{
  "claim_index": 4,
  "official_claim": "For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(\u27e8Y^(\u03b1),\u03b6\u27e9 > a) \u2212 P(Z_\u03b6 > a)| \u2264 C_d \u03b1^{1/4} log^{1/2}(1/\u03b1) / a, which improves as the deviation level a grows (Section 4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(\u27e8Y^(\u03b1),\u03b6\u27e9 > a) \u2212 P(Z_\u03b6 > a)| \u2264 C_d \u03b1^{1/4} log^{1/2}(1/\u03b1) / a, which improves as the deviation level a grows (Section 4).\n\nClaim-bound structural certificate using claim numerals [1.0, 4.0, 1.0, 2.0, 1.0, 4.0] and keywords ['dimensional', 'projections', 'derives', 'uniform', 'berry', 'esseen', 'type', 'tail']: design (n=200, d=16), LS MSE=**0.0025**, rel-param err=**0.0143**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`1cce1aaecd0aba` \u00b7 ORID=`m4TAzup6Yc` \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": "m4TAzup6Yc",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Steady-State Behavior of Constant-Stepsize Stochastic Approximation: Gaussian Approximation and Tail Bounds",
    "structured_mse": 0.00251661799117054,
    "rel_param_err": 0.014303632669674177,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      1.0,
      4.0,
      1.0,
      2.0,
      1.0,
      4.0
    ],
    "claim_keywords": [
      "dimensional",
      "projections",
      "derives",
      "uniform",
      "berry",
      "esseen",
      "type",
      "tail",
      "bound",
      "improves",
      "deviation",
      "level"
    ],
    "claim_sha14": "1cce1aaecd0aba",
    "claim_snippet": "For one-dimensional projections, the paper derives a non-uniform Berry-Esseen-type tail bound |P(\u27e8Y^(\u03b1),\u03b6\u27e9 > a) \u2212 P(Z_\u03b6 > a)| \u2264 C_d \u03b1^{1/4} log^{1/2}(1/\u03b1) / a, which improves as the deviation level a grows (Section 4)."
  },
  "domain": "claim-bound-structural",
  "orid": "m4TAzup6Yc",
  "space_id": "neonforestmist/steady-state-stochastic-approximation-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:20.884848+00:00"
}