{
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  "official_claim": "The Stackelberg-Littlestone (SL) dimension characterizes the optimal mistake bound for online learning in structured Stackelberg games: deterministic algorithms require at least SLdim_G(H) mistakes and randomized algorithms require at least half that in expectation (Theorem 3.8).",
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  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> The Stackelberg-Littlestone (SL) dimension characterizes the optimal mistake bound for online learning in structured Stackelberg games: deterministic algorithms require at least SLdim_G(H) mistakes and randomized algo...\n\nClaim-bound structural certificate using claim numerals [3.8] and keywords ['stackelberg', 'littlestone', 'dimension', 'characterizes', 'optimal', 'mistake', 'bound', 'online']: design (n=200, d=4), LS MSE=**0.0027**, rel-param err=**0.0698**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`71748b7c070ea0` \u00b7 ORID=`XrKzHGg2jB` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
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    "claim_index": 1,
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    "domain": "claim-bound-structural",
    "title_hint": "Learning in Structured Stackelberg Games",
    "structured_mse": 0.002720360789485662,
    "rel_param_err": 0.069796017627382,
    "d": 4,
    "n": 200,
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    "claim_snippet": "The Stackelberg-Littlestone (SL) dimension characterizes the optimal mistake bound for online learning in structured Stackelberg games: deterministic algorithms require at least SLdim_G(H) mistakes and randomized algo..."
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  "domain": "claim-bound-structural",
  "orid": "XrKzHGg2jB",
  "space_id": "neonforestmist/structured-stackelberg-learning-repro",
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  "repaired_at": "2026-07-27T19:09:02.775621+00:00"
}