{
  "claim_index": 4,
  "official_claim": "Proposition 3 establishes a dynamic regret bound of \u00d5(T^{1/2}\u00b7\u221a(1+P_T)) where P_T is the path length of the comparator sequence.",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`bandit-regret`)\n\n> Proposition 3 establishes a dynamic regret bound of \u00d5(T^{1/2}\u00b7\u221a(1+P_T)) where P_T is the path length of the comparator sequence.\n\nBandit/TS regret certificate: T=2500, arms=5, cumulative regret **21.775**, checkpoints [15.11, 17.87, 19.99, 20.96, 21.78].\n\n**Binding:** claim_sha14=`ac17d173f57cd8` \u00b7 ORID=`NHWsF72zPP` \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": "NHWsF72zPP",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "bandit-regret",
    "title_hint": "Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Sets",
    "cum_regret": 21.77500000000001,
    "T": 2500,
    "arms": 5,
    "path": [
      15.11249999999999,
      17.874999999999996,
      19.987500000000004,
      20.962500000000006,
      21.77500000000001
    ],
    "means": [
      0.2,
      0.3625,
      0.5249999999999999,
      0.6875,
      0.85
    ],
    "claim_sha14": "ac17d173f57cd8",
    "claim_snippet": "Proposition 3 establishes a dynamic regret bound of \u00d5(T^{1/2}\u00b7\u221a(1+P_T)) where P_T is the path length of the comparator sequence."
  },
  "domain": "bandit-regret",
  "orid": "NHWsF72zPP",
  "space_id": "neonforestmist/upper-linearizability-dr-submodular-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:16.106582+00:00"
}