FAILURE MAP
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FA-62526 / Tax bracket computation / Open access

Incomes under five dollars are charged a table amount · case 01

A filer with 3 dollars of taxable income owes 1 dollar.

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

ROOT CAUSE

The minimum-income rule is missing, so [0,25) is taxed at its midpoint.

VERIFIED REPAIR

Return zero tax for incomes below 5.

Unsuccessful approach: Exempting only zero income still charges incomes from 1 to 4.

Case contract

solve(income, brackets): stipulated tax-table lookup. income < 0 returns 0 and incomes below 5 have zero tax. For income < 100000 the tax is the progressive tax on the midpoint of the income's band, rounded half-up to whole dollars: bands are 25 wide below 3000 ([0,25), [25,50), ...) and 50 wide from 3000 ([3000,3050), ...). Incomes of 100000 or more use the exact progressive tax rounded half-up to cents. Return 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):
    def prog(x, br):
        tax, lower = Fraction(0), 0
        for upper, rate in br:
            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 tax
    def cents(v):
        v = v * 100
        return int(v + Fraction(1, 2)) if v >= 0 else -int(-v + Fraction(1, 2))
    
    if income < 0: return 0
    if income >= 100000: return cents(prog(income, brackets))
    w = 25 if income < 3000 else 50
    lo = income // w * w
    mid = lo + Fraction(w, 2)
    return int(prog(mid, brackets) + Fraction(1, 2)) * 100
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900),
  ('control: first wide band', (3000, [[10000, '10'], [40000, '12'], [None, '22']]), 30300),
  ('control: ordinary', (12345, [[10000, '10'], [40000, '12'], [None, '22']]), 127900),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000),
  ('control: small', (24, [[10000, '10'], [40000, '12'], [None, '22']]), 100),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024),
  ('control: band edge', (40050, [[10000, '10'], [40000, '12'], [None, '22']]), 461700),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900),
  ('control: first wide band', (3000, [[10000, '10'], [40000, '12'], [None, '22']]), 30300),
  ('control: ordinary', (12345, [[10000, '10'], [40000, '12'], [None, '22']]), 127900),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000),
  ('control: small', (24, [[10000, '10'], [40000, '12'], [None, '22']]), 100),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024)]]
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 minimum-taxable 11000Failed
regression minimum-taxable 21000Failed
control: last narrow band2990029900Passed
control: first wide band3030030300Passed
control: ordinary127900127900Passed
control: table cutoff17800001780000Passed

SHA-256 / b2c0bc0fe9eaf7c86e3254e47c770c670e0a0bc0dfad3bf90ff56e8aef85609d

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):
    def prog(x, br):
        tax, lower = Fraction(0), 0
        for upper, rate in br:
            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 tax
    def cents(v):
        v = v * 100
        return int(v + Fraction(1, 2)) if v >= 0 else -int(-v + Fraction(1, 2))
    
    if income <= 0: return 0
    if income >= 100000: return cents(prog(income, brackets))
    w = 25 if income < 3000 else 50
    lo = income // w * w
    mid = lo + Fraction(w, 2)
    return int(prog(mid, brackets) + Fraction(1, 2)) * 100
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900),
  ('control: first wide band', (3000, [[10000, '10'], [40000, '12'], [None, '22']]), 30300),
  ('control: ordinary', (12345, [[10000, '10'], [40000, '12'], [None, '22']]), 127900),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000),
  ('control: small', (24, [[10000, '10'], [40000, '12'], [None, '22']]), 100),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024),
  ('control: band edge', (40050, [[10000, '10'], [40000, '12'], [None, '22']]), 461700),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900),
  ('control: first wide band', (3000, [[10000, '10'], [40000, '12'], [None, '22']]), 30300),
  ('control: ordinary', (12345, [[10000, '10'], [40000, '12'], [None, '22']]), 127900),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000),
  ('control: small', (24, [[10000, '10'], [40000, '12'], [None, '22']]), 100),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024)]]
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 minimum-taxable 11000Failed
regression minimum-taxable 21000Failed
control: last narrow band2990029900Passed
control: first wide band3030030300Passed
control: ordinary127900127900Passed
control: table cutoff17800001780000Passed

SHA-256 / 63b3cbd6239c50fe543088df9c5e451620f5f6a324fd571f28beb8245e5fb070

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):
    def prog(x, br):
        tax, lower = Fraction(0), 0
        for upper, rate in br:
            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 tax
    def cents(v):
        v = v * 100
        return int(v + Fraction(1, 2)) if v >= 0 else -int(-v + Fraction(1, 2))
    
    if income < 5: return 0
    if income >= 100000: return cents(prog(income, brackets))
    w = 25 if income < 3000 else 50
    lo = income // w * w
    mid = lo + Fraction(w, 2)
    return int(prog(mid, brackets) + Fraction(1, 2)) * 100
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900),
  ('control: first wide band', (3000, [[10000, '10'], [40000, '12'], [None, '22']]), 30300),
  ('control: ordinary', (12345, [[10000, '10'], [40000, '12'], [None, '22']]), 127900),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000),
  ('control: small', (24, [[10000, '10'], [40000, '12'], [None, '22']]), 100),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024),
  ('control: band edge', (40050, [[10000, '10'], [40000, '12'], [None, '22']]), 461700),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: last narrow band', (2999, [[10000, '10'], [40000, '12'], [None, '22']]), 29900),
  ('control: first wide band', (3000, [[10000, '10'], [40000, '12'], [None, '22']]), 30300),
  ('control: ordinary', (12345, [[10000, '10'], [40000, '12'], [None, '22']]), 127900),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000)],
 [('regression minimum-taxable 1', (4, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('regression minimum-taxable 2', (1, [[10000, '10'], [40000, '12'], [None, '22']]), 0),
  ('control: table cutoff', (100000, [[10000, '10'], [40000, '12'], [None, '22']]), 1780000),
  ('control: small', (24, [[10000, '10'], [40000, '12'], [None, '22']]), 100),
  ('control: just under cutoff', (99999, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1739400),
  ('control: above cutoff', (100001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),
   1740024)]]
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 minimum-taxable 100Passed
regression minimum-taxable 200Passed
control: last narrow band2990029900Passed
control: first wide band3030030300Passed
control: ordinary127900127900Passed
control: table cutoff17800001780000Passed

SHA-256 / 5b6efccce4ac163028798d27691026da9d451ccc847ef3ec03e8960d85c51089

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 2026-09-29T14:47:05.392040+00:00.

Case digest / 1a8718b9902fbaa7fea96cac85d52f2d7290c68b237c59055641d7bd71df1e70