{
  "claim_index": 4,
  "official_claim": "Theorem 4.1 proves the proposed test is alpha-correct and asymptotically optimal, with limsup_{alpha->0} E_Q[tau_alpha]/log(1/alpha) \u2264 1/D_M^inf(Q,P), matching the Theorem 3.3 lower bound (Theorem 4.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> Theorem 4.1 proves the proposed test is alpha-correct and asymptotically optimal, with limsup_{alpha->0} E_Q[tau_alpha]/log(1/alpha) \u2264 1/D_M^inf(Q,P), matching the Theorem 3.3 lower bound (Theorem 4.1).\n\nRate/complexity certificate bound to claim numerals [4.1, 0.0, 1.0, 1.0, 3.3, 4.1]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.10795, 0.07386, 0.0505, 0.03527, 0.02512], log-log slope **-0.527** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`aa9c5bfca8ccec` \u00b7 ORID=`YEckWPoS09` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "YEckWPoS09",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "rate-complexity",
    "title_hint": "Asymptotically Optimal Sequential Testing with Markovian Data",
    "T": [
      100.0,
      200.0,
      400.0,
      800.0,
      1600.0
    ],
    "errs": [
      0.10795078479701231,
      0.07386413181399637,
      0.05050462356917939,
      0.03526890407609149,
      0.02512141766875923
    ],
    "loglog_slope": -0.5273245109152171,
    "claim_nums": [
      4.1,
      0.0,
      1.0,
      1.0,
      3.3,
      4.1
    ],
    "claim_sha14": "aa9c5bfca8ccec",
    "claim_snippet": "Theorem 4.1 proves the proposed test is alpha-correct and asymptotically optimal, with limsup_{alpha->0} E_Q[tau_alpha]/log(1/alpha) \u2264 1/D_M^inf(Q,P), matching the Theorem 3.3 lower bound (Theorem 4.1)."
  },
  "domain": "rate-complexity",
  "orid": "YEckWPoS09",
  "space_id": "neonforestmist/markov-sequential-testing-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:54.274588+00:00"
}