{
  "claim_index": 1,
  "official_claim": "Theorem 4.3 decomposes the task-t prediction error into an irreducible error term, a variance term scaling as O(M/(t^2(M+1)^2)) that decreases with more in-context examples, and a bias term measuring deviation \u2016(1/t)\u2211_s w_s - w_t\u2016^2 from task dissimilarity (Theorem 4.3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`continual-learning`)\n\n> Theorem 4.3 decomposes the task-t prediction error into an irreducible error term, a variance term scaling as O(M/(t^2(M+1)^2)) that decreases with more in-context examples, and a bias term measuring deviation \u2016(1/t)\u2211...\n\nContinual GD certificate: 5 tasks, d=12. Mean MSE over tasks seen: [0.0016, 6.5794, 13.9602, 20.8476, 19.6852].\n\n**Binding:** claim_sha14=`e88f29e7e4336c` \u00b7 ORID=`68AMoK2YNk` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "68AMoK2YNk",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "continual-learning",
    "title_hint": "Understanding Generalization and Forgetting in In-Context Continual Learning",
    "tasks": 5,
    "path": [
      {
        "task": 1,
        "mean_mse_so_far": 0.0015538365906726422,
        "last": 0.0015538365906726422
      },
      {
        "task": 2,
        "mean_mse_so_far": 6.579395304272035,
        "last": 0.003135851175613858
      },
      {
        "task": 3,
        "mean_mse_so_far": 13.960247655358247,
        "last": 0.004559771142191721
      },
      {
        "task": 4,
        "mean_mse_so_far": 20.84762610416157,
        "last": 0.0009346137012680052
      },
      {
        "task": 5,
        "mean_mse_so_far": 19.685166383427394,
        "last": 0.00218976100866812
      }
    ],
    "final_mean_mse": 19.685166383427394,
    "claim_sha14": "e88f29e7e4336c",
    "claim_snippet": "Theorem 4.3 decomposes the task-t prediction error into an irreducible error term, a variance term scaling as O(M/(t^2(M+1)^2)) that decreases with more in-context examples, and a bias term measuring deviation \u2016(1/t)\u2211..."
  },
  "domain": "continual-learning",
  "orid": "68AMoK2YNk",
  "space_id": "neonforestmist/icl-continual-learning-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:05:50.603461+00:00"
}