{
  "schema_version": 1,
  "title": "Reproduction: Set-Preserving Calibration from Conformal P-Values to E-Values",
  "emoji": "📏",
  "space_id": "snaykey/repro-embedding-collapse",
  "paper": {
    "arxiv_id": "2606.03600",
    "openreview_id": "jNv4sl4YZH"
  },
  "tags": [
    "icml2026-repro",
    "paper-jNv4sl4YZH"
  ],
  "updated_at": "2026-07-28T06:02:04+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Set-Preserving Calibration from Conformal P-Values to E-Values",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-definition-2-2-set-preserving",
        "title": "A calibrator is defined as set-preserving when converting conformal p-values at level alpha into e-values yields prediction sets identical to thresholding the e-values directly at 1/alpha (Section 2.1, Definition 2.2)",
        "file": "pages/claim-1-definition-2-2-set-preserving/page.md",
        "children": []
      },
      {
        "slug": "claim-2-proposition-2-3-theorem-2-6-equation-9",
        "title": "Among left-continuous p-to-e calibrators, only the all-or-nothing calibrator can be exactly set-preserving, which motivates a new sigmoid-based P2E construction (Proposition 2.3, Theorem 2.6, Equation 9)",
        "file": "pages/claim-2-proposition-2-3-theorem-2-6-equation-9/page.md",
        "children": []
      },
      {
        "slug": "claim-3-theorem-2-6-exact-smooth-invertible",
        "title": "The proposed sigmoid-based P2E calibrator is exact (expectation equal to 1), smooth, invertible, strictly positive, and strictly dominates the all-or-nothing calibrator in aggregation settings (Theorem 2.6)",
        "file": "pages/claim-3-theorem-2-6-exact-smooth-invertible/page.md",
        "children": []
      },
      {
        "slug": "claim-4-proposition-4-1-eccp-coverage",
        "title": "Applied to e-Cross-Conformal Prediction (ECCP), the P2E calibrator preserves exact 1-alpha coverage, whereas standard cross-conformal-prediction variants only guarantee approximate 1-2alpha coverage (Proposition 4.1)",
        "file": "pages/claim-4-proposition-4-1-eccp-coverage/page.md",
        "children": []
      },
      {
        "slug": "claim-5-proposition-4-2-weca-coverage",
        "title": "Applied to Weighted Conformal Aggregation (WECA), data-dependent weighted merging of e-values across multiple models retains valid coverage (Proposition 4.2)",
        "file": "pages/claim-5-proposition-4-2-weca-coverage/page.md",
        "children": []
      },
      {
        "slug": "claim-6-section-5-smaller-sets",
        "title": "Empirically, ECCP using the proposed P2E calibrator produces smaller prediction sets than baseline p-to-e conversion methods while maintaining valid coverage (Section 5)",
        "file": "pages/claim-6-section-5-smaller-sets/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}