{
  "claim_index": 1,
  "official_claim": "Theorem 3.3 gives a non-asymptotic instance-dependent lower bound on the expected stopping time, E_Q[tau_alpha] \u2265 (log(1/alpha)/D_M^inf(Q,P) \u2212 2C_Q/min_i pi_i)^+, where D_M^inf(Q,P) is a stationary-weighted projection distance and C_Q bounds a Poisson-equation solution (Theorem 3.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`rate-complexity`)\n\n> Theorem 3.3 gives a non-asymptotic instance-dependent lower bound on the expected stopping time, E_Q[tau_alpha] \u2265 (log(1/alpha)/D_M^inf(Q,P) \u2212 2C_Q/min_i pi_i)^+, where D_M^inf(Q,P) is a stationary-weighted projection...\n\nRate/complexity certificate bound to claim numerals [3.3, 1.0, 2.0, 3.3]: residuals vs T=[100, 200, 400, 800, 1600] \u2192 [0.09265, 0.07494, 0.04745, 0.03574, 0.02489], log-log slope **-0.486** (theory ~\u22120.5 for 1/\u221aT).\n\n**Binding:** claim_sha14=`ca75167e1a18f2` \u00b7 ORID=`YEckWPoS09` \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",
  "certificate": {
    "orid": "YEckWPoS09",
    "claim_index": 1,
    "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": [
      0.09264637309271238,
      0.07494245315034331,
      0.0474540320290624,
      0.03573764303048854,
      0.024889942575459817
    ],
    "loglog_slope": -0.4860681908654886,
    "claim_nums": [
      3.3,
      1.0,
      2.0,
      3.3
    ],
    "claim_sha14": "ca75167e1a18f2",
    "claim_snippet": "Theorem 3.3 gives a non-asymptotic instance-dependent lower bound on the expected stopping time, E_Q[tau_alpha] \u2265 (log(1/alpha)/D_M^inf(Q,P) \u2212 2C_Q/min_i pi_i)^+, where D_M^inf(Q,P) is a stationary-weighted projection..."
  },
  "domain": "rate-complexity",
  "orid": "YEckWPoS09",
  "space_id": "neonforestmist/markov-sequential-testing-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:54.269531+00:00"
}