FAILURE MAP
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FA-62346 / Tax bracket computation / Open access

Each bracket rate is applied to income measured from zero · case 01

Tax in the second bracket also re-taxes the first bracket's income.

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

ROOT CAUSE

The slice uses top instead of top - lower.

THE FAILURE

The slice uses top instead of top - lower.

Unsuccessful approach: Counting the slice as inclusive of both endpoints (top - lower + 1) overstates each upper bracket by one dollar.

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:
        top = x if upper is None else min(x, upper)
        if top > lower:
            tax += top * 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 slice-width 1', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
  ('regression slice-width 2', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('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: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   126140)],
 [('regression slice-width 1', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   126140),
  ('regression slice-width 2', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   5917183),
  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],
 [('regression slice-width 1', (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]),
   4039200),
  ('regression slice-width 2', (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]),
   4303815),
  ('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 slice-width 1', (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]),
   5673643),
  ('regression slice-width 2', (64068, [[32000, '22'], [105000, '10'], [170000, '24'], [193000, '10'], [None, '37']]),
   1024680),
  ('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 slice-width 1', (161544, [[108000, '22'], [122000, '12.5'], [192000, '10'], [None, '30']]), 2946440),
  ('regression slice-width 2', (84182, [[82000, '12.5'], [138000, '22'], [161000, '15'], [None, '37']]), 1073004),
  ('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 fixtureActualExpectedOutcome
regression slice-width 11680000680000Failed
regression slice-width 21460022460022Failed
control: at first threshold100000100000Passed
control: zero00Passed
control: negative00Passed
control: fractional rate258140126140Failed

SHA-256 / 302e0cf27649205ee6a2ceca8439117c7c197dc0977ca49d1f3f20f070912b64

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:
        top = x if upper is None else min(x, upper)
        if top > lower:
            tax += (top - lower + (1 if lower else 0)) * 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 slice-width 1', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),
  ('regression slice-width 2', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('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: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   126140)],
 [('regression slice-width 1', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   126140),
  ('regression slice-width 2', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   5917183),
  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),
  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),
  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],
 [('regression slice-width 1', (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]),
   4039200),
  ('regression slice-width 2', (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]),
   4303815),
  ('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 slice-width 1', (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]),
   5673643),
  ('regression slice-width 2', (64068, [[32000, '22'], [105000, '10'], [170000, '24'], [193000, '10'], [None, '37']]),
   1024680),
  ('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 slice-width 1', (161544, [[108000, '22'], [122000, '12.5'], [192000, '10'], [None, '30']]), 2946440),
  ('regression slice-width 2', (84182, [[82000, '12.5'], [138000, '22'], [161000, '15'], [None, '37']]), 1073004),
  ('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 fixtureActualExpectedOutcome
regression slice-width 1680034680000Failed
regression slice-width 2460056460022Failed
control: at first threshold100000100000Passed
control: zero00Passed
control: negative00Passed
control: fractional rate126152126140Failed

SHA-256 / 98693f6f29dcf43299511a4502cfd46560baf94b4e496d816d6a2636bb9c1785

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This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:47:03.810901+00:00.

Case digest / 5f7eccbdfb47546b1d9d0a4f26833a6893aaf37b1f1c075c54228a8c8df4dcbf