{"paper":{"title":"On the DJL conjecture for order 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Naomi Shaked-Monderer","submitted_at":"2015-01-11T07:23:54Z","abstract_excerpt":"In 1994 Drew, Johnson and Loewy conjectured that for $n \\ge 4$, the cp-rank of any $n\\times n$ completely positive matrices is at most $\\lfloor{n^2}/{4}\\rfloor$. Recently this conjecture has been proved for $n=5$ and disproved for $n\\ge 7$, leaving the case $n=6$ open. We make a step toward proving the conjecture for $n=6$. We show that if $A$ is a $6\\times 6$ completely positive matrix that is orthogonal to an exceptional extremal copositive matrix, then the cp-rank of $A$ is at most $9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02426","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}