{
  "abstract": "Sliced optimal transport replaces a transport problem in Rd by one-dimensional problems along scalar slices, and has been used both to lower bound the Wasserstein distance W1 (max-sliced distances) and, more recently, to upper bound it by lifting a one-dimensional optimal plan back to the ambient supports (min-sliced plans). We show that for 1-Lipschitz slicers these two directions are two sides of a single sandwich inequality and we characterize when it collapses to equality. If the slicer class contains an optimal Kantorovich-Rubinstein potential, then the same slicer simultaneously maximizes the max-sliced lower objective and minimizes the min-sliced upper objective, and both equal W1. We define the upper objective through a tie-broken transport problem, which removes the dependence on the one-dimensional ordering and yields the identities without any uniqueness assumption on the slice-optimal coupling. The result requires the slicer to be nonlinear in general, consistent with the known failure of exact linear max-sliced/W1 equivalence in dimension greater than or equal to 2, and identifies Kantorovich-Rubinstein potentials as optimal generalized slicers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05700",
  "author_total": 4,
  "authors": [
    {
      "name": "Rocio Diaz Martin"
    },
    {
      "name": "Xinran Liu"
    },
    {
      "name": "Matthew Thorpe"
    },
    {
      "name": "Soheil Kolouri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eye796r8qcbm0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05700",
  "fulltext_url": null,
  "id": "eye796r8qcbm0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05700",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212036592",
  "pdf_url": "https://arxiv.org/pdf/2609.05700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eye796r8qcbm0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05700"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sandwich Slice: Optimal Transport Potentials Are Optimal Generalized Slicers",
  "title_text": "Sandwich Slice: Optimal Transport Potentials Are Optimal Generalized Slicers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/eye796r8qcbm0",
  "venue": "arXiv",
  "versions": []
}