{
  "claim_index": 2,
  "official_claim": "Theorem 2 also shows a transfer guarantee for inlier tasks when B \u2272 min(1/\u03b5, m): \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 (Bd/mn + min(B\u03b4\u00b2, d/n) + B\u00b2\u03b5\u00b2d/n)\u03b6, achieved without knowing \u03b5, \u03b4, or the inlier set S (Section 5.1, Theorem 2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`spectral-kernel`)\n\n> Theorem 2 also shows a transfer guarantee for inlier tasks when B \u2272 min(1/\u03b5, m): \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 (Bd/mn + min(B\u03b4\u00b2, d/n) + B\u00b2\u03b5\u00b2d/n)\u03b6, achieved without knowing \u03b5, \u03b4, or the inlier set S (Section 5.1, Theorem 2).\n\nSpectral/kernel certificate: top eigenvalues [14.1178, 13.2099, 11.9161, 11.4529, 10.9917, 10.8439], effective rank **21.51**, cond **14117818868412.37**.\n\n**Binding:** claim_sha14=`e468bc5d11629f` \u00b7 ORID=`D5Ijcnz1L9` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "D5Ijcnz1L9",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "spectral-kernel",
    "title_hint": "Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety",
    "top_eigs": [
      14.117818868412368,
      13.209917495771375,
      11.916050421410219,
      11.452869111363672,
      10.991741440615634,
      10.843855104051807,
      10.205571743094165,
      10.080766715972148
    ],
    "effective_rank": 21.5129966977869,
    "cond": 14117818868412.367,
    "claim_sha14": "e468bc5d11629f",
    "claim_snippet": "Theorem 2 also shows a transfer guarantee for inlier tasks when B \u2272 min(1/\u03b5, m): \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 (Bd/mn + min(B\u03b4\u00b2, d/n) + B\u00b2\u03b5\u00b2d/n)\u03b6, achieved without knowing \u03b5, \u03b4, or the inlier set S (Section 5.1, Theorem 2)."
  },
  "domain": "spectral-kernel",
  "orid": "D5Ijcnz1L9",
  "space_id": "neonforestmist/mtlr-no-eigenvalue-lower-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:03.530472+00:00"
}