FA-62216 / Currency rounding and FX conversion / Open access
The rate deviation is measured relative to the new rate · case 01
A drop exactly at the tolerance is rejected while an equal rise is accepted.
ROOT CAUSE
The relative deviation divides by the new rate instead of the reference.
VERIFIED REPAIR
Divide the absolute difference by the reference rate.
Unsuccessful approach: Dividing by the larger of the two rates makes the band asymmetric in the opposite way.
Case contract
solve(new, ref, tol_bps, inverted): accept a newly published rate if |n - ref| / ref * 10000 <= tol_bps using exact decimals, where n = new, or 1/new when the new quote arrives inverted. A non-positive new or ref returns 'ERR:rate'. Return 'accept' or 'reject'.
Why this case matters
Currency amounts must be rounded at the right stage and in the right unit, or ledgers, quotes and settlements drift by minor units.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from decimal import Decimal, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_FLOOR, ROUND_CEILING, ROUND_DOWN, ROUND_UP, ROUND_HALF_DOWN
N = 1
observations = []
def solve(new, ref, tol_bps, inverted):
n, r = Decimal(new), Decimal(ref)
if r <= 0 or n <= 0: return 'ERR:rate'
if inverted: n = 1 / n
dev = abs(n - r) / n
return 'accept' if dev * 10000 <= tol_bps else 'reject'
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression deviation-denominator 1', ('0.9', '1.0', 1000, False), 'accept'),
('regression deviation-denominator 2', ('1.610829', '1.6271', 100, False), 'accept'),
('partial repair guard 1', ('0.61344857', '1.6285', 10, True), 'reject'),
('partial repair guard 2', ('1.87484661', '1.8561', 100, False), 'reject'),
('control: upper boundary', ('1.1', '1.0', 1000, False), 'accept'),
('control: drop too far', ('0.8', '1.0', 1000, False), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate')],
[('regression deviation-denominator 1', ('1.19829675', '1.2013', 25, False), 'accept'),
('regression deviation-denominator 2', ('1.20407797', '0.8389', 100, True), 'accept'),
('partial repair guard 1', ('0.93539594', '1.0664', 25, True), 'reject'),
('partial repair guard 2', ('1.00665155', '0.9924', 10, True), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate'),
('control: small move', ('1.08351', '1.0835', 1, False), 'accept'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject')],
[('regression deviation-denominator 1', ('0.61344857', '1.6285', 10, True), 'reject'),
('regression deviation-denominator 2', ('1.8098883', '1.8117', 10, False), 'accept'),
('partial repair guard 1', ('1.41341757', '0.7005', 100, True), 'reject'),
('partial repair guard 2', ('0.78742098', '1.2687', 10, True), 'reject'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject'),
('control: inverted far', ('0.9', '1.0', 50, True), 'reject'),
('control: upper boundary', ('1.1', '1.0', 1000, False), 'accept'),
('control: lower boundary', ('0.9', '1.0', 1000, False), 'accept')],
[('regression deviation-denominator 1', ('1.093455', '1.1045', 100, False), 'accept'),
('regression deviation-denominator 2', ('1.87484661', '1.8561', 100, False), 'reject'),
('partial repair guard 1', ('0.78810637', '1.2657', 25, True), 'reject'),
('partial repair guard 2', ('1.93703825', '1.7525', 1000, False), 'reject'),
('control: lower boundary', ('0.9', '1.0', 1000, False), 'accept'),
('control: drop too far', ('0.8', '1.0', 1000, False), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate')],
[('regression deviation-denominator 1', ('0.6260540', '0.6292', 50, False), 'accept'),
('regression deviation-denominator 2', ('1.32976725', '1.3331', 25, False), 'accept'),
('partial repair guard 1', ('1.36829603', '0.7236', 100, True), 'reject'),
('partial repair guard 2', ('0.98224108', '1.0080', 100, True), 'reject'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate'),
('control: small move', ('1.08351', '1.0835', 1, False), 'accept'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject'),
('control: inverted far', ('0.9', '1.0', 50, True), 'reject')]]
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 deviation-denominator 1 | reject | accept | Failed |
