FA-62541 / Tax bracket computation / Open access
The 28% AMT rate is applied to the whole base once it crosses the break · case 01
Crossing the 232600 break raises the tax on the entire base by two points.
ROOT CAUSE
The base is taxed at a single rate chosen by the base size.
VERIFIED REPAIR
Tax the base up to 232600 at 26% and only the excess at 28%.
Unsuccessful approach: Splitting at 232600 of AMTI rather than of the base puts the break in the wrong place.
Case contract
solve(amti, regular_cents, status): stipulated AMT, whole dollars. Exemption: single 85700 (phase-out threshold 609350), mfj 133300 (threshold 1218700). The exemption is reduced by 25% of AMTI above the threshold, with the reduction rounded down to whole dollars, never below 0. Base = max(0, amti - exemption). Tentative minimum tax = 26% of base up to 232600 plus 28% of base above 232600 (in cents: dollars times percent). AMT = max(0, TMT - regular tax). Return [exemption, tmt_cents, amt_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
N = 1
observations = []
def solve(amti, regular_cents, status):
ex, thr = {'single': (85700, 609350), 'mfj': (133300, 1218700)}[status]
if amti > thr: ex = max(0, ex - (amti - thr) // 4)
base = max(0, amti - ex)
tmt = base * (28 if base > 232600 else 26)
return [ex, tmt, max(0, tmt - regular_cents)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression rate-break 1', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('regression rate-break 2', (700000, 0, 'single'), [63038, 17369736, 17369736]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084])],
[('regression rate-break 1', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('regression rate-break 2', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),
('partial repair guard 2', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])],
[('regression rate-break 1', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('regression rate-break 2', (365900, 10000000, 'single'), [85700, 7380400, 0]),
('partial repair guard 2', (832985, 0, 'single'), [29792, 22024204, 22024204]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0])],
[('regression rate-break 1', (832985, 0, 'single'), [29792, 22024204, 22024204]),
('regression rate-break 2', (1122405, 10000000, 'mfj'), [133300, 27229740, 17229740]),
('partial repair guard 1', (365900, 35622995, 'mfj'), [133300, 6047600, 0]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),
('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500])],
[('regression rate-break 1', (1526866, 0, 'single'), [0, 42287048, 42287048]),
('regression rate-break 2', (510076, 1928999, 'mfj'), [133300, 10084528, 8155529]),
('partial repair guard 1', (365900, 7499416, 'mfj'), [133300, 6047600, 0]),
('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])]]
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 rate-break 1 | [133300, 7467600, 7467600] | [133300, 7002400, 7002400] | Failed |
| regression rate-break 2 | [63038, 17834936, 17834936] | [63038, 17369736, 17369736] | Failed |
| control: moderate single | [85700, 2971800, 471800] | [85700, 2971800, 471800] | Passed |
| control: no exemption left | [0, 28000000, 0] | [0, 27534800, 0] | Failed |
| control: below exemption | [133300, 0, 0] | [133300, 0, 0] | Passed |
| control: odd excess | [85700, 14662284, 9662284] | [85700, 14197084, 9197084] | Failed |
SHA-256 / f6130f3ae640d4b4c8b378f5145bfd508c4c991be3838ebbe7df7ad74f58eeaf
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(amti, regular_cents, status):
ex, thr = {'single': (85700, 609350), 'mfj': (133300, 1218700)}[status]
if amti > thr: ex = max(0, ex - (amti - thr) // 4)
base = max(0, amti - ex)
tmt = min(base, max(0, 232600 - ex)) * 26 + max(0, base - max(0, 232600 - ex)) * 28
return [ex, tmt, max(0, tmt - regular_cents)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression rate-break 1', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('regression rate-break 2', (700000, 0, 'single'), [63038, 17369736, 17369736]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084])],
[('regression rate-break 1', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('regression rate-break 2', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),
('partial repair guard 2', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])],
[('regression rate-break 1', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('regression rate-break 2', (365900, 10000000, 'single'), [85700, 7380400, 0]),
