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{
  "checks": [
    {
      "check": "finite performative fixed points",
      "value": 1,
      "criterion": "all",
      "passed": true
    },
    {
      "check": "positive optimal regularization",
      "value": 0.010077306820944612,
      "criterion": "> 0",
      "passed": true
    },
    {
      "check": "noise changes optimal regularization",
      "value": 99.21057050330083,
      "criterion": "> 1",
      "passed": true
    },
    {
      "check": "risk remains positive",
      "value": 0.00990099589870319,
      "criterion": "> 0",
      "passed": true
    }
  ],
  "scope": "Closed-form population fixed-point audit; over-parameterized theorem is covered by the pinned reference evidence.",
  "paper_id": "G4ve69pimc",
  "title": "Optimal Regularization for Performative Learning",
  "seed": 31072026,
  "executed_at": "2026-07-31T17:37:42.221168+00:00",
  "all_checks_passed": true,
  "environment": {
    "python": "3.10.12",
    "numpy": "1.24.4",
    "scipy": "1.14.0",
    "platform": "Linux-5.15.0-139-generic-x86_64-with-glibc2.35"
  },
  "reference_evidence": {
    "space": "ai-sherpa/optimal-reg-performative-repro",
    "sha": "02683e99272034b88a3d289c39bac8b5a694aa80",
    "relationship": "separately attributed public reference"
  }
}