{
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  "official_claim": "Information-theoretic lower bounds (Theorems 8-9) establish that regret must scale at least as H*(1/n + epsilon_q) for deterministic experts and H*(sqrt(1/n) + epsilon_q) for stochastic experts, matching the achievable upper bounds (Section 5, Theorems 8-9).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> Information-theoretic lower bounds (Theorems 8-9) establish that regret must scale at least as H*(1/n + epsilon_q) for deterministic experts and H*(sqrt(1/n) + epsilon_q) for stochastic experts, matching the achievabl...\n\nRate/complexity certificate bound to claim numerals [8.0, 9.0, 1.0, 1.0, 5.0, 8.0]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.10089, 0.07356, 0.04849, 0.03514, 0.02473], log-log slope **-0.512** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`2e106667696f26` \u00b7 ORID=`9uENnRAcSl` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
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    "claim_index": 5,
    "cpu_only": true,
    "domain": "rate-complexity",
    "title_hint": "Understanding Behavior Cloning with Action Quantization",
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    "errs": [
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    "loglog_slope": -0.5122732009485177,
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    "claim_sha14": "2e106667696f26",
    "claim_snippet": "Information-theoretic lower bounds (Theorems 8-9) establish that regret must scale at least as H*(1/n + epsilon_q) for deterministic experts and H*(sqrt(1/n) + epsilon_q) for stochastic experts, matching the achievabl..."
  },
  "domain": "rate-complexity",
  "orid": "9uENnRAcSl",
  "space_id": "neonforestmist/repro-quantized-behavior-cloning",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:11.211144+00:00"
}