FA-64166 / Medication dosing calculations / Open access

Percentage taper schedule rounded to tablets: rounding stall guard · case 01

The taper stalls at 10 mg because 10% rounds back to the same dose.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The stall guard triggers only when rounding increases the dose, not when it leaves it unchanged.

VERIFIED REPAIR

Whenever rounding fails to lower the dose, subtract one tablet_mg.

Unsuccessful approach: Subtracting 1 mg ignores tablet granularity and produces undispensable doses.

Case contract

Input {start_mg, step_pct, every_days, min_mg, tablet_mg, days}. Day 0 uses start_mg. On each day d > 0 with d % every_days == 0 (while the dose is non-zero), the dose becomes current*(100-step_pct)/100 rounded half-up to a tablet_mg multiple; if that does not lower the dose, it is lowered by one tablet_mg instead; a result below min_mg stops the taper (0). Return the list of daily doses for days days.

Why this case matters

Tapers compound percentage reductions with dispensing granularity; stepping day, rounding and stop rules are distinct decisions.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    dose = Fraction(str(x['start_mg']))
    t = Fraction(str(x['tablet_mg']))
    out = []
    for day in range(x['days']):
        if day > 0 and day % x['every_days'] == 0 and dose > 0:
            new = dose * (100 - x['step_pct']) / 100
            new = math.floor(new / t + Fraction(1, 2)) * t
            if new > dose:
                new = dose - t
            dose = new if new >= Fraction(str(x['min_mg'])) else Fraction(0)
        out.append(float(dose))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 11},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 4},
   [50.0, 50.0, 45.0, 45.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 6},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 8},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 12},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [50.0, 50.0, 45.0, 45.0, 40.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 1, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 7.5, 5.0, 2.5, 0.0, 0.0, 0.0, 0.0]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 7},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 5.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 9},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 13},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 6},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 8},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 10},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 14},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 7},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0, 35.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 1, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 7.5, 5.0, 2.5, 0.0, 0.0, 0.0, 0.0]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 9},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 5.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 11},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0, 6.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 15},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0, 20.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 8},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0, 35.0, 35.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 10},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 12},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0, 6.0, 6.0])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
weekly 25 percent taper	`[60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]`	`[60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]`	Passed
half-tablet boundary rounds up	`[50.0, 50.0, 45.0, 45.0]`	`[50.0, 50.0, 45.0, 45.0]`	Passed
rounding stall forces one tablet step	`[10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0]`	`[10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]`	Failed
stops below minimum	`[20.0, 20.0, 10.0, 10.0, 0.0, 0.0]`	`[20.0, 20.0, 10.0, 10.0, 0.0, 0.0]`	Passed
dose equal to minimum continues	`[40.0, 20.0, 10.0, 0.0, 0.0]`	`[40.0, 20.0, 10.0, 0.0, 0.0]`	Passed
fractional tablet percentages	`[30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0]`	`[30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0]`	Passed

SHA-256 / 8839ce700845f651756a703c2d895a99db3e9eb2a8e59d0385e39096c5fae2b3

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    dose = Fraction(str(x['start_mg']))
    t = Fraction(str(x['tablet_mg']))
    out = []
    for day in range(x['days']):
        if day > 0 and day % x['every_days'] == 0 and dose > 0:
            new = dose * (100 - x['step_pct']) / 100
            new = math.floor(new / t + Fraction(1, 2)) * t
            if new >= dose:
                new = dose - 1
            dose = new if new >= Fraction(str(x['min_mg'])) else Fraction(0)
        out.append(float(dose))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 11},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 4},
   [50.0, 50.0, 45.0, 45.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 6},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 8},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 12},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [50.0, 50.0, 45.0, 45.0, 40.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 1, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 7.5, 5.0, 2.5, 0.0, 0.0, 0.0, 0.0]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 7},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 5.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 9},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 13},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 6},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 8},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 10},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 14},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 7},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0, 35.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 1, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 7.5, 5.0, 2.5, 0.0, 0.0, 0.0, 0.0]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 9},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 5.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 11},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0, 6.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 15},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0, 20.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 8},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0, 35.0, 35.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 10},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 12},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0, 6.0, 6.0])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
weekly 25 percent taper	`[60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]`	`[60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]`	Passed
half-tablet boundary rounds up	`[50.0, 50.0, 45.0, 45.0]`	`[50.0, 50.0, 45.0, 45.0]`	Passed
rounding stall forces one tablet step	`[10.0, 10.0, 9.0, 9.0, 7.5, 7.5, 6.5, 6.5]`	`[10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]`	Failed
stops below minimum	`[20.0, 20.0, 10.0, 10.0, 0.0, 0.0]`	`[20.0, 20.0, 10.0, 10.0, 0.0, 0.0]`	Passed
dose equal to minimum continues	`[40.0, 20.0, 10.0, 0.0, 0.0]`	`[40.0, 20.0, 10.0, 0.0, 0.0]`	Passed
fractional tablet percentages	`[30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0]`	`[30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0]`	Passed

