{
  "rows": [
    {
      "row": 5,
      "remaining": 785,
      "next_capacity": 785,
      "next_lifespan": 365
    },
    {
      "row": 7,
      "remaining": 653,
      "next_capacity": 653,
      "next_lifespan": 653
    },
    {
      "row": 8,
      "remaining": 601,
      "next_capacity": 601,
      "next_lifespan": null
    }
  ],
  "theorem": "If L_i=c_i and c_i=b_i+c_next, then L_i-b_i=c_next. This equals L_next precisely when that next life also meets capacity.",
  "source_example": "Methuselah remainder653 equals Lamech653; Jared remainder785 is Enoch capacity, not Enoch365"
}