{
  "claim_index": 1,
  "official_claim": "Theorem 1 proves that non-monotone DR-submodular functions over down-closed convex sets are 1/e-Upper-Linearizable via the exponential reparameterization h(x) = 1 - e^{-x} combined with a designed surrogate potential.",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`online-convex`)\n\n> Theorem 1 proves that non-monotone DR-submodular functions over down-closed convex sets are 1/e-Upper-Linearizable via the exponential reparameterization h(x) = 1 - e^{-x} combined with a designed surrogate potential.\n\nOCO certificate: T=1000, d=10, average regret path [1.028, 1.0373, 1.0339, 1.0082, 1.0107], final avg regret **1.0107**.\n\n**Binding:** claim_sha14=`b859e734132a90` \u00b7 ORID=`NHWsF72zPP` \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": "NHWsF72zPP",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "online-convex",
    "title_hint": "Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Sets",
    "T": 1000,
    "avg_regret_path": [
      1.0279541331502344,
      1.0373236019281273,
      1.0338806859414087,
      1.0082405895901574,
      1.0106801858496004
    ],
    "final_avg_regret": 1.0106801858496004,
    "claim_sha14": "b859e734132a90",
    "claim_snippet": "Theorem 1 proves that non-monotone DR-submodular functions over down-closed convex sets are 1/e-Upper-Linearizable via the exponential reparameterization h(x) = 1 - e^{-x} combined with a designed surrogate potential."
  },
  "domain": "online-convex",
  "orid": "NHWsF72zPP",
  "space_id": "neonforestmist/upper-linearizability-dr-submodular-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:16.064721+00:00"
}