{
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  "official_claim": "A measure-space variant DeepSets-bar-infinity (Equation 6), replacing the sum with a normalized integral under a growth condition, is proven universal on the Wasserstein space of probability measures (Theorem 4.5, Theorem 4.6).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`optimal-transport`)\n\n> A measure-space variant DeepSets-bar-infinity (Equation 6), replacing the sum with a normalized integral under a growth condition, is proven universal on the Wasserstein space of probability measures (Theorem 4.5, The...\n\nSinkhorn OT: cost **0.0409**, plan mass **1.000000**, m=24.\n\n**Binding:** claim_sha14=`5010e00e7ac3b0` \u00b7 ORID=`wRVTDcEMv8` \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": "wRVTDcEMv8",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "optimal-transport",
    "title_hint": "Any-dimensional invariant universality",
    "sinkhorn_cost": 0.040872328088434474,
    "mass": 0.9999999999681707,
    "m": 24,
    "claim_sha14": "5010e00e7ac3b0",
    "claim_snippet": "A measure-space variant DeepSets-bar-infinity (Equation 6), replacing the sum with a normalized integral under a growth condition, is proven universal on the Wasserstein space of probability measures (Theorem 4.5, The..."
  },
  "domain": "optimal-transport",
  "orid": "wRVTDcEMv8",
  "space_id": "neonforestmist/any-dimensional-invariant-universality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:00.345130+00:00"
}