{
  "abstract": "We prove that Lipschitz differentiability spaces which bi-Lipschitz embed into an RNP-space are countably rectifiable. In contrast to earlier methods of Cheeger and Kleiner, our approach does not rely on differentiating RNP-targets, and uses instead decomposability bundles and a careful blow-up analysis. We also present decomposability bundles in a way which avoids the mention of Alberti representations and generalizes the approach of Alberti--Marchese to measures in RNP-spaces. We moreover study fragment-wise differentiability into RNP-targets, give a new ${\\rm Lip}-{\\rm lip}$-type characterization of RNP-differentiability spaces, and address a question of Le Donne asking for a characterization of spaces $(X,μ)\\subset\\ell^2$ whose Gromov--Hausdorff tangents are Hausdorff limits of $r^{-1} (X-x)$ in $\\ell^2$ as $r\\to 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06700",
  "author_total": 3,
  "authors": [
    {
      "name": "Ivan Caamano"
    },
    {
      "name": "Sylvester Eriksson-Bique"
    },
    {
      "name": "Elefterios Soultanis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb0fcv5az1c8j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06700",
  "fulltext_url": null,
  "id": "cb0fcv5az1c8j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06700",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212045803",
  "pdf_url": "https://arxiv.org/pdf/2609.06700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb0fcv5az1c8j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06700"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Embeddability and rectifiability of Lipschitz differentiability spaces",
  "title_text": "Embeddability and rectifiability of Lipschitz differentiability spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cb0fcv5az1c8j",
  "venue": "arXiv",
  "versions": []
}