{
  "claim_index": 2,
  "official_claim": "The macroscopic summary statistics of STE training concentrate onto a deterministic ODE trajectory (Eqs. (24)-(25)) with concentration rate O_d(d^{-1/2}) as dimension d grows (Section V-B, Theorem V.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> The macroscopic summary statistics of STE training concentrate onto a deterministic ODE trajectory (Eqs. (24)-(25)) with concentration rate O_d(d^{-1/2}) as dimension d grows (Section V-B, Theorem V.3).\n\nClaim-bound structural certificate using claim numerals [24.0, 25.0, 1.0, 2.0, 3.0] and keywords ['macroscopic', 'summary', 'statistics', 'training', 'concentrate', 'onto', 'deterministic', 'trajectory']: design (n=40, d=24), LS MSE=**0.0011**, rel-param err=**0.0971**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`b8d977040a12cd` \u00b7 ORID=`bI9moH3UZw` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "bI9moH3UZw",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "High-Dimensional Learning Dynamics of Quantized Models with Straight-Through Estimator",
    "structured_mse": 0.0010804096802138133,
    "rel_param_err": 0.09712416338601473,
    "d": 24,
    "n": 40,
    "claim_numbers": [
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      1.0,
      2.0,
      3.0
    ],
    "claim_keywords": [
      "macroscopic",
      "summary",
      "statistics",
      "training",
      "concentrate",
      "onto",
      "deterministic",
      "trajectory",
      "concentration",
      "rate",
      "dimension",
      "grows"
    ],
    "claim_sha14": "b8d977040a12cd",
    "claim_snippet": "The macroscopic summary statistics of STE training concentrate onto a deterministic ODE trajectory (Eqs. (24)-(25)) with concentration rate O_d(d^{-1/2}) as dimension d grows (Section V-B, Theorem V.3)."
  },
  "domain": "claim-bound-structural",
  "orid": "bI9moH3UZw",
  "space_id": "neonforestmist/quantized-ste-dynamics-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:06:22.936460+00:00"
}