FA-62671 / Tax bracket computation / Open access

The exclusion amount is subtracted from the tax as if it were a credit · case 01

Estates owe no tax far above the exclusion because 13.6 million of tax is forgiven.

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

ROOT CAUSE

The unified credit is set to the exclusion amount itself instead of the tax on it.

VERIFIED REPAIR

The unified credit is the tentative tax on the exclusion amount.

Unsuccessful approach: Multiplying the exclusion by the top 40% rate overstates the credit because lower slices are taxed below 40%.

Case contract

solve(estate, gifts, dsue): stipulated unified transfer tax in whole dollars. T is the progressive schedule 18% to 10000 rising to 40% above 1000000. The exclusion is 13610000 + dsue; the unified credit is T(exclusion). Tentative tax = T(estate + gifts). Gift credit = max(0, T(gifts) - unified credit). Tax = max(0, tentative - gift credit - unified credit), returned in 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(estate, gifts, dsue):
    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))
    
    sched = [[10000, '18'], [20000, '20'], [40000, '22'], [60000, '24'], [80000, '26'], [100000, '28'], [150000, '30'], [250000, '32'], [500000, '34'], [750000, '37'], [1000000, '39'], [None, '40']]
    T = lambda x: prog(x, sched)
    credit = Fraction(13610000 + dsue)
    tent = T(estate + gifts)
    gift_credit = max(0, T(gifts) - credit)
    return cents(max(0, tent - gift_credit - credit))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression credit-not-exclusion 1', (20000000, 0, 0), 255600000),
  ('regression credit-not-exclusion 2', (10000000, 5000000, 0), 55600000),
  ('control: under exclusion', (10000000, 0, 0), 0), ('control: ported exclusion', (20000000, 0, 5000000), 55600000),
  ('control: gifts above exclusion', (5000000, 15000000, 0), 200000000), ('control: modest', (1500000, 200000, 0), 0)],
 [('regression credit-not-exclusion 1', (20000000, 0, 5000000), 55600000),
  ('regression credit-not-exclusion 2', (5000000, 15000000, 0), 200000000),
  ('partial repair guard 2', (8632782, 5000000, 0), 911280), ('control: modest', (1500000, 200000, 0), 0),
  ('control: large estate', (20000000, 0, 0), 255600000), ('control: under exclusion', (10000000, 0, 0), 0),
  ('control: with prior gifts', (10000000, 5000000, 0), 55600000)],
 [('regression credit-not-exclusion 1', (13610000, 15000000, 0), 544400000),
  ('regression credit-not-exclusion 2', (8632782, 5000000, 0), 911280),
  ('partial repair guard 1', (21431981, 500000, 0), 332879240),
  ('partial repair guard 2', (13610000, 500000, 0), 20000000), ('control: large estate', (20000000, 0, 0), 255600000),
  ('control: under exclusion', (10000000, 0, 0), 0), ('control: with prior gifts', (10000000, 5000000, 0), 55600000),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000)],
 [('regression credit-not-exclusion 1', (788866, 18885032, 2000000), 31554640),
  ('regression credit-not-exclusion 2', (21431981, 500000, 0), 332879240),
  ('partial repair guard 1', (13610000, 5000000, 2000000), 120000000),
  ('partial repair guard 2', (13610000, 5703648, 0), 228145920),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000),
  ('control: gifts above exclusion', (5000000, 15000000, 0), 200000000), ('control: modest', (1500000, 200000, 0), 0),
  ('control: large estate', (20000000, 0, 0), 255600000)],
 [('regression credit-not-exclusion 1', (13610000, 500000, 0), 20000000),
  ('regression credit-not-exclusion 2', (13610000, 5000000, 2000000), 120000000),
  ('partial repair guard 1', (27783445, 500000, 5000000), 386937800),
  ('partial repair guard 2', (22327855, 5000000, 2000000), 468714200),
  ('control: large estate', (20000000, 0, 0), 255600000), ('control: under exclusion', (10000000, 0, 0), 0),
  ('control: with prior gifts', (10000000, 5000000, 0), 55600000),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000)]]
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 credit-not-exclusion 1	`0`	`255600000`	Failed
regression credit-not-exclusion 2	`0`	`55600000`	Failed
control: under exclusion	`0`	`0`	Passed
control: ported exclusion	`0`	`55600000`	Failed
control: gifts above exclusion	`0`	`200000000`	Failed
control: modest	`0`	`0`	Passed

