{"paper":{"title":"Complete metric spaces with property (Z) are length metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes","submitted_at":"2018-08-02T09:04:55Z","abstract_excerpt":"We prove that every complete metric space with property (Z) is a length space. These answers questions posed by Garc\\'{i}a-Lirola, Proch\\'{a}zka and Rueda Zoca, and by Becerra Guerrero, L\\'{o}pez-P\\'{e}rez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00715","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":""},"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"}