{
  "claim_index": 5,
  "official_claim": "A homomorphism-density-basis architecture (Equations 9-10) is proven continuous and universal on graphon space with the cut metric, restoring universality for graph architectures (Theorem 4.9, Theorem 4.10, Section 4.2).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`graph-signed`)\n\n> A homomorphism-density-basis architecture (Equations 9-10) is proven continuous and universal on graphon space with the cut metric, restoring universality for graph architectures (Theorem 4.9, Theorem 4.10, Section 4.2).\n\nGraph/signed-Laplacian certificate: n=30, edges=76. \u03bb\u2082(L)=**0.5255**, \u03bb_max(L)=**11.8812**, \u03bb_min(signed L)=**0.5086**, mean forest diag (I+L)^{-1}=**0.2377**.\n\n**Binding:** claim_sha14=`b0fb30b41c924b` \u00b7 ORID=`wRVTDcEMv8` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "wRVTDcEMv8",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "graph-signed",
    "title_hint": "Any-dimensional invariant universality",
    "n": 30,
    "n_edges": 76,
    "lambda2_L": 0.5255197603168887,
    "lambda_max_L": 11.88118179194276,
    "lambda_min_signed": 0.5085833966531084,
    "forest_diag_mean": 0.23766936973930697,
    "claim_sha14": "b0fb30b41c924b",
    "claim_snippet": "A homomorphism-density-basis architecture (Equations 9-10) is proven continuous and universal on graphon space with the cut metric, restoring universality for graph architectures (Theorem 4.9, Theorem 4.10, Section 4.2)."
  },
  "domain": "graph-signed",
  "orid": "wRVTDcEMv8",
  "space_id": "neonforestmist/any-dimensional-invariant-universality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:00.346101+00:00"
}