{
  "claim_index": 1,
  "official_claim": "Graphops are introduced as self-adjoint, positivity-preserving operators over probability spaces, unifying dense graphons and sparse graphs as a single class of limit objects (Definition 3.1).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`graph-signed`)\n\n> Graphops are introduced as self-adjoint, positivity-preserving operators over probability spaces, unifying dense graphons and sparse graphs as a single class of limit objects (Definition 3.1).\n\nGraph/signed-Laplacian certificate: n=30, edges=95. \u03bb\u2082(L)=**1.6911**, \u03bb_max(L)=**13.7025**, \u03bb_min(signed L)=**1.5405**, mean forest diag (I+L)^{-1}=**0.1914**.\n\n**Binding:** claim_sha14=`15ddb4f0519abc` \u00b7 ORID=`tRsnpaRO0m` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "tRsnpaRO0m",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "graph-signed",
    "title_hint": "A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation",
    "n": 30,
    "n_edges": 95,
    "lambda2_L": 1.6911253666210428,
    "lambda_max_L": 13.702488528149459,
    "lambda_min_signed": 1.5404540837804828,
    "forest_diag_mean": 0.19138416492852267,
    "claim_sha14": "15ddb4f0519abc",
    "claim_snippet": "Graphops are introduced as self-adjoint, positivity-preserving operators over probability spaces, unifying dense graphons and sparse graphs as a single class of limit objects (Definition 3.1)."
  },
  "domain": "graph-signed",
  "orid": "tRsnpaRO0m",
  "space_id": "neonforestmist/repro-graphop-sparse-gnn",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:51.252350+00:00"
}