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FA-62596 / Tax bracket computation / Open access

First-time-buyer relief is applied above the price cap · case 01

A 700000 purchase by a first-time buyer is taxed only on the 425000-625000 slice.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Relief eligibility omits the price <= 625000 condition.

VERIFIED REPAIR

Grant relief only when price <= 625000; otherwise use the normal slices for the whole price.

Unsuccessful approach: Testing price < 625000 denies relief at exactly the cap.

Case contract

solve(price, ftb, additional, nonresident): stipulated property transfer tax in whole pounds. Normal slices: 0% to 250000, 5% to 925000, 10% to 1500000, 12% above. First-time-buyer slices (0% to 425000, 5% to 625000) apply only when ftb is true, the purchase is not an additional dwelling, and price <= 625000; otherwise normal slices. Surcharges add percentage points to every slice including 0% slices: +3 for an additional dwelling when price >= 40000, +2 for a non-resident buyer; they stack. Return the tax rounded down to whole pounds.

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(price, ftb, additional, nonresident):
    normal = [(250000, 0), (925000, 5), (1500000, 10), (None, 12)]
    first = [(425000, 0), (625000, 5)]
    use_ftb = ftb and not additional
    bands = first if use_ftb else normal
    sur = (3 if additional and price >= 40000 else 0) + (2 if nonresident else 0)
    tax, lower = 0, 0
    for upper, rate in bands:
        top = price if upper is None else min(price, upper)
        if top > lower: tax += (top - lower) * (rate + sur)
        if upper is None or price <= upper: break
        lower = upper
    return tax // 100
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression first-time-buyer-cap 1', (625001, True, False, False), 18750),
  ('regression first-time-buyer-cap 2', (925000, True, False, False), 33750),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: normal', (300000, False, False, False), 2500),
  ('control: first-time buyer', (500000, True, False, False), 3750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500)],
 [('regression first-time-buyer-cap 1', (2087334, True, False, False), 161730),
  ('regression first-time-buyer-cap 2', (1462530, True, False, False), 87503),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: ftb over cap', (625001, True, False, False), 18750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500),
  ('control: below surcharge floor', (39999, False, True, False), 0)],
 [('regression first-time-buyer-cap 1', (1130152, True, False, False), 54265),
  ('regression first-time-buyer-cap 2', (1943189, True, False, True), 183296),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: below surcharge floor', (39999, False, True, False), 0),
  ('control: nonresident cheap', (39999, False, False, True), 799),
  ('control: ftb additional', (400000, True, True, False), 19500),
  ('control: expensive', (2000000, False, False, False), 151250)],
 [('regression first-time-buyer-cap 1', (906584, True, False, False), 32829),
  ('regression first-time-buyer-cap 2', (1946173, True, False, False), 144790),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: expensive', (2000000, False, False, False), 151250),
  ('control: odd pounds', (250013, False, False, False), 0), ('control: normal', (300000, False, False, False), 2500),
  ('control: first-time buyer', (500000, True, False, False), 3750)],
 [('regression first-time-buyer-cap 1', (625001, True, False, True), 31250),
  ('regression first-time-buyer-cap 2', (2255703, True, False, True), 227048),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: first-time buyer', (500000, True, False, False), 3750),
  ('control: ftb over cap', (625001, True, False, False), 18750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500)]]
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 first-time-buyer-cap 11000018750Failed
regression first-time-buyer-cap 21000033750Failed
partial repair guard 11000010000Passed
partial repair guard 22250022500Passed
control: normal25002500Passed
control: first-time buyer37503750Passed
control: additional dwelling1150011500Passed
control: additional nonresident1750017500Passed

