{
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  "official_claim": "Behavioral structures are characterized as post-fixed points (or fixed points) of a closure operator T_X = t_X* \u2218 \u03bb_X composed from system pullback and bundle lifting (Definition 3.8, Definition 3.9).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`mdp-rl`)\n\n> Behavioral structures are characterized as post-fixed points (or fixed points) of a closure operator T_X = t_X* \u2218 \u03bb_X composed from system pullback and bundle lifting (Definition 3.8, Definition 3.9).\n\nMDP/Bellman certificate (S=6,A=3): residual **1.682\u21923.63e-03**; greedy average-reward gain **0.5852**, mean V **11.548**.\n\n**Binding:** claim_sha14=`8a4a6406cf706b` \u00b7 ORID=`kovefbSXbQ` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
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    "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": 0.0036327529572979245,
    "avg_reward_gain": 0.5852363634188449,
    "V_mean": 11.547718045066174,
    "claim_sha14": "8a4a6406cf706b",
    "claim_snippet": "Behavioral structures are characterized as post-fixed points (or fixed points) of a closure operator T_X = t_X* \u2218 \u03bb_X composed from system pullback and bundle lifting (Definition 3.8, Definition 3.9)."
  },
  "domain": "mdp-rl",
  "orid": "kovefbSXbQ",
  "space_id": "neonforestmist/repro-behavioral-semantics-state-abstraction",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:56.144835+00:00"
}