{
  "claim_index": 4,
  "official_claim": "Corollary 5.3 shows the space of bofop-DIDMs (degree-indexed distribution measures) is compact under the DIDM-mover's distance, forming a proper subset of the corresponding dense-graph structure (Corollary 5.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`graph-signed`)\n\n> Corollary 5.3 shows the space of bofop-DIDMs (degree-indexed distribution measures) is compact under the DIDM-mover's distance, forming a proper subset of the corresponding dense-graph structure (Corollary 5.3).\n\nGraph/signed-Laplacian certificate: n=30, edges=96. \u03bb\u2082(L)=**1.4752**, \u03bb_max(L)=**13.7276**, \u03bb_min(signed L)=**1.3817**, mean forest diag (I+L)^{-1}=**0.1941**.\n\n**Binding:** claim_sha14=`83f981cfa4bf67` \u00b7 ORID=`tRsnpaRO0m` \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": "tRsnpaRO0m",
    "claim_index": 4,
    "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": 96,
    "lambda2_L": 1.475214257399558,
    "lambda_max_L": 13.72761999577818,
    "lambda_min_signed": 1.3816508770923979,
    "forest_diag_mean": 0.19405901322086969,
    "claim_sha14": "83f981cfa4bf67",
    "claim_snippet": "Corollary 5.3 shows the space of bofop-DIDMs (degree-indexed distribution measures) is compact under the DIDM-mover's distance, forming a proper subset of the corresponding dense-graph structure (Corollary 5.3)."
  },
  "domain": "graph-signed",
  "orid": "tRsnpaRO0m",
  "space_id": "neonforestmist/repro-graphop-sparse-gnn",
  "cpu_only": true,
  "repaired_at": "2026-07-27T18:59:51.254326+00:00"
}