad C_{6a}=\\sum_{n\\ge1}c_{6a}(n)q^n,\\qquad C_{6b}=\\sum_{n\\ge1}c_{6b}(n)q^n, \\] we prove the stronger denominator-one statements \\[ \\frac{c_4(n)}n,\\qquad \\frac{c_{6a}(n)}{n^2},\\qquad \\frac{c_{6b}(n)}{n^2}\\in\\mathbb Z \\qquad(n\\ge1). \\] The weight-four case is reduced to a termwise binomial divisibility by a hypergeometric change of Hauptmodul. Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19427","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/2607.19427/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"}