{
  "claim_index": 3,
  "official_claim": "Assumption 1 (Balancedness) replaces the classical Lower Boundedness of Second Moments condition \u03c1I \u2aaf \u03a3\u2c7c with the one-sided condition \u03a3\u2c7c \u2aaf B\u00b7\u03a3_S, accommodating rank-deficient or decaying covariate spectra where prior eigenvalue-lower-bound approaches (e.g. Duan & Wang 2023, depending on 1/\u03c1\u00b2) fail (Section 4, Assumption 1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`spectral-kernel`)\n\n> Assumption 1 (Balancedness) replaces the classical Lower Boundedness of Second Moments condition \u03c1I \u2aaf \u03a3\u2c7c with the one-sided condition \u03a3\u2c7c \u2aaf B\u00b7\u03a3_S, accommodating rank-deficient or decaying covariate spectra where prior ...\n\nSpectral/kernel certificate: top eigenvalues [15.8647, 13.2444, 12.9633, 11.5767, 11.0161, 10.4694], effective rank **20.82**, cond **15864733536505.98**.\n\n**Binding:** claim_sha14=`76d2618ec45c32` \u00b7 ORID=`D5Ijcnz1L9` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "D5Ijcnz1L9",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "spectral-kernel",
    "title_hint": "Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety",
    "top_eigs": [
      15.86473353650598,
      13.244429020488012,
      12.963332622520001,
      11.576662899067323,
      11.016091956445674,
      10.469429697875265,
      9.788323826597463,
      9.346878900418442
    ],
    "effective_rank": 20.815505400531233,
    "cond": 15864733536505.98,
    "claim_sha14": "76d2618ec45c32",
    "claim_snippet": "Assumption 1 (Balancedness) replaces the classical Lower Boundedness of Second Moments condition \u03c1I \u2aaf \u03a3\u2c7c with the one-sided condition \u03a3\u2c7c \u2aaf B\u00b7\u03a3_S, accommodating rank-deficient or decaying covariate spectra where prior ..."
  },
  "domain": "spectral-kernel",
  "orid": "D5Ijcnz1L9",
  "space_id": "neonforestmist/mtlr-no-eigenvalue-lower-bounds-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:03.532489+00:00"
}