SHA-256 / d25f3aa2be275362e835e335a8ea9692929c2249b11180130f4328938b5ddbd0

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(price, ftb, additional, nonresident):
    normal = [(250000, 0), (925000, 5), (1500000, 10), (None, 12)]
    first = [(425000, 0), (625000, 5)]
    use_ftb = ftb and not additional and price < 625000
    bands = first if use_ftb else normal
    sur = (3 if additional and price >= 40000 else 0) + (2 if nonresident else 0)
    tax, lower = 0, 0
    for upper, rate in bands:
        top = price if upper is None else min(price, upper)
        if top > lower: tax += (top - lower) * (rate + sur)
        if upper is None or price <= upper: break
        lower = upper
    return tax // 100
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression first-time-buyer-cap 1', (625001, True, False, False), 18750),
  ('regression first-time-buyer-cap 2', (925000, True, False, False), 33750),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: normal', (300000, False, False, False), 2500),
  ('control: first-time buyer', (500000, True, False, False), 3750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500)],
 [('regression first-time-buyer-cap 1', (2087334, True, False, False), 161730),
  ('regression first-time-buyer-cap 2', (1462530, True, False, False), 87503),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: ftb over cap', (625001, True, False, False), 18750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500),
  ('control: below surcharge floor', (39999, False, True, False), 0)],
 [('regression first-time-buyer-cap 1', (1130152, True, False, False), 54265),
  ('regression first-time-buyer-cap 2', (1943189, True, False, True), 183296),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: below surcharge floor', (39999, False, True, False), 0),
  ('control: nonresident cheap', (39999, False, False, True), 799),
  ('control: ftb additional', (400000, True, True, False), 19500),
  ('control: expensive', (2000000, False, False, False), 151250)],
 [('regression first-time-buyer-cap 1', (906584, True, False, False), 32829),
  ('regression first-time-buyer-cap 2', (1946173, True, False, False), 144790),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: expensive', (2000000, False, False, False), 151250),
  ('control: odd pounds', (250013, False, False, False), 0), ('control: normal', (300000, False, False, False), 2500),
  ('control: first-time buyer', (500000, True, False, False), 3750)],
 [('regression first-time-buyer-cap 1', (625001, True, False, True), 31250),
  ('regression first-time-buyer-cap 2', (2255703, True, False, True), 227048),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: first-time buyer', (500000, True, False, False), 3750),
  ('control: ftb over cap', (625001, True, False, False), 18750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500)]]
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 first-time-buyer-cap 11875018750Passed
regression first-time-buyer-cap 23375033750Passed
partial repair guard 11875010000Failed
partial repair guard 23125022500Failed
control: normal25002500Passed
control: first-time buyer37503750Passed
control: additional dwelling1150011500Passed
control: additional nonresident1750017500Passed

SHA-256 / d2e0d06f8a0660479a1d479f9aa224c96f7a36bb048b8a9060cde61b8c530995

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(price, ftb, additional, nonresident):
    normal = [(250000, 0), (925000, 5), (1500000, 10), (None, 12)]
    first = [(425000, 0), (625000, 5)]
    use_ftb = ftb and not additional and price <= 625000
    bands = first if use_ftb else normal
    sur = (3 if additional and price >= 40000 else 0) + (2 if nonresident else 0)
    tax, lower = 0, 0
    for upper, rate in bands:
        top = price if upper is None else min(price, upper)
        if top > lower: tax += (top - lower) * (rate + sur)
        if upper is None or price <= upper: break
        lower = upper
    return tax // 100
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression first-time-buyer-cap 1', (625001, True, False, False), 18750),
  ('regression first-time-buyer-cap 2', (925000, True, False, False), 33750),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: normal', (300000, False, False, False), 2500),
  ('control: first-time buyer', (500000, True, False, False), 3750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500)],
 [('regression first-time-buyer-cap 1', (2087334, True, False, False), 161730),
  ('regression first-time-buyer-cap 2', (1462530, True, False, False), 87503),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: ftb over cap', (625001, True, False, False), 18750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500),
  ('control: below surcharge floor', (39999, False, True, False), 0)],
 [('regression first-time-buyer-cap 1', (1130152, True, False, False), 54265),
  ('regression first-time-buyer-cap 2', (1943189, True, False, True), 183296),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: below surcharge floor', (39999, False, True, False), 0),
  ('control: nonresident cheap', (39999, False, False, True), 799),
  ('control: ftb additional', (400000, True, True, False), 19500),
  ('control: expensive', (2000000, False, False, False), 151250)],
 [('regression first-time-buyer-cap 1', (906584, True, False, False), 32829),
  ('regression first-time-buyer-cap 2', (1946173, True, False, False), 144790),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: expensive', (2000000, False, False, False), 151250),
  ('control: odd pounds', (250013, False, False, False), 0), ('control: normal', (300000, False, False, False), 2500),
  ('control: first-time buyer', (500000, True, False, False), 3750)],
 [('regression first-time-buyer-cap 1', (625001, True, False, True), 31250),
  ('regression first-time-buyer-cap 2', (2255703, True, False, True), 227048),
  ('partial repair guard 1', (625000, True, False, False), 10000),
  ('partial repair guard 2', (625000, True, False, True), 22500),
  ('control: first-time buyer', (500000, True, False, False), 3750),
  ('control: ftb over cap', (625001, True, False, False), 18750),
  ('control: additional dwelling', (300000, False, True, False), 11500),
  ('control: additional nonresident', (300000, False, True, True), 17500)]]
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 first-time-buyer-cap 11875018750Passed
regression first-time-buyer-cap 23375033750Passed
partial repair guard 11000010000Passed
partial repair guard 22250022500Passed
control: normal25002500Passed
control: first-time buyer37503750Passed
control: additional dwelling1150011500Passed
control: additional nonresident1750017500Passed

SHA-256 / 10f6450a3ec6112b501071f83b578616b56f9d325d7f67290e84b688caa0e56b

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 2026-09-29T14:47:06.029007+00:00.

Case digest / c75d5bc8958a42e90a6c7097363bdaf0183a491d8f7a4e688ddc7523a3be466d