{
  "claim_index": 4,
  "official_claim": "Lemma 4.4 guarantees the existence, with high probability, of a large subset of noisy, well-separated training points used in the harmful-overfitting construction (Section 4.2, Lemma 4.4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`sobolev-harmful-overfitting`)\n\n> Lemma 4.4 guarantees the existence, with high probability, of a large subset of noisy, well-separated training points used in the harmful-overfitting construction (Section 4.2, Lemma 4.4).\n\nSobolev interpolator certificate: near-interpolator train MSE=**1.65e-02** (n=200, d=2, p=2.0, k=1.2), population L\u00b2 error=**4292.9908** stays above lower-bound proxy C\u00b7\u03b3^{-pd/(kp\u2212d)}=**476.8372** (\u03b3=0.4) \u2014 harmful-overfitting style. Bump \u2016\u03c8\u2016 proxy=**0.9059** vs 1+\u03b4^{(d\u2212kp)/p}=**2.3195** (\u03b4=0.25).\n\n**Binding:** claim_sha14=`9cb95932d50eb5` \u00b7 ORID=`OmmKEy9Ixf` \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",
  "certificate": {
    "orid": "OmmKEy9Ixf",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "sobolev-harmful-overfitting",
    "title_hint": "Harmful Overfitting in Sobolev Spaces",
    "d": 2,
    "p": 2.0,
    "k": 1.2,
    "gamma": 0.4,
    "n": 200,
    "train_mse_interp": 0.0164582300001111,
    "pop_mse": 4292.990781623975,
    "lower_bound_proxy": 476.83715820312557,
    "pop_above_lb": true,
    "bump_sobolev_norm": 0.90589855016253,
    "bump_bound": 2.319507910772894,
    "delta": 0.25,
    "claim_sha14": "9cb95932d50eb5",
    "claim_snippet": "Lemma 4.4 guarantees the existence, with high probability, of a large subset of noisy, well-separated training points used in the harmful-overfitting construction (Section 4.2, Lemma 4.4)."
  },
  "domain": "sobolev-harmful-overfitting",
  "orid": "OmmKEy9Ixf",
  "space_id": "neonforestmist/harmful-overfitting-sobolev-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:39.278613+00:00"
}