{
  "kind": "authored-hypothetical-arithmetic",
  "executedAt": "2026-11-05T09:07:51.439127+00:00",
  "runtime": {
    "python": "3.14.5"
  },
  "scope": "No training, generation, tokenizer, model accuracy, cost or speed measurements. Effective scored completion-token lengths assumed; no masked or missing-signal tokens.",
  "domains": [
    "calculation",
    "code",
    "format"
  ],
  "cases": [
    {
      "id": "baseline",
      "promptCounts": [
        40,
        40,
        20
      ],
      "meanScoredTokens": [
        2000,
        4000,
        200
      ],
      "tokenCounts": [
        80000,
        160000,
        4000
      ],
      "tokenShares": [
        0.32786885245901637,
        0.6557377049180327,
        0.01639344262295082
      ]
    },
    {
      "id": "equal-length",
      "promptCounts": [
        40,
        40,
        20
      ],
      "meanScoredTokens": [
        2000,
        2000,
        2000
      ],
      "tokenShares": [
        0.4,
        0.4,
        0.2
      ]
    },
    {
      "id": "code-length-doubles",
      "promptCounts": [
        40,
        40,
        20
      ],
      "meanScoredTokens": [
        2000,
        8000,
        200
      ],
      "tokenShares": [
        0.19801980198019803,
        0.7920792079207921,
        0.009900990099009901
      ]
    },
    {
      "id": "target-format-20-percent",
      "promptProbabilities": [
        0.10526315789473684,
        0.10526315789473684,
        0.7894736842105263
      ],
      "meanScoredTokens": [
        2000,
        4000,
        200
      ],
      "tokenShares": [
        0.26666666666666666,
        0.5333333333333333,
        0.2
      ],
      "limit": "Expectation under fixed lengths, not exact batch quota; not a training recommendation."
    },
    {
      "id": "window-aggregation",
      "formatTokens": [
        50,
        0
      ],
      "allTokens": [
        100,
        900
      ],
      "correctShare": 0.05,
      "incorrectMeanOfShares": 0.25
    }
  ]
}