SHA-256 / 8316e4ffc27200405446df23b13ba0ea7071416aeef7cb3b293bf6043a1429c3

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(estate, gifts, dsue):
    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))
    
    sched = [[10000, '18'], [20000, '20'], [40000, '22'], [60000, '24'], [80000, '26'], [100000, '28'], [150000, '30'], [250000, '32'], [500000, '34'], [750000, '37'], [1000000, '39'], [None, '40']]
    T = lambda x: prog(x, sched)
    credit = Fraction(13610000 + dsue) * 40 / 100
    tent = T(estate + gifts)
    gift_credit = max(0, T(gifts) - credit)
    return cents(max(0, tent - gift_credit - credit))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression credit-not-exclusion 1', (20000000, 0, 0), 255600000),
  ('regression credit-not-exclusion 2', (10000000, 5000000, 0), 55600000),
  ('control: under exclusion', (10000000, 0, 0), 0), ('control: ported exclusion', (20000000, 0, 5000000), 55600000),
  ('control: gifts above exclusion', (5000000, 15000000, 0), 200000000), ('control: modest', (1500000, 200000, 0), 0)],
 [('regression credit-not-exclusion 1', (20000000, 0, 5000000), 55600000),
  ('regression credit-not-exclusion 2', (5000000, 15000000, 0), 200000000),
  ('partial repair guard 2', (8632782, 5000000, 0), 911280), ('control: modest', (1500000, 200000, 0), 0),
  ('control: large estate', (20000000, 0, 0), 255600000), ('control: under exclusion', (10000000, 0, 0), 0),
  ('control: with prior gifts', (10000000, 5000000, 0), 55600000)],
 [('regression credit-not-exclusion 1', (13610000, 15000000, 0), 544400000),
  ('regression credit-not-exclusion 2', (8632782, 5000000, 0), 911280),
  ('partial repair guard 1', (21431981, 500000, 0), 332879240),
  ('partial repair guard 2', (13610000, 500000, 0), 20000000), ('control: large estate', (20000000, 0, 0), 255600000),
  ('control: under exclusion', (10000000, 0, 0), 0), ('control: with prior gifts', (10000000, 5000000, 0), 55600000),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000)],
 [('regression credit-not-exclusion 1', (788866, 18885032, 2000000), 31554640),
  ('regression credit-not-exclusion 2', (21431981, 500000, 0), 332879240),
  ('partial repair guard 1', (13610000, 5000000, 2000000), 120000000),
  ('partial repair guard 2', (13610000, 5703648, 0), 228145920),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000),
  ('control: gifts above exclusion', (5000000, 15000000, 0), 200000000), ('control: modest', (1500000, 200000, 0), 0),
  ('control: large estate', (20000000, 0, 0), 255600000)],
 [('regression credit-not-exclusion 1', (13610000, 500000, 0), 20000000),
  ('regression credit-not-exclusion 2', (13610000, 5000000, 2000000), 120000000),
  ('partial repair guard 1', (27783445, 500000, 5000000), 386937800),
  ('partial repair guard 2', (22327855, 5000000, 2000000), 468714200),
  ('control: large estate', (20000000, 0, 0), 255600000), ('control: under exclusion', (10000000, 0, 0), 0),
  ('control: with prior gifts', (10000000, 5000000, 0), 55600000),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000)]]
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 credit-not-exclusion 1	`250180000`	`255600000`	Failed
regression credit-not-exclusion 2	`50180000`	`55600000`	Failed
control: under exclusion	`0`	`0`	Passed
control: ported exclusion	`50180000`	`55600000`	Failed
control: gifts above exclusion	`200000000`	`200000000`	Passed
control: modest	`0`	`0`	Passed

