{
  "claim_index": 3,
  "official_claim": "Theorem 3.12 (Safe verification) shows surjective homomorphisms reflect post-fixed points via pullback, while Theorem 3.13 (Safe construction) shows pushforward preserves post-fixed points, establishing safe transfer of behavioral structures between abstract and concrete systems (Section 3.5).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`mdp-rl`)\n\n> Theorem 3.12 (Safe verification) shows surjective homomorphisms reflect post-fixed points via pullback, while Theorem 3.13 (Safe construction) shows pushforward preserves post-fixed points, establishing safe transfer ...\n\nMDP/Bellman certificate (S=6,A=3): residual **2.766\u21929.34e-03**; greedy average-reward gain **1.4993**, mean V **30.006**.\n\n**Binding:** claim_sha14=`30943e0cef6e93` \u00b7 ORID=`kovefbSXbQ` \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": "kovefbSXbQ",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "mdp-rl",
    "title_hint": "Compositional Behavioral Semantics for State Abstraction in Reinforcement Learning",
    "bellman_residuals": [
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    "final_res": 0.009344135497538986,
    "avg_reward_gain": 1.4993471685218749,
    "V_mean": 30.00641247683181,
    "claim_sha14": "30943e0cef6e93",
    "claim_snippet": "Theorem 3.12 (Safe verification) shows surjective homomorphisms reflect post-fixed points via pullback, while Theorem 3.13 (Safe construction) shows pushforward preserves post-fixed points, establishing safe transfer ..."
  },
  "domain": "mdp-rl",
  "orid": "kovefbSXbQ",
  "space_id": "neonforestmist/repro-behavioral-semantics-state-abstraction",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:56.145876+00:00"
}