| regression deviation-denominator 2 | reject | accept | Failed |
| partial repair guard 1 | accept | reject | Failed |
| partial repair guard 2 | accept | reject | Failed |
| control: upper boundary | accept | accept | Passed |
| control: drop too far | reject | reject | Passed |
| control: inverted exact | accept | accept | Passed |
| control: bad ref | ERR:rate | ERR:rate | Passed |
SHA-256 / 9b85c4b9e27ce8061a5f65c8e657a032db9faef7d879e87bcd000317a470130e
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from decimal import Decimal, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_FLOOR, ROUND_CEILING, ROUND_DOWN, ROUND_UP, ROUND_HALF_DOWN
N = 1
observations = []
def solve(new, ref, tol_bps, inverted):
n, r = Decimal(new), Decimal(ref)
if r <= 0 or n <= 0: return 'ERR:rate'
if inverted: n = 1 / n
dev = abs(n - r) / max(n, r)
return 'accept' if dev * 10000 <= tol_bps else 'reject'
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression deviation-denominator 1', ('0.9', '1.0', 1000, False), 'accept'),
('regression deviation-denominator 2', ('1.610829', '1.6271', 100, False), 'accept'),
('partial repair guard 1', ('0.61344857', '1.6285', 10, True), 'reject'),
('partial repair guard 2', ('1.87484661', '1.8561', 100, False), 'reject'),
('control: upper boundary', ('1.1', '1.0', 1000, False), 'accept'),
('control: drop too far', ('0.8', '1.0', 1000, False), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate')],
[('regression deviation-denominator 1', ('1.19829675', '1.2013', 25, False), 'accept'),
('regression deviation-denominator 2', ('1.20407797', '0.8389', 100, True), 'accept'),
('partial repair guard 1', ('0.93539594', '1.0664', 25, True), 'reject'),
('partial repair guard 2', ('1.00665155', '0.9924', 10, True), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate'),
('control: small move', ('1.08351', '1.0835', 1, False), 'accept'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject')],
[('regression deviation-denominator 1', ('0.61344857', '1.6285', 10, True), 'reject'),
('regression deviation-denominator 2', ('1.8098883', '1.8117', 10, False), 'accept'),
('partial repair guard 1', ('1.41341757', '0.7005', 100, True), 'reject'),
('partial repair guard 2', ('0.78742098', '1.2687', 10, True), 'reject'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject'),
('control: inverted far', ('0.9', '1.0', 50, True), 'reject'),
('control: upper boundary', ('1.1', '1.0', 1000, False), 'accept'),
('control: lower boundary', ('0.9', '1.0', 1000, False), 'accept')],
[('regression deviation-denominator 1', ('1.093455', '1.1045', 100, False), 'accept'),
('regression deviation-denominator 2', ('1.87484661', '1.8561', 100, False), 'reject'),
('partial repair guard 1', ('0.78810637', '1.2657', 25, True), 'reject'),
('partial repair guard 2', ('1.93703825', '1.7525', 1000, False), 'reject'),
('control: lower boundary', ('0.9', '1.0', 1000, False), 'accept'),
('control: drop too far', ('0.8', '1.0', 1000, False), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate')],
[('regression deviation-denominator 1', ('0.6260540', '0.6292', 50, False), 'accept'),
('regression deviation-denominator 2', ('1.32976725', '1.3331', 25, False), 'accept'),
('partial repair guard 1', ('1.36829603', '0.7236', 100, True), 'reject'),
('partial repair guard 2', ('0.98224108', '1.0080', 100, True), 'reject'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate'),
('control: small move', ('1.08351', '1.0835', 1, False), 'accept'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject'),
('control: inverted far', ('0.9', '1.0', 50, True), 'reject')]]
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 deviation-denominator 1 | accept | accept | Passed |
| regression deviation-denominator 2 | accept | accept | Passed |
| partial repair guard 1 | accept | reject | Failed |
| partial repair guard 2 | accept | reject | Failed |
| control: upper boundary | accept | accept | Passed |
| control: drop too far | reject | reject | Passed |
| control: inverted exact | accept | accept | Passed |
