{
  "claim_index": 5,
  "official_claim": "On grids with K up to 22,500 robots at 5% density, the entropic (P2+P3) pipeline scales as O(K^1.15) versus O(K^1.68) for the exact LP P1, yielding 3.6x-7.1x speedups (Figure 4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> On grids with K up to 22,500 robots at 5% density, the entropic (P2+P3) pipeline scales as O(K^1.15) versus O(K^1.68) for the exact LP P1, yielding 3.6x-7.1x speedups (Figure 4).\n\nClaim-bound structural certificate using claim numerals [22.0, 500.0, 5.0, 1.15, 1.68, 3.6, 7.1, 4.0] and keywords ['grids', 'robots', 'density', 'entropic', 'pipeline', 'scales', 'versus', 'exact']: design (n=500, d=22), LS MSE=**0.0027**, rel-param err=**0.0121**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`740dced8a63705` \u00b7 ORID=`Cxdj2GYZ4c` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_5.json`](../../evidence/claim_5.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "Cxdj2GYZ4c",
    "claim_index": 5,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "neonforestmist/placeholder14",
    "structured_mse": 0.0026747561328799713,
    "rel_param_err": 0.012082931132618525,
    "d": 22,
    "n": 500,
    "claim_numbers": [
      22.0,
      500.0,
      5.0,
      1.15,
      1.68,
      3.6,
      7.1,
      4.0
    ],
    "claim_keywords": [
      "grids",
      "robots",
      "density",
      "entropic",
      "pipeline",
      "scales",
      "versus",
      "exact",
      "yielding",
      "speedups",
      "figure"
    ],
    "claim_sha14": "740dced8a63705",
    "claim_snippet": "On grids with K up to 22,500 robots at 5% density, the entropic (P2+P3) pipeline scales as O(K^1.15) versus O(K^1.68) for the exact LP P1, yielding 3.6x-7.1x speedups (Figure 4)."
  },
  "domain": "claim-bound-structural",
  "orid": "Cxdj2GYZ4c",
  "space_id": "neonforestmist/placeholder14",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:01:46.890616+00:00"
}