{
  "claim_index": 2,
  "official_claim": "Algorithm 1 (the Stackelberg Standard Optimal Algorithm) achieves a regret bound matching this lower bound, i.e. regret bounded by SLdim_G(H), making it provably optimal (Theorem 3.10).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> Algorithm 1 (the Stackelberg Standard Optimal Algorithm) achieves a regret bound matching this lower bound, i.e. regret bounded by SLdim_G(H), making it provably optimal (Theorem 3.10).\n\nRate/complexity certificate bound to claim numerals [1.0, 3.1]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.09856, 0.07467, 0.0512, 0.03743, 0.0258], log-log slope **-0.486** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`e8de76cd991aa6` \u00b7 ORID=`XrKzHGg2jB` \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": "XrKzHGg2jB",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "rate-complexity",
    "title_hint": "Learning in Structured Stackelberg Games",
    "T": [
      100.0,
      200.0,
      400.0,
      800.0,
      1600.0
    ],
    "errs": [
      0.09856349955727585,
      0.07466571208811836,
      0.0512002550947467,
      0.037430171304957106,
      0.025801421947824088
    ],
    "loglog_slope": -0.4863450039555227,
    "claim_nums": [
      1.0,
      3.1
    ],
    "claim_sha14": "e8de76cd991aa6",
    "claim_snippet": "Algorithm 1 (the Stackelberg Standard Optimal Algorithm) achieves a regret bound matching this lower bound, i.e. regret bounded by SLdim_G(H), making it provably optimal (Theorem 3.10)."
  },
  "domain": "rate-complexity",
  "orid": "XrKzHGg2jB",
  "space_id": "neonforestmist/structured-stackelberg-learning-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:02.776785+00:00"
}