{
  "family_id": "089",
  "title": "Bounded-distortion <i>L</i><sub>1</sub> embeddings of planar and bounded-treewidth graphs",
  "discipline": "Convex and metric geometry",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Planar Graph Metrics Embed into L1 with Constant Distortion",
      "path": "preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/paper.pdf",
      "readme_path": "preprints/Planar-Graph-Metrics-Embed-into-L1-with-Constant-Distortion-September-23-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "L1 Embeddings of Graphs of Bounded Treewidth",
      "path": "preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/paper.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/paper.pdf",
      "readme_path": "preprints/L1-Embeddings-of-Graphs-of-Bounded-Treewidth-September-23-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/089.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/089.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}