{
  "claim_index": 4,
  "official_claim": "Theorem 3 extends the in-sample MSE guarantees of Theorem 2 to population risk via an empirical-to-population comparability constant \u03bd\u2c7c, retaining an intrinsic-dimension fallback for the safety guarantee (Section 5.2, Theorem 3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`spectral-kernel`)\n\n> Theorem 3 extends the in-sample MSE guarantees of Theorem 2 to population risk via an empirical-to-population comparability constant \u03bd\u2c7c, retaining an intrinsic-dimension fallback for the safety guarantee (Section 5.2,...\n\nSpectral/kernel certificate: top eigenvalues [14.8449, 14.0027, 11.9188, 11.2928, 11.0515, 10.6772], effective rank **21.48**, cond **14844855226281.62**.\n\n**Binding:** claim_sha14=`4ccd4220ac6ae6` \u00b7 ORID=`D5Ijcnz1L9` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
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    "orid": "D5Ijcnz1L9",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "spectral-kernel",
    "title_hint": "Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety",
    "top_eigs": [
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      11.918822537089635,
      11.292817087495756,
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    "effective_rank": 21.476808599553973,
    "cond": 14844855226281.62,
    "claim_sha14": "4ccd4220ac6ae6",
    "claim_snippet": "Theorem 3 extends the in-sample MSE guarantees of Theorem 2 to population risk via an empirical-to-population comparability constant \u03bd\u2c7c, retaining an intrinsic-dimension fallback for the safety guarantee (Section 5.2,..."
  },
  "domain": "spectral-kernel",
  "orid": "D5Ijcnz1L9",
  "space_id": "neonforestmist/mtlr-no-eigenvalue-lower-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:03.534444+00:00"
}