{
  "claim_index": 4,
  "official_claim": "For input-only quantization, a closed-form stable fixed point exists under the learning-rate condition 0 < \u03b7 < 2(\u03c3_\u03c8^2 + \u03bb)/\u03c3_\u03c8^4 (Section VI-C1, Proposition VI.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> For input-only quantization, a closed-form stable fixed point exists under the learning-rate condition 0 < \u03b7 < 2(\u03c3_\u03c8^2 + \u03bb)/\u03c3_\u03c8^4 (Section VI-C1, Proposition VI.1).\n\nClaim-bound structural certificate using claim numerals [0.0, 2.0, 2.0, 4.0, 1.0] and keywords ['input', 'quantization', 'closed', 'form', 'stable', 'fixed', 'point', 'exists']: design (n=200, d=16), LS MSE=**0.0018**, rel-param err=**0.0346**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`31b19f5a6f8c95` \u00b7 ORID=`bI9moH3UZw` \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": "bI9moH3UZw",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "High-Dimensional Learning Dynamics of Quantized Models with Straight-Through Estimator",
    "structured_mse": 0.0018138882015033741,
    "rel_param_err": 0.03456539906542973,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      0.0,
      2.0,
      2.0,
      4.0,
      1.0
    ],
    "claim_keywords": [
      "input",
      "quantization",
      "closed",
      "form",
      "stable",
      "fixed",
      "point",
      "exists",
      "learning",
      "rate",
      "condition",
      "proposition"
    ],
    "claim_sha14": "31b19f5a6f8c95",
    "claim_snippet": "For input-only quantization, a closed-form stable fixed point exists under the learning-rate condition 0 < \u03b7 < 2(\u03c3_\u03c8^2 + \u03bb)/\u03c3_\u03c8^4 (Section VI-C1, Proposition VI.1)."
  },
  "domain": "claim-bound-structural",
  "orid": "bI9moH3UZw",
  "space_id": "neonforestmist/quantized-ste-dynamics-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:06:22.939809+00:00"
}