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        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
        "cost": "Supplied USD basis; router overhead applies to every utility-routed request and to neither always-arm bypass.",
        "lambda": "nonnegative; exact crossings, intervening intervals and the cost-minimizing limit",
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        "selection": "least calibration cost, then smaller signed quality loss, router bypass, smaller lambda, always-strong bypass tie",
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        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
        "cost": "Supplied USD basis; router overhead applies to every utility-routed request and to neither always-arm bypass.",
        "lambda": "nonnegative; exact crossings, intervening intervals and the cost-minimizing limit",
        "quality": "Empirical signed gap versus always strong; rescues offset regressions. Not a future-risk guarantee.",
        "rule": "strong iff (p_strong-p_cheap) - lambda*(expected_USD_strong-expected_USD_cheap) >= 0",
        "selection": "least calibration cost, then smaller signed quality loss, router bypass, smaller lambda, always-strong bypass tie",
        "tie": "strong on equal utility; at the cost limit, lower expected cost then higher probability then strong",
        "unknown_router_cost": "None means unpriced: select by answer costs and report no native net-cost claim."
      },
      "randomized_hull_candidate_ids": [
        1,
        385,
        333,
        97,
        0
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      "randomized_hull_interpretation": "Mixtures between saved rules; not additional deterministic policies",
      "router_kind": "native",
      "score_sha256": "f9a3fdc554776f2fe77a4de2cbcc45ff1f83cad8a954bd5e8e78b2b825e09365",
      "selection_cost_basis": "answer USD only; router unpriced"
    },
    "embedding": {
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        "strong"
      ],
      "candidates": [
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        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
        "cost": "Supplied USD basis; router overhead applies to every utility-routed request and to neither always-arm bypass.",
        "lambda": "nonnegative; exact crossings, intervening intervals and the cost-minimizing limit",
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        "selection": "least calibration cost, then smaller signed quality loss, router bypass, smaller lambda, always-strong bypass tie",
        "tie": "strong on equal utility; at the cost limit, lower expected cost then higher probability then strong",
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      "n": 385,
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        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
        "cost": "Supplied USD basis; router overhead applies to every utility-routed request and to neither always-arm bypass.",
        "lambda": "nonnegative; exact crossings, intervening intervals and the cost-minimizing limit",
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        "rule": "strong iff (p_strong-p_cheap) - lambda*(expected_USD_strong-expected_USD_cheap) >= 0",
        "selection": "least calibration cost, then smaller signed quality loss, router bypass, smaller lambda, always-strong bypass tie",
        "tie": "strong on equal utility; at the cost limit, lower expected cost then higher probability then strong",
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        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
        "cost": "Supplied USD basis; router overhead applies to every utility-routed request and to neither always-arm bypass.",
        "lambda": "nonnegative; exact crossings, intervening intervals and the cost-minimizing limit",
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        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
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      ],
      "metadata_assisted": false,
      "model_sha256": "ceeebb0333508c1288cde679a43902c69865d735b2dfcc7a03b3f892781d760c",
      "n": 385,
      "no_preferred_quality_target": true,
      "protocol": {
        "arithmetic": "Float64 inputs are exact for utility/cost comparison; gap targets use their decimal spelling. No rounding tolerance changes ties.",
        "cost": "Supplied USD basis; router overhead applies to every utility-routed request and to neither always-arm bypass.",
        "lambda": "nonnegative; exact crossings, intervening intervals and the cost-minimizing limit",
        "quality": "Empirical signed gap versus always strong; rescues offset regressions. Not a future-risk guarantee.",
        "rule": "strong iff (p_strong-p_cheap) - lambda*(expected_USD_strong-expected_USD_cheap) >= 0",
        "selection": "least calibration cost, then smaller signed quality loss, router bypass, smaller lambda, always-strong bypass tie",
        "tie": "strong on equal utility; at the cost limit, lower expected cost then higher probability then strong",
        "unknown_router_cost": "None means unpriced: select by answer costs and report no native net-cost claim."
      },
      "randomized_hull_candidate_ids": [
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      ],
      "randomized_hull_interpretation": "Mixtures between saved rules; not additional deterministic policies",
      "router_kind": "cpu",
      "score_sha256": "f97c8eb2b51e1cc71fb8972fde825f48a58380ea69896c53e90ac0da35c91a48",
      "selection_cost_basis": "answer USD only; router unpriced"
    }
  },
  "pair_sha256": "79995e7f2274c97eee847d46276e1b0a48d396533bba1c4b768667d209d30ead",
  "plan_sha256": "3f0c8cbb3ab74a59e8f195d3412718f0a11905b7b46225951d272c5804a0d36f",
  "protocol": {
    "bootstrap": {
      "draws": 2000,
      "seed": 89,
      "unit": "paired whole family within task, fixed observed task weights"
    },
    "cost": "Selected answer USD plus validated singleton encoder fee when applicable; other hosting unpriced, no zero imputation",
    "final": "Replay saved calibration candidates only; never select on final quality",
    "format": "bbeh-frontier-evaluation-v1",
    "interval_scope": "Pointwise for calibration-frontier rules, conditional on observed tasks; no simultaneous curve guarantee",
    "population": "Uniform per retained question; exact original source roles/families",
    "random": "Analytic expected mixtures; p for each matched calibration-budget comparator is frozen on calibration",
    "thresholds": "All calibration crossings/intervals, cost limit and always-arm bypasses; no preferred gap target"
  },
  "random": {
    "analytic_expectation": true,
    "strong_probability_range": [
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  },
  "source_plan_sha256": "b15e9c2d9db284fe170e0460550f02fc2cb48f2b9234b697d181716264984a53"
}