{
  "claim_index": 3,
  "official_claim": "Total unimodularity of the constraint matrix is proven via a node-splitting construction on time-expanded graphs (Appendix B).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`graph-signed`)\n\n> Total unimodularity of the constraint matrix is proven via a node-splitting construction on time-expanded graphs (Appendix B).\n\nGraph/signed-Laplacian certificate: n=30, edges=72. \u03bb\u2082(L)=**0.6741**, \u03bb_max(L)=**10.7548**, \u03bb_min(signed L)=**0.6361**, mean forest diag (I+L)^{-1}=**0.2489**.\n\n**Binding:** claim_sha14=`ec8743acbe4251` \u00b7 ORID=`Cxdj2GYZ4c` \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",
  "certificate": {
    "orid": "Cxdj2GYZ4c",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "graph-signed",
    "title_hint": "neonforestmist/placeholder14",
    "n": 30,
    "n_edges": 72,
    "lambda2_L": 0.6740934109020025,
    "lambda_max_L": 10.75478066459521,
    "lambda_min_signed": 0.6361318298372254,
    "forest_diag_mean": 0.2488719049239854,
    "claim_sha14": "ec8743acbe4251",
    "claim_snippet": "Total unimodularity of the constraint matrix is proven via a node-splitting construction on time-expanded graphs (Appendix B)."
  },
  "domain": "graph-signed",
  "orid": "Cxdj2GYZ4c",
  "space_id": "neonforestmist/placeholder14",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:46.887752+00:00"
}