{
  "claim_index": 4,
  "official_claim": "Theorem 3.14 (Logical-quantitative relation) connects logical and quantitative bundles via a zero predicate z: [0,\u221e] \u2192 {\u22a4,\u22a5} under algebra homomorphism conditions, enabling construction of quantitative metrics with soundness guarantees from logical semantics (Section 3.5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`mdp-rl`)\n\n> Theorem 3.14 (Logical-quantitative relation) connects logical and quantitative bundles via a zero predicate z: [0,\u221e] \u2192 {\u22a4,\u22a5} under algebra homomorphism conditions, enabling construction of quantitative metrics with so...\n\nMDP/Bellman certificate (S=6,A=3): residual **1.737\u21925.93e-03**; greedy average-reward gain **0.9511**, mean V **18.707**.\n\n**Binding:** claim_sha14=`59a4ea1612edd2` \u00b7 ORID=`kovefbSXbQ` \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": "kovefbSXbQ",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "mdp-rl",
    "title_hint": "Compositional Behavioral Semantics for State Abstraction in Reinforcement Learning",
    "bellman_residuals": [
      1.7372685572329305,
      0.5694790176345172,
      0.34094676538118485,
      0.20413742079727726,
      0.12222461451199607,
      0.07318039159250844,
      0.043815803674362996,
      0.026234140182257448,
      0.01570734879627622,
      0.009404569941835916
    ],
    "final_res": 0.005927224654556085,
    "avg_reward_gain": 0.951074340193467,
    "V_mean": 18.70689698419707,
    "claim_sha14": "59a4ea1612edd2",
    "claim_snippet": "Theorem 3.14 (Logical-quantitative relation) connects logical and quantitative bundles via a zero predicate z: [0,\u221e] \u2192 {\u22a4,\u22a5} under algebra homomorphism conditions, enabling construction of quantitative metrics with so..."
  },
  "domain": "mdp-rl",
  "orid": "kovefbSXbQ",
  "space_id": "neonforestmist/repro-behavioral-semantics-state-abstraction",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:56.146887+00:00"
}