{"paper":{"title":"Dimension dependence and dimension-free $\\ell^2$ estimates for variation seminorms of spherical means on the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rafa{\\l} {\\L}y\\.zwa","submitted_at":"2026-05-18T17:45:53Z","abstract_excerpt":"We prove that the $\\ell^2 \\to \\ell^2$ norm of the $r$-variation seminorm of spherical means on the hypercube admits no dimension-free bounds for any $r \\in [1, \\infty)$ when the variation is taken over all possible radii. Furthermore, we establish that if the radii are restricted to a fixed parity, dimension-free estimates hold for all $r \\in (2, \\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18713","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/2605.18713/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.054618Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fd66e25cd45d70055e0516eccf75c497b3902f2fed7d415eae6268ac037c7d01"},"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"}