{
  "claim_index": 1,
  "official_claim": "Theorem 2 establishes an in-sample MSE bound for each task j that guarantees safety, \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 q\u00b2(d/n)\u03b6 regardless of the balancedness constant B, outlier fraction \u03b5, or heterogeneity \u03b4 (Section 5.1, Theorem 2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`spectral-kernel`)\n\n> Theorem 2 establishes an in-sample MSE bound for each task j that guarantees safety, \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 q\u00b2(d/n)\u03b6 regardless of the balancedness constant B, outlier fraction \u03b5, or heterogeneity \u03b4 (Section 5.1, Theorem 2).\n\nSpectral/kernel certificate: top eigenvalues [14.673, 13.263, 12.7825, 11.9561, 11.0365, 10.8484], effective rank **21.40**, cond **14672995551852.18**.\n\n**Binding:** claim_sha14=`62d74ffa561ba0` \u00b7 ORID=`D5Ijcnz1L9` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "D5Ijcnz1L9",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "spectral-kernel",
    "title_hint": "Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety",
    "top_eigs": [
      14.67299555185218,
      13.263022886753893,
      12.782519908536097,
      11.95611828921398,
      11.036468013950136,
      10.848369319366713,
      10.540123562901075,
      9.772227566226835
    ],
    "effective_rank": 21.401268274713107,
    "cond": 14672995551852.18,
    "claim_sha14": "62d74ffa561ba0",
    "claim_snippet": "Theorem 2 establishes an in-sample MSE bound for each task j that guarantees safety, \u2130\u2c7c\u2071\u207f(\u03b8\u0302\u2c7c) \u2272 q\u00b2(d/n)\u03b6 regardless of the balancedness constant B, outlier fraction \u03b5, or heterogeneity \u03b4 (Section 5.1, Theorem 2)."
  },
  "domain": "spectral-kernel",
  "orid": "D5Ijcnz1L9",
  "space_id": "neonforestmist/mtlr-no-eigenvalue-lower-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:03.528261+00:00"
}