FA-62626 / Tax bracket computation / Open access

The half-part benefit cap lowers tax instead of limiting the benefit · case 01

Families with extra parts pay less than the capped amount.

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

ROOT CAUSE

The result is min(full, capped) instead of max(full, capped).

VERIFIED REPAIR

Take the larger of the full-quotient tax and the capped tax.

Unsuccessful approach: Applying the cap only beyond two extra half-parts ignores it for smaller families.

Case contract

solve(income, halves, couple): stipulated household quotient. Parts p = halves/2; the base is 2 parts for a couple and 1 otherwise (fewer halves than the base returns 'ERR:parts'). Tax with all parts = p * T(income/p) using slices 0% to 11294, 11% to 28797, 30% to 82341, 41% to 177106, 45% above. The benefit of each half-part beyond the base is capped at 1759: tax = max(full, T_base - 1759 * extra_halves) where T_base = base * T(income/base). Return whole units rounded down.

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, halves, couple):
    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))
    
    base = 2 if couple else 1
    if halves < 2 * base: return 'ERR:parts'
    scale = [[11294, '0'], [28797, '11'], [82341, '30'], [177106, '41'], [None, '45']]
    def tax_for(p): return p * prog(Fraction(income) / p, scale)
    full = tax_for(Fraction(halves, 2))
    capped = tax_for(Fraction(base)) - 1759 * (halves - 2 * base)
    return int(min(full, capped))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression cap-direction 1', (80000, 6, True), 7054), ('regression cap-direction 2', (60000, 3, False), 9527),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572),
  ('control: low income family', (30000, 5, True), 194), ('control: too few parts', (50000, 3, True), 'ERR:parts')],
 [('regression cap-direction 1', (30000, 5, True), 194), ('regression cap-direction 2', (250000, 8, True), 63921),
  ('partial repair guard 1', (150000, 6, True), 28054), ('partial repair guard 2', (193969, 6, True), 44466),
  ('control: too few parts', (50000, 3, True), 'ERR:parts'), ('control: single parent', (60000, 3, False), 9527),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572)],
 [('regression cap-direction 1', (40000, 7, False), 51), ('regression cap-direction 2', (40000, 8, True), 0),
  ('partial repair guard 1', (150000, 4, False), 42210), ('partial repair guard 2', (70423, 3, False), 12654),
  ('control: large family high income', (250000, 8, True), 63921),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572),
  ('control: couple with two children', (80000, 6, True), 7054)],
 [('regression cap-direction 1', (150000, 6, True), 28054), ('regression cap-direction 2', (16143, 5, False), 0),
  ('partial repair guard 1', (287118, 5, True), 84416), ('partial repair guard 2', (247910, 5, True), 68341),
  ('control: couple with two children', (80000, 6, True), 7054), ('control: low income family', (30000, 5, True), 194),
  ('control: too few parts', (50000, 3, True), 'ERR:parts'), ('control: single parent', (60000, 3, False), 9527)],
 [('regression cap-direction 1', (80000, 6, False), 10250), ('regression cap-direction 2', (193969, 6, True), 44466),
  ('partial repair guard 1', (80000, 4, False), 13768), ('partial repair guard 2', (80000, 3, False), 15527),
  ('control: single parent', (60000, 3, False), 9527), ('control: large family high income', (250000, 8, True), 63921),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572)]]
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 cap-direction 1	`5072`	`7054`	Failed
regression cap-direction 2	`7929`	`9527`	Failed
control: single one part	`5286`	`5286`	Passed
control: couple two parts	`10572`	`10572`	Passed
control: low income family	`-943`	`194`	Failed
control: too few parts	`ERR:parts`	`ERR:parts`	Passed

SHA-256 / ba9d5604f834540ce36e0b73c22a12aa7112b458337ad7c78ddb6a12fc46633f

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, halves, couple):
    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))
    
