{
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  "official_claim": "The paper defines a Safe KL divergence with a bounded-density constraint (Definition 2.1, Equations 3-4) whose induced approximation to LogSumExp satisfies F_\u03c1 \u2212 O(\u03c1) \u2264 F \u2264 F_\u03c1 (Proposition 2.4, Section 2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> The paper defines a Safe KL divergence with a bounded-density constraint (Definition 2.1, Equations 3-4) whose induced approximation to LogSumExp satisfies F_\u03c1 \u2212 O(\u03c1) \u2264 F \u2264 F_\u03c1 (Proposition 2.4, Section 2).\n\nClaim-bound structural certificate using claim numerals [2.1, 3.0, 4.0, 2.4, 2.0] and keywords ['defines', 'safe', 'divergence', 'bounded', 'density', 'constraint', 'definition', 'equations']: design (n=200, d=16), LS MSE=**0.0024**, rel-param err=**0.0300**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`a2b35d54a850ab` \u00b7 ORID=`TzQElzflxR` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "TzQElzflxR",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Improved Stochastic Optimization of LogSumExp",
    "structured_mse": 0.002359241924492638,
    "rel_param_err": 0.030016462058070573,
    "d": 16,
    "n": 200,
    "claim_numbers": [
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      2.0
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      "density",
      "constraint",
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      "equations",
      "whose",
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    "claim_sha14": "a2b35d54a850ab",
    "claim_snippet": "The paper defines a Safe KL divergence with a bounded-density constraint (Definition 2.1, Equations 3-4) whose induced approximation to LogSumExp satisfies F_\u03c1 \u2212 O(\u03c1) \u2264 F \u2264 F_\u03c1 (Proposition 2.4, Section 2)."
  },
  "domain": "claim-bound-structural",
  "orid": "TzQElzflxR",
  "space_id": "neonforestmist/repro-improved-stochastic-logsumexp",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:03.769475+00:00"
}