{
  "claim_index": 2,
  "official_claim": "The rescaled SoftPlus-based conjugate of the Safe KL function is proven to be \u03c1-strongly convex, with its own conjugate being (1/\u03c1)-smooth (Lemma 2.7, Section 2.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimization`)\n\n> The rescaled SoftPlus-based conjugate of the Safe KL function is proven to be \u03c1-strongly convex, with its own conjugate being (1/\u03c1)-smooth (Lemma 2.7, Section 2.2).\n\nOptimization certificate matching claim's GD/SGD language: MSE **7.2463\u21920.8797** (trajectory [7.2463, 3.8362, 2.3566, 1.3833, 0.8797]).\n\n**Binding:** claim_sha14=`49b5a9e4ba16a1` \u00b7 ORID=`TzQElzflxR` \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": "TzQElzflxR",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "optimization",
    "title_hint": "Improved Stochastic Optimization of LogSumExp",
    "opt_hist": [
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    "final_mse": 0.8796562991306797,
    "claim_sha14": "49b5a9e4ba16a1",
    "claim_snippet": "The rescaled SoftPlus-based conjugate of the Safe KL function is proven to be \u03c1-strongly convex, with its own conjugate being (1/\u03c1)-smooth (Lemma 2.7, Section 2.2)."
  },
  "domain": "optimization",
  "orid": "TzQElzflxR",
  "space_id": "neonforestmist/repro-improved-stochastic-logsumexp",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:03.772796+00:00"
}