{"paper":{"title":"On yielding and jointly yielding entries of Euclidean distance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"A. Y. Alfakih","submitted_at":"2016-09-22T16:35:23Z","abstract_excerpt":"An $n \\times n$ matrix D is a Euclidean distance matrix (EDM) if there exist $p^1, \\ldots, p^n$ in some Euclidean space such that $d_{ij} = || p^i - p^j||^2$ for all $i,j=1,\\ldots,n$. Let D be an EDM and let $E^{ij}$ be the $n \\times n$ symmetric matrix with 1's in the $ij$th and $ji$th entries and 0's elsewhere. We say that $[l_{ij},u_{ij}]$ is the yielding interval of entry $d_{ij}$ if it holds that $D+t E^{ij}$ is an EDM iff $l_{ij} \\leq t \\leq u_{ij}$. If the yielding interval of entry $d_{ij}$ has length 0, i.e., if $l_{ij}=u_{ij}$, then $d_{ij}$ is said to be unyielding. Otherwise, if $l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07055","kind":"arxiv","version":2},"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"}