FA-62356 / Tax bracket computation / Open access
A schedule with non-increasing thresholds is accepted · case 01
A mis-keyed bracket table silently produces a tax figure.
ROOT CAUSE
Only the open final bracket is validated; threshold order is not checked.
VERIFIED REPAIR
Reject schedules whose uppers are not strictly increasing and positive.
Unsuccessful approach: Checking only adjacent pairs after the first bracket misses a bad first threshold.
Case contract
solve(income, brackets): brackets is [[upper, rate_percent], ...] with strictly increasing positive uppers and a final open bracket [None, rate]; otherwise return 'ERR:brackets'. Each rate applies only to the slice of income in (previous upper, upper]. Negative income is taxed as zero. The tax is summed exactly and rounded half-up to cents once, returned as integer cents.
Why this case matters
Tax computations hinge on which slice, threshold, ordering and rounding rule applies at each step; a misplaced boundary silently misstates liabilities.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(income, brackets):
if not brackets or brackets[-1][0] is not None: return 'ERR:brackets'
uppers = [u for u, _ in brackets[:-1]]
x = max(0, income)
tax, lower = Fraction(0), 0
for upper, rate in brackets:
top = x if upper is None else min(x, upper)
if top > lower:
tax += (top - lower) * Fraction(rate) / 100
if upper is None or x <= upper: break
lower = upper
return int(tax * 100 + Fraction(1, 2))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression threshold-validation 1', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
('regression threshold-validation 2', (500, [[0, '10'], [None, '30']]), 'ERR:brackets'),
('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],
[('regression threshold-validation 1', (1, [[44000, '15'], [44000, '22'], [None, '40.5']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[60000, '22'], [60000, '15'], [188000, '33.3'], [None, '37']]),
'ERR:brackets'),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
126140),
('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets')],
[('regression threshold-validation 1', (999, [[24000, '33.3'], [24000, '22'], [150000, '10'], [None, '37']]),
'ERR:brackets'),
('regression threshold-validation 2',
(40000, [[83000, '5'], [83000, '10'], [156000, '10'], [192000, '10'], [None, '37']]), 'ERR:brackets'),
('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets'),
('control: high earner', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
5917183),
('control: single bracket', (777, [[None, '12.5']]), 9713)],
[('regression threshold-validation 1', (10000, [[178000, '24'], [178000, '33.3'], [None, '45']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[44000, '5'], [44000, '15'], [None, '37']]), 'ERR:brackets'),
('control: single bracket', (777, [[None, '12.5']]), 9713),
('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],
[('regression threshold-validation 1', (999, [[105000, '15'], [105000, '24'], [None, '30']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[138000, '15'], [138000, '33.3'], [None, '45']]), 'ERR:brackets'),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
126140)]]
for label, args, expected in cases[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 |
|---|---|---|---|
| regression threshold-validation 1 | 100000 | ERR:brackets | Failed |
| regression threshold-validation 2 | 15000 | ERR:brackets | Failed |
| control: three brackets | 680000 | 680000 | Passed |
| control: at first threshold | 100000 | 100000 | Passed |
| control: zero | 0 | 0 | Passed |
| control: negative | 0 | 0 | Passed |
SHA-256 / a3c0c41470e8e0f982e6da184724f5e528ce6f2b9fb8e69ba7c2fc0c183c32f1
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(income, brackets):
if not brackets or brackets[-1][0] is not None: return 'ERR:brackets'
uppers = [u for u, _ in brackets[:-1]]
if any(b <= a for a, b in zip(uppers[1:], uppers[2:])): return 'ERR:brackets'
x = max(0, income)
tax, lower = Fraction(0), 0
for upper, rate in brackets:
top = x if upper is None else min(x, upper)
if top > lower:
tax += (top - lower) * Fraction(rate) / 100
if upper is None or x <= upper: break
lower = upper
return int(tax * 100 + Fraction(1, 2))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression threshold-validation 1', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
('regression threshold-validation 2', (500, [[0, '10'], [None, '30']]), 'ERR:brackets'),
('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],
[('regression threshold-validation 1', (1, [[44000, '15'], [44000, '22'], [None, '40.5']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[60000, '22'], [60000, '15'], [188000, '33.3'], [None, '37']]),
'ERR:brackets'),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
126140),