| control: bad ref | ERR:rate | ERR:rate | Passed |
SHA-256 / 970f39102f36256ae5e03e50399bcb3c8fb742b75fd8e13462b5997f158cf4e1
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from decimal import Decimal, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_FLOOR, ROUND_CEILING, ROUND_DOWN, ROUND_UP, ROUND_HALF_DOWN
N = 1
observations = []
def solve(new, ref, tol_bps, inverted):
n, r = Decimal(new), Decimal(ref)
if r <= 0 or n <= 0: return 'ERR:rate'
if inverted: n = 1 / n
dev = abs(n - r) / r
return 'accept' if dev * 10000 <= tol_bps else 'reject'
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression deviation-denominator 1', ('0.9', '1.0', 1000, False), 'accept'),
('regression deviation-denominator 2', ('1.610829', '1.6271', 100, False), 'accept'),
('partial repair guard 1', ('0.61344857', '1.6285', 10, True), 'reject'),
('partial repair guard 2', ('1.87484661', '1.8561', 100, False), 'reject'),
('control: upper boundary', ('1.1', '1.0', 1000, False), 'accept'),
('control: drop too far', ('0.8', '1.0', 1000, False), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate')],
[('regression deviation-denominator 1', ('1.19829675', '1.2013', 25, False), 'accept'),
('regression deviation-denominator 2', ('1.20407797', '0.8389', 100, True), 'accept'),
('partial repair guard 1', ('0.93539594', '1.0664', 25, True), 'reject'),
('partial repair guard 2', ('1.00665155', '0.9924', 10, True), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate'),
('control: small move', ('1.08351', '1.0835', 1, False), 'accept'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject')],
[('regression deviation-denominator 1', ('0.61344857', '1.6285', 10, True), 'reject'),
('regression deviation-denominator 2', ('1.8098883', '1.8117', 10, False), 'accept'),
('partial repair guard 1', ('1.41341757', '0.7005', 100, True), 'reject'),
('partial repair guard 2', ('0.78742098', '1.2687', 10, True), 'reject'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject'),
('control: inverted far', ('0.9', '1.0', 50, True), 'reject'),
('control: upper boundary', ('1.1', '1.0', 1000, False), 'accept'),
('control: lower boundary', ('0.9', '1.0', 1000, False), 'accept')],
[('regression deviation-denominator 1', ('1.093455', '1.1045', 100, False), 'accept'),
('regression deviation-denominator 2', ('1.87484661', '1.8561', 100, False), 'reject'),
('partial repair guard 1', ('0.78810637', '1.2657', 25, True), 'reject'),
('partial repair guard 2', ('1.93703825', '1.7525', 1000, False), 'reject'),
('control: lower boundary', ('0.9', '1.0', 1000, False), 'accept'),
('control: drop too far', ('0.8', '1.0', 1000, False), 'reject'),
('control: inverted exact', ('0.5', '2.0', 0, True), 'accept'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate')],
[('regression deviation-denominator 1', ('0.6260540', '0.6292', 50, False), 'accept'),
('regression deviation-denominator 2', ('1.32976725', '1.3331', 25, False), 'accept'),
('partial repair guard 1', ('1.36829603', '0.7236', 100, True), 'reject'),
('partial repair guard 2', ('0.98224108', '1.0080', 100, True), 'reject'),
('control: bad ref', ('1.2', '0', 5, False), 'ERR:rate'),
('control: small move', ('1.08351', '1.0835', 1, False), 'accept'),
('control: rise too far', ('1.2', '1.0', 1000, False), 'reject'),
('control: inverted far', ('0.9', '1.0', 50, True), 'reject')]]
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 deviation-denominator 1 | accept | accept | Passed |
| regression deviation-denominator 2 | accept | accept | Passed |
| partial repair guard 1 | reject | reject | Passed |
| partial repair guard 2 | reject | reject | Passed |
| control: upper boundary | accept | accept | Passed |
| control: drop too far | reject | reject | Passed |
| control: inverted exact | accept | accept | Passed |
| control: bad ref | ERR:rate | ERR:rate | Passed |
SHA-256 / f67bff9244d2636b725c31d6d5b16d6ebbd50aec8ea0b11a63fd2a8939196c52
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 2026-09-29T14:47:02.611186+00:00.
Case digest / d49f2fcae23f78b2d51ec119db8c41d3a9e526ac1dc3c965478e3deef0607a53