SHA-256 / ff443dbfc968858094051fc4fa9d1a90af1f66d710ea241605199e57bd611989

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(estate, gifts, dsue):
    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))
    
    sched = [[10000, '18'], [20000, '20'], [40000, '22'], [60000, '24'], [80000, '26'], [100000, '28'], [150000, '30'], [250000, '32'], [500000, '34'], [750000, '37'], [1000000, '39'], [None, '40']]
    T = lambda x: prog(x, sched)
    credit = T(13610000 + dsue)
    tent = T(estate + gifts)
    gift_credit = max(0, T(gifts) - credit)
    return cents(max(0, tent - gift_credit - credit))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression credit-not-exclusion 1', (20000000, 0, 0), 255600000),
  ('regression credit-not-exclusion 2', (10000000, 5000000, 0), 55600000),
  ('control: under exclusion', (10000000, 0, 0), 0), ('control: ported exclusion', (20000000, 0, 5000000), 55600000),
  ('control: gifts above exclusion', (5000000, 15000000, 0), 200000000), ('control: modest', (1500000, 200000, 0), 0)],
 [('regression credit-not-exclusion 1', (20000000, 0, 5000000), 55600000),
  ('regression credit-not-exclusion 2', (5000000, 15000000, 0), 200000000),
  ('partial repair guard 2', (8632782, 5000000, 0), 911280), ('control: modest', (1500000, 200000, 0), 0),
  ('control: large estate', (20000000, 0, 0), 255600000), ('control: under exclusion', (10000000, 0, 0), 0),
  ('control: with prior gifts', (10000000, 5000000, 0), 55600000)],
 [('regression credit-not-exclusion 1', (13610000, 15000000, 0), 544400000),
  ('regression credit-not-exclusion 2', (8632782, 5000000, 0), 911280),
  ('partial repair guard 1', (21431981, 500000, 0), 332879240),
  ('partial repair guard 2', (13610000, 500000, 0), 20000000), ('control: large estate', (20000000, 0, 0), 255600000),
  ('control: under exclusion', (10000000, 0, 0), 0), ('control: with prior gifts', (10000000, 5000000, 0), 55600000),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000)],
 [('regression credit-not-exclusion 1', (788866, 18885032, 2000000), 31554640),
  ('regression credit-not-exclusion 2', (21431981, 500000, 0), 332879240),
  ('partial repair guard 1', (13610000, 5000000, 2000000), 120000000),
  ('partial repair guard 2', (13610000, 5703648, 0), 228145920),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000),
  ('control: gifts above exclusion', (5000000, 15000000, 0), 200000000), ('control: modest', (1500000, 200000, 0), 0),
  ('control: large estate', (20000000, 0, 0), 255600000)],
 [('regression credit-not-exclusion 1', (13610000, 500000, 0), 20000000),
  ('regression credit-not-exclusion 2', (13610000, 5000000, 2000000), 120000000),
  ('partial repair guard 1', (27783445, 500000, 5000000), 386937800),
  ('partial repair guard 2', (22327855, 5000000, 2000000), 468714200),
  ('control: large estate', (20000000, 0, 0), 255600000), ('control: under exclusion', (10000000, 0, 0), 0),
  ('control: with prior gifts', (10000000, 5000000, 0), 55600000),
  ('control: ported exclusion', (20000000, 0, 5000000), 55600000)]]
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 credit-not-exclusion 1	`255600000`	`255600000`	Passed
regression credit-not-exclusion 2	`55600000`	`55600000`	Passed
control: under exclusion	`0`	`0`	Passed
control: ported exclusion	`55600000`	`55600000`	Passed
control: gifts above exclusion	`200000000`	`200000000`	Passed
control: modest	`0`	`0`	Passed

SHA-256 / 70170e6d33f3036e2c0627420753e001e79948fd3fcf3577ca31d8ddbea93783

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 2026-09-29T14:47:06.704422+00:00.

Case digest / 7f3cbf9aa2d3527a048b8d57c33e0e8b444dbd00ee1c4a4ea24130d40ce5d696