{
  "claim_index": 6,
  "official_claim": "Algorithm 1 solves a joint convex objective \u2112(\u0398)=\u03a3\u2c7c w\u2c7c(f\u2c7c(\u03b8\u2c7c)+\u03bb\u2c7c\u2016\u03b8\u2c7c-\u03b2\u2016_{\u03a3\u2c7c}) that penalizes disagreement in prediction space (via task-specific norms) rather than raw parameter space (Section 3, Algorithm 1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`spectral-kernel`)\n\n> Algorithm 1 solves a joint convex objective \u2112(\u0398)=\u03a3\u2c7c w\u2c7c(f\u2c7c(\u03b8\u2c7c)+\u03bb\u2c7c\u2016\u03b8\u2c7c-\u03b2\u2016_{\u03a3\u2c7c}) that penalizes disagreement in prediction space (via task-specific norms) rather than raw parameter space (Section 3, Algorithm 1).\n\nSpectral/kernel certificate: top eigenvalues [13.4528, 12.7316, 12.292, 12.0994, 10.8393, 10.4463], effective rank **21.52**, cond **13452765735529.35**.\n\n**Binding:** claim_sha14=`e0c5c517ff4151` \u00b7 ORID=`D5Ijcnz1L9` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_6.json`](../../evidence/claim_6.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "D5Ijcnz1L9",
    "claim_index": 6,
    "cpu_only": true,
    "domain": "spectral-kernel",
    "title_hint": "Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety",
    "top_eigs": [
      13.452765735529347,
      12.731551662330027,
      12.291976192482329,
      12.099352338518667,
      10.839277353925372,
      10.446324114190244,
      10.14686413776211,
      9.424744836681217
    ],
    "effective_rank": 21.521327636824527,
    "cond": 13452765735529.348,
    "claim_sha14": "e0c5c517ff4151",
    "claim_snippet": "Algorithm 1 solves a joint convex objective \u2112(\u0398)=\u03a3\u2c7c w\u2c7c(f\u2c7c(\u03b8\u2c7c)+\u03bb\u2c7c\u2016\u03b8\u2c7c-\u03b2\u2016_{\u03a3\u2c7c}) that penalizes disagreement in prediction space (via task-specific norms) rather than raw parameter space (Section 3, Algorithm 1)."
  },
  "domain": "spectral-kernel",
  "orid": "D5Ijcnz1L9",
  "space_id": "neonforestmist/mtlr-no-eigenvalue-lower-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:03.538818+00:00"
}