('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets')],
[('regression threshold-validation 1', (999, [[24000, '33.3'], [24000, '22'], [150000, '10'], [None, '37']]),
'ERR:brackets'),
('regression threshold-validation 2',
(40000, [[83000, '5'], [83000, '10'], [156000, '10'], [192000, '10'], [None, '37']]), 'ERR:brackets'),
('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets'),
('control: high earner', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
5917183),
('control: single bracket', (777, [[None, '12.5']]), 9713)],
[('regression threshold-validation 1', (10000, [[178000, '24'], [178000, '33.3'], [None, '45']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[44000, '5'], [44000, '15'], [None, '37']]), 'ERR:brackets'),
('control: single bracket', (777, [[None, '12.5']]), 9713),
('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],
[('regression threshold-validation 1', (999, [[105000, '15'], [105000, '24'], [None, '30']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[138000, '15'], [138000, '33.3'], [None, '45']]), 'ERR:brackets'),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
126140)]]
for label, args, expected in cases[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 |
|---|---|---|---|
| regression threshold-validation 1 | 100000 | ERR:brackets | Failed |
| regression threshold-validation 2 | 15000 | ERR:brackets | Failed |
| control: three brackets | 680000 | 680000 | Passed |
| control: at first threshold | 100000 | 100000 | Passed |
| control: zero | 0 | 0 | Passed |
| control: negative | 0 | 0 | Passed |
SHA-256 / 0429aa19ae80b45b0b0fc87f18ea894f127b535d0e07047826f14ff1804ba856
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(income, brackets):
if not brackets or brackets[-1][0] is not None: return 'ERR:brackets'
uppers = [u for u, _ in brackets[:-1]]
if any(b <= a for a, b in zip([0] + uppers, uppers)): return 'ERR:brackets'
x = max(0, income)
tax, lower = Fraction(0), 0
for upper, rate in brackets:
top = x if upper is None else min(x, upper)
if top > lower:
tax += (top - lower) * Fraction(rate) / 100
if upper is None or x <= upper: break
lower = upper
return int(tax * 100 + Fraction(1, 2))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression threshold-validation 1', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
('regression threshold-validation 2', (500, [[0, '10'], [None, '30']]), 'ERR:brackets'),
('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],
[('regression threshold-validation 1', (1, [[44000, '15'], [44000, '22'], [None, '40.5']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[60000, '22'], [60000, '15'], [188000, '33.3'], [None, '37']]),
'ERR:brackets'),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
126140),
('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets')],
[('regression threshold-validation 1', (999, [[24000, '33.3'], [24000, '22'], [150000, '10'], [None, '37']]),
'ERR:brackets'),
('regression threshold-validation 2',
(40000, [[83000, '5'], [83000, '10'], [156000, '10'], [192000, '10'], [None, '37']]), 'ERR:brackets'),
('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets'),
('control: high earner', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
5917183),
('control: single bracket', (777, [[None, '12.5']]), 9713)],
[('regression threshold-validation 1', (10000, [[178000, '24'], [178000, '33.3'], [None, '45']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[44000, '5'], [44000, '15'], [None, '37']]), 'ERR:brackets'),
('control: single bracket', (777, [[None, '12.5']]), 9713),
('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],
[('regression threshold-validation 1', (999, [[105000, '15'], [105000, '24'], [None, '30']]), 'ERR:brackets'),
('regression threshold-validation 2', (10000, [[138000, '15'], [138000, '33.3'], [None, '45']]), 'ERR:brackets'),
('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
126140)]]
for label, args, expected in cases[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 |
|---|---|---|---|
| regression threshold-validation 1 | ERR:brackets | ERR:brackets | Passed |
| regression threshold-validation 2 | ERR:brackets | ERR:brackets | Passed |
| control: three brackets | 680000 | 680000 | Passed |
| control: at first threshold | 100000 | 100000 | Passed |
| control: zero | 0 | 0 | Passed |
| control: negative | 0 | 0 | Passed |
SHA-256 / bc4394eb6be7cee552ab42fa5a848dcfd149528b9ee8b9ae496b18d0899782c7
Verification & scope
A deterministic, bounded teaching model with a stipulated toy contract; it makes no claim of conformance to any real regulation, standard, or institution's rules. 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 2026-09-29T14:47:03.931305+00:00.
Case digest / 2e7b77d349947626df02824b847824f240c406d82ef135137653fb13e346f628