SHA-256 / 661465a42646478c9c8a60a337ac4e78983c1e68d81b5a9019ce349972fdc18e

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    dose = Fraction(str(x['start_mg']))
    t = Fraction(str(x['tablet_mg']))
    out = []
    for day in range(x['days']):
        if day > 0 and day % x['every_days'] == 0 and dose > 0:
            new = dose * (100 - x['step_pct']) / 100
            new = math.floor(new / t + Fraction(1, 2)) * t
            if new >= dose:
                new = dose - t
            dose = new if new >= Fraction(str(x['min_mg'])) else Fraction(0)
        out.append(float(dose))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 11},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 4},
   [50.0, 50.0, 45.0, 45.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 6},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 8},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 12},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [50.0, 50.0, 45.0, 45.0, 40.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 1, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 7.5, 5.0, 2.5, 0.0, 0.0, 0.0, 0.0]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 7},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 5.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 9},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 13},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 6},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 8},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 10},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 14},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 7},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0, 35.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 1, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 7.5, 5.0, 2.5, 0.0, 0.0, 0.0, 0.0]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 9},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 5, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 5.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 11},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0, 6.0])],
 [('weekly 25 percent taper',
   {'start_mg': 60, 'step_pct': 25, 'every_days': 3, 'min_mg': 5, 'tablet_mg': 5, 'days': 15},
   [60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0, 25.0, 20.0, 20.0, 20.0]),
  ('half-tablet boundary rounds up',
   {'start_mg': 50, 'step_pct': 15, 'every_days': 2, 'min_mg': 5, 'tablet_mg': 5, 'days': 8},
   [50.0, 50.0, 45.0, 45.0, 40.0, 40.0, 35.0, 35.0]),
  ('rounding stall forces one tablet step',
   {'start_mg': 10, 'step_pct': 10, 'every_days': 2, 'min_mg': '2.5', 'tablet_mg': '2.5', 'days': 8},
   [10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]),
  ('stops below minimum',
   {'start_mg': 20, 'step_pct': 50, 'every_days': 2, 'min_mg': 10, 'tablet_mg': 5, 'days': 10},
   [20.0, 20.0, 10.0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]),
  ('dose equal to minimum continues',
   {'start_mg': 40, 'step_pct': 50, 'every_days': 1, 'min_mg': 10, 'tablet_mg': 5, 'days': 5},
   [40.0, 20.0, 10.0, 0.0, 0.0]),
  ('fractional tablet percentages',
   {'start_mg': 30, 'step_pct': 30, 'every_days': 2, 'min_mg': 1, 'tablet_mg': 1, 'days': 12},
   [30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0, 8.0, 8.0, 6.0, 6.0])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
weekly 25 percent taper	`[60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]`	`[60.0, 60.0, 60.0, 45.0, 45.0, 45.0, 35.0, 35.0, 35.0, 25.0, 25.0]`	Passed
half-tablet boundary rounds up	`[50.0, 50.0, 45.0, 45.0]`	`[50.0, 50.0, 45.0, 45.0]`	Passed
rounding stall forces one tablet step	`[10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]`	`[10.0, 10.0, 7.5, 7.5, 5.0, 5.0, 2.5, 2.5]`	Passed
stops below minimum	`[20.0, 20.0, 10.0, 10.0, 0.0, 0.0]`	`[20.0, 20.0, 10.0, 10.0, 0.0, 0.0]`	Passed
dose equal to minimum continues	`[40.0, 20.0, 10.0, 0.0, 0.0]`	`[40.0, 20.0, 10.0, 0.0, 0.0]`	Passed
fractional tablet percentages	`[30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0]`	`[30.0, 30.0, 21.0, 21.0, 15.0, 15.0, 11.0, 11.0]`	Passed

SHA-256 / 0255bd4022b2d660efaf1d803e7a2f28240979cf27268e4975ea59ee413fd554

Verification & scope

A deterministic toy software model with explicitly stipulated thresholds and formulas; it is not clinical guidance, not a validated medical calculator, and makes no claim of conformance to any published protocol. Numbered variants vary patient and order inputs. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:21.845802+00:00.

Case digest / bc8d70e1546b20abfe628ebe8b698ce153fa04968abc1ebce1ed4d74bd9cc547