FA-62361 / Tax bracket computation / Open access

Income above the last threshold escapes tax · case 01

High earners pay the same tax as someone exactly at the final threshold.

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

ROOT CAUSE

The loop skips the open-ended final bracket.

VERIFIED REPAIR

Apply the final rate to all income above the last threshold.

Unsuccessful approach: Taxing the excess at the second-to-last rate still ignores the top rate.

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]]
    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[:-1]:
        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 open-top-bracket 1',
   (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), 5917183),
  ('regression open-top-bracket 2', (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),
  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022)],
 [('regression open-top-bracket 1', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('regression open-top-bracket 2', (777, [[None, '12.5']]), 9713),
  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('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'),
  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],
 [('regression open-top-bracket 1',
   (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]), 4039200),
  ('regression open-top-bracket 2', (40000, [[None, '45']]), 1800000),
  ('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 open-top-bracket 1', (139460, [[None, '40.5']]), 5648130),
  ('regression open-top-bracket 2',
   (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]), 4303815),
  ('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 open-top-bracket 1',
   (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]), 5673643),
  ('regression open-top-bracket 2', (172773, [[None, '30']]), 5183190),
  ('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 open-top-bracket 1	`3710400`	`5917183`	Failed
regression open-top-bracket 2	`460000`	`680000`	Failed
control: at first threshold	`100000`	`100000`	Passed
control: zero	`0`	`0`	Passed
control: negative	`0`	`0`	Passed
control: one over threshold	`460000`	`460022`	Failed

SHA-256 / 3390111d10f109f93b7318c6bb0cc0952fee7a433bfc340984b3c322b7a5f781

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([0] + uppers, uppers)): return 'ERR:brackets'
    x = max(0, income)
    tax, lower = Fraction(0), 0
    for upper, rate in brackets[:-1]:
        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
    if len(brackets) > 1 and x > brackets[-2][0]: tax += (x - brackets[-2][0]) * Fraction(brackets[-2][1]) / 100
    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 open-top-bracket 1',
   (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), 5917183),
  ('regression open-top-bracket 2', (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),
  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022)],
 [('regression open-top-bracket 1', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('regression open-top-bracket 2', (777, [[None, '12.5']]), 9713),
  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('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'),
  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],
 [('regression open-top-bracket 1',
   (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]), 4039200),
  ('regression open-top-bracket 2', (40000, [[None, '45']]), 1800000),
  ('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 open-top-bracket 1', (139460, [[None, '40.5']]), 5648130),
  ('regression open-top-bracket 2',
   (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]), 4303815),
  ('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 open-top-bracket 1',
   (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]), 5673643),
  ('regression open-top-bracket 2', (172773, [[None, '30']]), 5183190),
  ('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 open-top-bracket 1	`5340024`	`5917183`	Failed
regression open-top-bracket 2	`580000`	`680000`	Failed
control: at first threshold	`100000`	`100000`	Passed
control: zero	`0`	`0`	Passed
control: negative	`0`	`0`	Passed
control: one over threshold	`460012`	`460022`	Failed

SHA-256 / 91d9dbd0e2dd7f117786bb9633fd492330acbff23d3a729aa7ab46580fc7d948

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 open-top-bracket 1',
   (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), 5917183),
  ('regression open-top-bracket 2', (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),
  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022)],
 [('regression open-top-bracket 1', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('regression open-top-bracket 2', (777, [[None, '12.5']]), 9713),
  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('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'),
  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],
 [('regression open-top-bracket 1',
   (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]), 4039200),
  ('regression open-top-bracket 2', (40000, [[None, '45']]), 1800000),
  ('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 open-top-bracket 1', (139460, [[None, '40.5']]), 5648130),
  ('regression open-top-bracket 2',
   (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]), 4303815),
  ('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 open-top-bracket 1',
   (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]), 5673643),
  ('regression open-top-bracket 2', (172773, [[None, '30']]), 5183190),
  ('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 open-top-bracket 1	`5917183`	`5917183`	Passed
regression open-top-bracket 2	`680000`	`680000`	Passed
control: at first threshold	`100000`	`100000`	Passed
control: zero	`0`	`0`	Passed
control: negative	`0`	`0`	Passed
control: one over threshold	`460022`	`460022`	Passed

SHA-256 / 61d141b524b830050dba721acfd893b7dc0147e15090a93ee5aec81242983f79

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 2026-09-29T14:47:03.985243+00:00.

Case digest / c47028d45dd4e648f7208b4e4e856c5d4bd9e3f9ce8edadb092c2af463f1c4eb