{"paper":{"title":"Towards a characterization of idempotent Schur multipliers","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"math.CA","authors_text":"Hamed Hatami, Marcel K. Goh","submitted_at":"2026-07-15T19:25:30Z","abstract_excerpt":"It is conjectured that every idempotent Schur multiplier can be written as a finite sum of contractive idempotents. This conjecture is equivalent to the statement that any boolean matrix $A$ with factorization norm $\\lVert A\\rVert_{\\gamma_2}$ at most $\\gamma$ can be expressed as a signed sum $$A = \\sum_{i=1}^L \\pm B_i,$$ where, up to permutation of rows and columns, each $B_i$ is a blow-up of an identity matrix, and $L$ depends only on $\\gamma$. In this note we show that if $A$ is an $n\\times n$ boolean matrix with $\\lVert A\\rVert_{\\gamma_2} \\le \\gamma$, then it admits such an expression with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14316","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/2607.14316/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"}