{"paper":{"title":"New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Ivan N. Mikhailov","submitted_at":"2025-04-20T14:11:57Z","abstract_excerpt":"In the paper we prove that, for arbitrary unbounded subset $A\\subset R$ and an arbitrary bounded metric space~$X$, a curve $A\\times_{\\ell^1} (tX)$, $t\\in[0,\\,\\infty)$ is a geodesic line in the Gromov--Hausdorff class. We also show that, for abitrary $\\lambda > 1$, $n\\in\\mathbb{N}$, the following inequality holds: $d_{GH}\\bigl(\\mathbb{Z}^n,\\,\\lambda\\mathbb{Z}^n\\bigr)\\ge\\frac{1}{2}$. We conclude that a curve $t\\mathbb{Z}^n$, $t\\in(0,\\,\\infty)$ is not continuous with respect to the Gromov--Hausdorff distance, and, therefore, is not a gedesic line. Moreover, it follows that multiplication of all m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14629","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/2504.14629/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"}