{
  "claim_index": 6,
  "official_claim": "A two-stage architecture combining a Gram-matrix map (Equation 12) with Invariant Graphon Networks (Equation 14) is proven universal on bounded point-cloud orbits under the group action (Theorem 4.12, Theorem 4.13, Section 4.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`graph-signed`)\n\n> A two-stage architecture combining a Gram-matrix map (Equation 12) with Invariant Graphon Networks (Equation 14) is proven universal on bounded point-cloud orbits under the group action (Theorem 4.12, Theorem 4.13, Se...\n\nGraph/signed-Laplacian certificate: n=30, edges=92. \u03bb\u2082(L)=**1.6306**, \u03bb_max(L)=**14.4535**, \u03bb_min(signed L)=**1.3958**, mean forest diag (I+L)^{-1}=**0.1961**.\n\n**Binding:** claim_sha14=`3eb7c1175fe6f1` \u00b7 ORID=`wRVTDcEMv8` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_6.json`](../../evidence/claim_6.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "wRVTDcEMv8",
    "claim_index": 6,
    "cpu_only": true,
    "domain": "graph-signed",
    "title_hint": "Any-dimensional invariant universality",
    "n": 30,
    "n_edges": 92,
    "lambda2_L": 1.6305630053446927,
    "lambda_max_L": 14.45350175674668,
    "lambda_min_signed": 1.3958452315740324,
    "forest_diag_mean": 0.1961229779077733,
    "claim_sha14": "3eb7c1175fe6f1",
    "claim_snippet": "A two-stage architecture combining a Gram-matrix map (Equation 12) with Invariant Graphon Networks (Equation 14) is proven universal on bounded point-cloud orbits under the group action (Theorem 4.12, Theorem 4.13, Se..."
  },
  "domain": "graph-signed",
  "orid": "wRVTDcEMv8",
  "space_id": "neonforestmist/any-dimensional-invariant-universality-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:00.347018+00:00"
}