cap round fibre law.json

{
  "law": "For y below Q(c), fibre is {L>=0:Q(L)=y}, provided nonempty below c. For y=Q(c), fibre is all L>=max(0,Q(c)-2). Values y>Q(c) are impossible.",
  "proof": "Below the capacity cell clipping cannot affect the value. At the capacity cell, all uncapped values in that cell and every capped input merge.",
  "examples": [
    {
      "c": 10,
      "Q_c": 10,
      "first_input": 8,
      "finite_scan": [
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30
      ]
    },
    {
      "c": 11,
      "Q_c": 10,
      "first_input": 8,
      "finite_scan": [
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30
      ]
    },
    {
      "c": 12,
      "Q_c": 10,
      "first_input": 8,
      "finite_scan": [
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30
      ]
    },
    {
      "c": 13,
      "Q_c": 15,
      "first_input": 13,
      "finite_scan": [
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30
      ]
    },
    {
      "c": 14,
      "Q_c": 15,
      "first_input": 13,
      "finite_scan": [
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30
      ]
    }
  ],
  "scope": "integer nonnegativeL,c; nearest5; no upper baseline bound supplied"
}