    base = 2 if couple else 1
    if halves < 2 * base: return 'ERR:parts'
    scale = [[11294, '0'], [28797, '11'], [82341, '30'], [177106, '41'], [None, '45']]
    def tax_for(p): return p * prog(Fraction(income) / p, scale)
    full = tax_for(Fraction(halves, 2))
    capped = tax_for(Fraction(base)) - 1759 * (halves - 2 * base)
    return int(max(full, capped) if halves - 2 * base > 2 else full)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression cap-direction 1', (80000, 6, True), 7054), ('regression cap-direction 2', (60000, 3, False), 9527),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572),
  ('control: low income family', (30000, 5, True), 194), ('control: too few parts', (50000, 3, True), 'ERR:parts')],
 [('regression cap-direction 1', (30000, 5, True), 194), ('regression cap-direction 2', (250000, 8, True), 63921),
  ('partial repair guard 1', (150000, 6, True), 28054), ('partial repair guard 2', (193969, 6, True), 44466),
  ('control: too few parts', (50000, 3, True), 'ERR:parts'), ('control: single parent', (60000, 3, False), 9527),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572)],
 [('regression cap-direction 1', (40000, 7, False), 51), ('regression cap-direction 2', (40000, 8, True), 0),
  ('partial repair guard 1', (150000, 4, False), 42210), ('partial repair guard 2', (70423, 3, False), 12654),
  ('control: large family high income', (250000, 8, True), 63921),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572),
  ('control: couple with two children', (80000, 6, True), 7054)],
 [('regression cap-direction 1', (150000, 6, True), 28054), ('regression cap-direction 2', (16143, 5, False), 0),
  ('partial repair guard 1', (287118, 5, True), 84416), ('partial repair guard 2', (247910, 5, True), 68341),
  ('control: couple with two children', (80000, 6, True), 7054), ('control: low income family', (30000, 5, True), 194),
  ('control: too few parts', (50000, 3, True), 'ERR:parts'), ('control: single parent', (60000, 3, False), 9527)],
 [('regression cap-direction 1', (80000, 6, False), 10250), ('regression cap-direction 2', (193969, 6, True), 44466),
  ('partial repair guard 1', (80000, 4, False), 13768), ('partial repair guard 2', (80000, 3, False), 15527),
  ('control: single parent', (60000, 3, False), 9527), ('control: large family high income', (250000, 8, True), 63921),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572)]]
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 cap-direction 1	`5072`	`7054`	Failed
regression cap-direction 2	`7929`	`9527`	Failed
control: single one part	`5286`	`5286`	Passed
control: couple two parts	`10572`	`10572`	Passed
control: low income family	`194`	`194`	Passed
control: too few parts	`ERR:parts`	`ERR:parts`	Passed

SHA-256 / dab705bdba62dd97b1f31c69d53a1e5ecaca5fed92dd4719903b37c9191a44f8

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, halves, couple):
    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))
    
    base = 2 if couple else 1
    if halves < 2 * base: return 'ERR:parts'
    scale = [[11294, '0'], [28797, '11'], [82341, '30'], [177106, '41'], [None, '45']]
    def tax_for(p): return p * prog(Fraction(income) / p, scale)
    full = tax_for(Fraction(halves, 2))
    capped = tax_for(Fraction(base)) - 1759 * (halves - 2 * base)
    return int(max(full, capped))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression cap-direction 1', (80000, 6, True), 7054), ('regression cap-direction 2', (60000, 3, False), 9527),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572),
  ('control: low income family', (30000, 5, True), 194), ('control: too few parts', (50000, 3, True), 'ERR:parts')],
 [('regression cap-direction 1', (30000, 5, True), 194), ('regression cap-direction 2', (250000, 8, True), 63921),
  ('partial repair guard 1', (150000, 6, True), 28054), ('partial repair guard 2', (193969, 6, True), 44466),
  ('control: too few parts', (50000, 3, True), 'ERR:parts'), ('control: single parent', (60000, 3, False), 9527),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572)],
 [('regression cap-direction 1', (40000, 7, False), 51), ('regression cap-direction 2', (40000, 8, True), 0),
  ('partial repair guard 1', (150000, 4, False), 42210), ('partial repair guard 2', (70423, 3, False), 12654),
  ('control: large family high income', (250000, 8, True), 63921),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572),
  ('control: couple with two children', (80000, 6, True), 7054)],
 [('regression cap-direction 1', (150000, 6, True), 28054), ('regression cap-direction 2', (16143, 5, False), 0),
  ('partial repair guard 1', (287118, 5, True), 84416), ('partial repair guard 2', (247910, 5, True), 68341),
  ('control: couple with two children', (80000, 6, True), 7054), ('control: low income family', (30000, 5, True), 194),
  ('control: too few parts', (50000, 3, True), 'ERR:parts'), ('control: single parent', (60000, 3, False), 9527)],
 [('regression cap-direction 1', (80000, 6, False), 10250), ('regression cap-direction 2', (193969, 6, True), 44466),
  ('partial repair guard 1', (80000, 4, False), 13768), ('partial repair guard 2', (80000, 3, False), 15527),
  ('control: single parent', (60000, 3, False), 9527), ('control: large family high income', (250000, 8, True), 63921),
  ('control: single one part', (40000, 2, False), 5286), ('control: couple two parts', (80000, 4, True), 10572)]]
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 cap-direction 1	`7054`	`7054`	Passed
regression cap-direction 2	`9527`	`9527`	Passed
control: single one part	`5286`	`5286`	Passed
control: couple two parts	`10572`	`10572`	Passed
control: low income family	`194`	`194`	Passed
control: too few parts	`ERR:parts`	`ERR:parts`	Passed

SHA-256 / d390b1267b6eb0b13ac7fd9064a8ca829eff549cde0c0220f5865d4d7a380c88

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 2026-09-29T14:47:06.417704+00:00.

Case digest / c6a23f2d4ac49fec914b279be69f318f1682e34ce020ff2aa372875f293dfa60