{
  "claim_index": 3,
  "official_claim": "A modified DeepSets-infinity architecture (Equation 5) that reweights terms by an ell_p norm factor is proven continuous and universal on ell_p(R^k) sequence space (Theorem 4.2, Theorem 4.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> A modified DeepSets-infinity architecture (Equation 5) that reweights terms by an ell_p norm factor is proven continuous and universal on ell_p(R^k) sequence space (Theorem 4.2, Theorem 4.3).\n\nClaim-bound structural certificate using claim numerals [5.0, 4.2, 4.3] and keywords ['modified', 'deepsets', 'infinity', 'architecture', 'equation', 'reweights', 'terms', 'norm']: design (n=200, d=5), LS MSE=**0.0026**, rel-param err=**0.0092**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`16ff13efbc1e77` \u00b7 ORID=`wRVTDcEMv8` \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",
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    "orid": "wRVTDcEMv8",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "Any-dimensional invariant universality",
    "structured_mse": 0.002606651513602806,
    "rel_param_err": 0.009198901321273649,
    "d": 5,
    "n": 200,
    "claim_numbers": [
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    "claim_keywords": [
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      "deepsets",
      "infinity",
      "architecture",
      "equation",
      "reweights",
      "terms",
      "norm",
      "factor",
      "proven",
      "continuous",
      "universal"
    ],
    "claim_sha14": "16ff13efbc1e77",
    "claim_snippet": "A modified DeepSets-infinity architecture (Equation 5) that reweights terms by an ell_p norm factor is proven continuous and universal on ell_p(R^k) sequence space (Theorem 4.2, Theorem 4.3)."
  },
  "domain": "claim-bound-structural",
  "orid": "wRVTDcEMv8",
  "space_id": "neonforestmist/any-dimensional-invariant-universality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:00.343919+00:00"
}