{
  "mode": "correct subtraction",
  "working_decimal_digits": 50,
  "stability_decimal_digits": 70,
  "r": "1/2 fixed",
  "parameter": "u=log(b), real b>0",
  "background": "positive-H homogeneous S3 family; zero flavor mass",
  "integral_Hessian": "1.233700550136169827354",
  "tau_RR": "0.25",
  "high_precision_comparisons": 5,
  "comparison_tolerance": "1e-35",
  "all_high_precision_comparisons_pass": true,
  "finite_integral_cutoffs": [
    {
      "L": 12,
      "integral_to_L": "1.233688261711470335683",
      "analytic_tail_upper": "0.00001228842470712032408343"
    },
    {
      "L": 24,
      "integral_to_L": "1.233700550060667136469",
      "analytic_tail_upper": "7.550269088558195503301e-11"
    },
    {
      "L": 48,
      "integral_to_L": "1.233700550136169827351",
      "analytic_tail_upper": "2.850328165481870212571e-21"
    }
  ],
  "literal_mode_shells": [
    {
      "K": 8,
      "finite_sum": "1.165005437938156891637",
      "tail_interval_lower": "1.231902785112320674797",
      "tail_interval_upper": "1.23582435373977165519"
    },
    {
      "K": 32,
      "finite_sum": "1.215750618640762435509",
      "tail_interval_lower": "1.233580993394214112038",
      "tail_interval_upper": "1.233825193638414356238"
    },
    {
      "K": 128,
      "finite_sum": "1.229160971484948984059",
      "tail_interval_lower": "1.233692960361893878506",
      "tail_interval_upper": "1.233708219383790574927"
    }
  ],
  "physical_finite_differences": [
    {
      "delta": "0.1",
      "central": "1.237127720332114383221",
      "richardson": "1.233698606953733187985",
      "central_error": "0.003427170195944555866326",
      "richardson_error": "0.000001943182436639369694154"
    },
    {
      "delta": "0.05",
      "central": "1.234555885298328486794",
      "richardson": "1.233700428565058860514",
      "central_error": "0.0008553351621586594393109",
      "richardson_error": "1.215711109668403428759e-7"
    },
    {
      "delta": "0.025",
      "central": "1.233914292748376267084",
      "richardson": "1.23370054253605486412",
      "central_error": "0.0002137426122064397295706",
      "richardson_error": "7.600114963234355252728e-9"
    }
  ],
  "finite_source_path_comparison": [
    {
      "log_b": "0.2",
      "fixed_R_minus_fixed_shift": "0.0005667504627467425162506"
    },
    {
      "log_b": "0.1",
      "fixed_R_minus_fixed_shift": "0.00003583836073117432344705"
    }
  ],
  "intentional_error_detected": false,
  "precision_note": "Tail bounds are analytic; quadrature is precision-tested, not interval-certified. Finite differences retain truncation errors."
}