{"paper":{"title":"Near-Optimal Embeddings of Constant-Dimensional Subspaces of $L^p$ into $\\ell_p^N$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Yi Li","submitted_at":"2026-07-13T16:06:14Z","abstract_excerpt":"For $d\\geq 2$, $p\\geq 1$ and $\\epsilon > 0$, let $N_{p}(d,\\epsilon)$ be the smallest integer $N$ such that every $d$-dimensional subspace of $L^{p}[0,1]$ admits a linear embedding into $\\ell_{p}^{N}$ with distortion at most $1+\\epsilon$. For fixed $d$ and $p$, the bound \\[ N_{p}(d,\\epsilon) = \\widetilde{O}_{d,p}\\!\\left(\\epsilon^{-2(d-1)/(d+2p)}\\right) \\] is established. For $p\\notin 2\\mathbb{Z}$, this is optimal up to logarithmic factors; for positive even integers $p$, isometric embeddings of dimension independent of $\\epsilon$ are known. The stated upper bound was previously known only for i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11747","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/2607.11747/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"}