{
  "generated_at_utc": "2026-10-08T23:59:50.425573+00:00",
  "cases": [
    {
      "case": "nilpotent_sharp",
      "grid": 32,
      "elapsed_seconds": 0.09187699999893084,
      "charged_arithmetic": 84404,
      "direct_arithmetic_at_completion": 231,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "11/5",
      "supremum_upper": "18365645/16777216",
      "source_conditional_upper": "18365645/8388608",
      "prior_upper": "1774121307/671088640",
      "source_conditional_meets": true,
      "prior_meets": false
    },
    {
      "case": "normal_segment",
      "grid": 8,
      "elapsed_seconds": 0.0031835830013733357,
      "charged_arithmetic": 2633,
      "direct_arithmetic_at_completion": 222,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "2",
      "supremum_upper": "2",
      "source_conditional_upper": "4",
      "prior_upper": "483/100",
      "source_conditional_meets": false,
      "prior_meets": false
    },
    {
      "case": "complex_point",
      "grid": 8,
      "elapsed_seconds": 0.0008289169927593321,
      "charged_arithmetic": 562,
      "direct_arithmetic_at_completion": 52,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "1",
      "supremum_upper": "1",
      "source_conditional_upper": "2",
      "prior_upper": "483/200",
      "source_conditional_meets": false,
      "prior_meets": false
    },
    {
      "case": "constant_matrix",
      "grid": 8,
      "elapsed_seconds": 0.020476833000429906,
      "charged_arithmetic": 16669,
      "direct_arithmetic_at_completion": 815,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "2",
      "supremum_upper": "2",
      "source_conditional_upper": "4",
      "prior_upper": "483/100",
      "source_conditional_meets": false,
      "prior_meets": false
    },
    {
      "case": "matrix_coefficients",
      "grid": 8,
      "elapsed_seconds": 0.02464233299542684,
      "charged_arithmetic": 21037,
      "direct_arithmetic_at_completion": 1301,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "10",
      "supremum_upper": "951703870966049/281474976710656",
      "source_conditional_upper": "951703870966049/140737488355328",
      "prior_upper": "459672969676601667/56294995342131200",
      "source_conditional_meets": true,
      "prior_meets": true
    },
    {
      "case": "zero",
      "grid": 8,
      "elapsed_seconds": 0.0031412919925060123,
      "charged_arithmetic": 2722,
      "direct_arithmetic_at_completion": 1109,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "1/100",
      "supremum_upper": "0",
      "source_conditional_upper": "0",
      "prior_upper": "0",
      "source_conditional_meets": true,
      "prior_meets": true
    },
    {
      "case": "imaginary_hermitian",
      "grid": 8,
      "elapsed_seconds": 0.01397191699652467,
      "charged_arithmetic": 10773,
      "direct_arithmetic_at_completion": 297,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "2",
      "supremum_upper": "129/64",
      "source_conditional_upper": "129/32",
      "prior_upper": "62307/12800",
      "source_conditional_meets": false,
      "prior_meets": false
    },
    {
      "case": "nilpotent_cancellation",
      "grid": 8,
      "elapsed_seconds": 0.02062754100188613,
      "charged_arithmetic": 16427,
      "direct_arithmetic_at_completion": 327,
      "direct_finite_norm_at_most_tolerance": true,
      "tolerance": "1/100",
      "supremum_upper": "82297259229095/17592186044416",
      "source_conditional_upper": "82297259229095/8796093022208",
      "prior_upper": "7949915241530577/703687441776640",
      "source_conditional_meets": false,
      "prior_meets": false
    }
  ],
  "scope": "Eight generated exact finite cases; elapsed times are one local run, not a performance/customer benchmark. Direct checks do not require source theorem. Source constant two remains conditional; published prior constant rounds upward."
}