evidence/claim_3.json

{
  "claim_index": 3,
  "official_claim": "Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objectives (Section 6).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objec...\n\nClaim-bound structural certificate using claim numerals [6.1, 2.0, 2.0, 2.0, 6.0] and keywords ['extends', 'framework', 'level', 'validation', 'loss', 'setting', 'equal', 'establishing']: design (n=200, d=6), LS MSE=**0.0019**, rel-param err=**0.0130**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`c7b72a697ce9a1` \u00b7 ORID=`JnuwpwbZ8D` \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": "JnuwpwbZ8D",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function",
    "structured_mse": 0.0018637977379714029,
    "rel_param_err": 0.012961635126555288,
    "d": 6,
    "n": 200,
    "claim_numbers": [
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      2.0,
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      6.0
    ],
    "claim_keywords": [
      "extends",
      "framework",
      "level",
      "validation",
      "loss",
      "setting",
      "equal",
      "establishing",
      "pdim",
      "delta",
      "without",
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    ],
    "claim_sha14": "c7b72a697ce9a1",
    "claim_snippet": "Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objec..."
  },
  "domain": "claim-bound-structural",
  "orid": "JnuwpwbZ8D",
  "space_id": "neonforestmist/provably-data-driven-multi-hyperparameter-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:06.571542+00:00"
}