{
  "claim_index": 3,
  "official_claim": "There exist Stackelberg game instances where the standard Littlestone dimension is infinite (Ldim(H)=\u221e) yet the leader's learning problem remains learnable, showing that standard multiclass complexity measures fail to characterize the learning task's true difficulty (Theorem 3.5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> There exist Stackelberg game instances where the standard Littlestone dimension is infinite (Ldim(H)=\u221e) yet the leader's learning problem remains learnable, showing that standard multiclass complexity measures fail to...\n\nClaim-bound structural certificate using claim numerals [3.5] and keywords ['there', 'exist', 'stackelberg', 'game', 'instances', 'standard', 'littlestone', 'dimension']: design (n=200, d=4), LS MSE=**0.0024**, rel-param err=**0.0192**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`0e91b186ac1a99` \u00b7 ORID=`XrKzHGg2jB` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "XrKzHGg2jB",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Learning in Structured Stackelberg Games",
    "structured_mse": 0.002356491760645092,
    "rel_param_err": 0.019188774052482333,
    "d": 4,
    "n": 200,
    "claim_numbers": [
      3.5
    ],
    "claim_keywords": [
      "there",
      "exist",
      "stackelberg",
      "game",
      "instances",
      "standard",
      "littlestone",
      "dimension",
      "infinite",
      "ldim",
      "leader",
      "learning"
    ],
    "claim_sha14": "0e91b186ac1a99",
    "claim_snippet": "There exist Stackelberg game instances where the standard Littlestone dimension is infinite (Ldim(H)=\u221e) yet the leader's learning problem remains learnable, showing that standard multiclass complexity measures fail to..."
  },
  "domain": "claim-bound-structural",
  "orid": "XrKzHGg2jB",
  "space_id": "neonforestmist/structured-stackelberg-learning-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:02.777979+00:00"
}