('partial repair guard 2', (832985, 0, 'single'), [29792, 22024204, 22024204]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0])],
[('regression rate-break 1', (832985, 0, 'single'), [29792, 22024204, 22024204]),
('regression rate-break 2', (1122405, 10000000, 'mfj'), [133300, 27229740, 17229740]),
('partial repair guard 1', (365900, 35622995, 'mfj'), [133300, 6047600, 0]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),
('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500])],
[('regression rate-break 1', (1526866, 0, 'single'), [0, 42287048, 42287048]),
('regression rate-break 2', (510076, 1928999, 'mfj'), [133300, 10084528, 8155529]),
('partial repair guard 1', (365900, 7499416, 'mfj'), [133300, 6047600, 0]),
('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])]]
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 rate-break 1 | [133300, 7269000, 7269000] | [133300, 7002400, 7002400] | Failed |
| regression rate-break 2 | [63038, 17495812, 17495812] | [63038, 17369736, 17369736] | Failed |
| control: moderate single | [85700, 2971800, 471800] | [85700, 2971800, 471800] | Passed |
| control: no exemption left | [0, 27534800, 0] | [0, 27534800, 0] | Passed |
| control: below exemption | [133300, 0, 0] | [133300, 0, 0] | Passed |
| control: odd excess | [85700, 14368484, 9368484] | [85700, 14197084, 9197084] | Failed |
SHA-256 / 57024dc4ba1e3e5cbd5459eee7a3ed0d44fde2557b92ae6c31545270d48f8da6
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(amti, regular_cents, status):
ex, thr = {'single': (85700, 609350), 'mfj': (133300, 1218700)}[status]
if amti > thr: ex = max(0, ex - (amti - thr) // 4)
base = max(0, amti - ex)
tmt = min(base, 232600) * 26 + max(0, base - 232600) * 28
return [ex, tmt, max(0, tmt - regular_cents)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression rate-break 1', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('regression rate-break 2', (700000, 0, 'single'), [63038, 17369736, 17369736]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084])],
[('regression rate-break 1', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('regression rate-break 2', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),
('partial repair guard 2', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])],
[('regression rate-break 1', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('regression rate-break 2', (365900, 10000000, 'single'), [85700, 7380400, 0]),
('partial repair guard 2', (832985, 0, 'single'), [29792, 22024204, 22024204]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0])],
[('regression rate-break 1', (832985, 0, 'single'), [29792, 22024204, 22024204]),
('regression rate-break 2', (1122405, 10000000, 'mfj'), [133300, 27229740, 17229740]),
('partial repair guard 1', (365900, 35622995, 'mfj'), [133300, 6047600, 0]),
('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),
('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),
('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),
('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500])],
[('regression rate-break 1', (1526866, 0, 'single'), [0, 42287048, 42287048]),
('regression rate-break 2', (510076, 1928999, 'mfj'), [133300, 10084528, 8155529]),
('partial repair guard 1', (365900, 7499416, 'mfj'), [133300, 6047600, 0]),
('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),
('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),
('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),
('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])]]
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 rate-break 1 | [133300, 7002400, 7002400] | [133300, 7002400, 7002400] | Passed |
| regression rate-break 2 | [63038, 17369736, 17369736] | [63038, 17369736, 17369736] | Passed |
| control: moderate single | [85700, 2971800, 471800] | [85700, 2971800, 471800] | Passed |
| control: no exemption left | [0, 27534800, 0] | [0, 27534800, 0] | Passed |
| control: below exemption | [133300, 0, 0] | [133300, 0, 0] | Passed |
| control: odd excess | [85700, 14197084, 9197084] | [85700, 14197084, 9197084] | Passed |
SHA-256 / 62d46d8fce32d343effe01351567b34e9253c77d36e1477e5012aeb078d7f6b8
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 2026-09-29T14:47:05.596838+00:00.
Case digest / 5b2956465b07b24ae33705c7758ec9a00e1359ea42d4bd73f68cf8bebbe36e79