{
  "claim_index": 2,
  "official_claim": "Under Probabilistic Incremental Input-to-State Stability (P-IISS) of the dynamics and Relaxed Total Variation Continuity (RTVC) of the expert policy, the regret bound has only polynomial (not exponential) dependence on the horizon H with respect to quantization error epsilon_q (Theorem 3, Definition 3, Definition 4, Section 3.1-3.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Under Probabilistic Incremental Input-to-State Stability (P-IISS) of the dynamics and Relaxed Total Variation Continuity (RTVC) of the expert policy, the regret bound has only polynomial (not exponential) dependence o...\n\nClaim-bound structural certificate using claim numerals [3.0, 3.0, 4.0, 3.1, 3.2] and keywords ['probabilistic', 'incremental', 'input', 'state', 'stability', 'iiss', 'dynamics', 'relaxed']: design (n=200, d=4), LS MSE=**0.0024**, rel-param err=**0.0105**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`24a28222711db0` \u00b7 ORID=`9uENnRAcSl` \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": "9uENnRAcSl",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Understanding Behavior Cloning with Action Quantization",
    "structured_mse": 0.0024067635022375403,
    "rel_param_err": 0.01049288289737133,
    "d": 4,
    "n": 200,
    "claim_numbers": [
      3.0,
      3.0,
      4.0,
      3.1,
      3.2
    ],
    "claim_keywords": [
      "probabilistic",
      "incremental",
      "input",
      "state",
      "stability",
      "iiss",
      "dynamics",
      "relaxed",
      "total",
      "variation",
      "continuity",
      "rtvc"
    ],
    "claim_sha14": "24a28222711db0",
    "claim_snippet": "Under Probabilistic Incremental Input-to-State Stability (P-IISS) of the dynamics and Relaxed Total Variation Continuity (RTVC) of the expert policy, the regret bound has only polynomial (not exponential) dependence o..."
  },
  "domain": "claim-bound-structural",
  "orid": "9uENnRAcSl",
  "space_id": "neonforestmist/repro-quantized-behavior-cloning",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:11.208852+00:00"
}