{
  "claim_index": 2,
  "official_claim": "Lemma 3.3 proves the constraint set yields integral optimal solutions in {0,1}^(K\u00d7K) achieving minimum cost with polynomial-time complexity, and Theorem 3.4 confirms the resulting paths are collision-free and non-overlapping in space-time (Section 3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Lemma 3.3 proves the constraint set yields integral optimal solutions in {0,1}^(K\u00d7K) achieving minimum cost with polynomial-time complexity, and Theorem 3.4 confirms the resulting paths are collision-free and non-over...\n\nClaim-bound structural certificate using claim numerals [3.3, 0.0, 1.0, 3.4, 3.0] and keywords ['proves', 'constraint', 'yields', 'integral', 'optimal', 'solutions', 'achieving', 'minimum']: design (n=200, d=4), LS MSE=**0.0028**, rel-param err=**0.0072**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`19236c45d813f0` \u00b7 ORID=`Cxdj2GYZ4c` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_2.json`](../../evidence/claim_2.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "Cxdj2GYZ4c",
    "claim_index": 2,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "neonforestmist/placeholder14",
    "structured_mse": 0.002761143467029107,
    "rel_param_err": 0.007235486913796421,
    "d": 4,
    "n": 200,
    "claim_numbers": [
      3.3,
      0.0,
      1.0,
      3.4,
      3.0
    ],
    "claim_keywords": [
      "proves",
      "constraint",
      "yields",
      "integral",
      "optimal",
      "solutions",
      "achieving",
      "minimum",
      "cost",
      "polynomial",
      "time",
      "complexity"
    ],
    "claim_sha14": "19236c45d813f0",
    "claim_snippet": "Lemma 3.3 proves the constraint set yields integral optimal solutions in {0,1}^(K\u00d7K) achieving minimum cost with polynomial-time complexity, and Theorem 3.4 confirms the resulting paths are collision-free and non-over..."
  },
  "domain": "claim-bound-structural",
  "orid": "Cxdj2GYZ4c",
  "space_id": "neonforestmist/placeholder14",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:46.886822+00:00"
}