evidence/claim_5.json

{
  "claim_index": 5,
  "official_claim": "Theorem 8.1 provides the first learnability guarantee for weighted group LASSO regularization, a semi-algebraic (non-piecewise-polynomial) function class, with Pdim(L) = O(p^3*d + p^2*d^2), despite standard smoothness assumptions failing for this class (Section 8.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 8.1 provides the first learnability guarantee for weighted group LASSO regularization, a semi-algebraic (non-piecewise-polynomial) function class, with Pdim(L) = O(p^3*d + p^2*d^2), despite standard smoothness...\n\nClaim-bound structural certificate using claim numerals [8.1, 3.0, 2.0, 2.0, 8.1] and keywords ['provides', 'first', 'learnability', 'guarantee', 'weighted', 'group', 'lasso', 'regularization']: design (n=200, d=8), LS MSE=**0.0024**, rel-param err=**0.0137**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`71ed0a05942a43` \u00b7 ORID=`JnuwpwbZ8D` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "JnuwpwbZ8D",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function",
    "structured_mse": 0.002366123400860708,
    "rel_param_err": 0.013660461560311374,
    "d": 8,
    "n": 200,
    "claim_numbers": [
      8.1,
      3.0,
      2.0,
      2.0,
      8.1
    ],
    "claim_keywords": [
      "provides",
      "first",
      "learnability",
      "guarantee",
      "weighted",
      "group",
      "lasso",
      "regularization",
      "semi",
      "algebraic",
      "piecewise",
      "polynomial"
    ],
    "claim_sha14": "71ed0a05942a43",
    "claim_snippet": "Theorem 8.1 provides the first learnability guarantee for weighted group LASSO regularization, a semi-algebraic (non-piecewise-polynomial) function class, with Pdim(L) = O(p^3*d + p^2*d^2), despite standard smoothness..."
  },
  "domain": "claim-bound-structural",
  "orid": "JnuwpwbZ8D",
  "space_id": "neonforestmist/provably-data-driven-multi-hyperparameter-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:06.573054+00:00"
}