FA-62266 / Currency rounding and FX conversion / Open access

Inverted USD legs are rounded to four decimals · case 01

Crosses built from EURUSD or GBPUSD drift in the fourth significant digit.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

1/quote is quantized to 0.0001 before being used as a leg.

VERIFIED REPAIR

Keep the inverted leg at full working precision.

Unsuccessful approach: Rounding the inverted leg to eight decimals still perturbs the sixth decimal of large crosses.

Case contract

solve(quotes, target): quotes maps six-letter pairs to rates (QUOTE units per BASE unit). For currency c, units per USD are: 1 for USD; quotes['USD'+c] if present (authoritative when both orientations exist); else 1/quotes[c+'USD']; else unknown. The target BBBQQQ rate = (QQQ per USD)/(BBB per USD), rounded half-even to 6 decimals and returned as a string; an unknown leg returns 'ERR:no-quote'.

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(quotes, target):
    def per_usd(c):
        if c == 'USD': return Decimal(1)
        if 'USD' + c in quotes: return Decimal(quotes['USD' + c])
        if c + 'USD' in quotes: return (1 / Decimal(quotes[c + 'USD'])).quantize(Decimal('0.0001'))
        return None
    b, q = target[:3], target[3:]
    pb, pq = per_usd(b), per_usd(q)
    if pb is None or pq is None: return 'ERR:no-quote'
    return format((pq / pb).quantize(Decimal('0.000001'), rounding=ROUND_HALF_EVEN), 'f')
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513'),
  ('partial repair guard 2',
   ({'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDCAD': '1.3577'}, 'GBPCAD'),
   '1.717490'),
  ('control: direct usd base',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDJPY'),
   '151.370000'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: franc aussie',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDCAD': '1.3577'}, 'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'USDEUR': '0.9231'},
    'GBPCAD'),
   '1.717490'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: euro yen',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDEUR': '0.9231'}, 'AUDCHF'),
   '0.581922'),
  ('regression inverse-leg-precision 2',
   ({'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'JPYUSD': '0.006610'},
    'CHFGBP'),
   '0.898209'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'USDCAD': '1.3577',
     'JPYUSD': '0.006610'},
    'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'USDEUR': '0.9231'},
    'GBPJPY'),
   '191.483050'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: usd to euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935'),
  ('control: euro yen',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395'),
  ('control: sterling euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'EURAUD'),
   '1.638687'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'USDGBP'),
   '0.790514'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'USDCAD': '1.3577'}, 'EURJPY'),
   '164.009395'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'GBPCHF'),
   '1.113326'),
  ('control: sterling euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513'),
  ('control: direct usd base',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDJPY'),
   '151.370000'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote')],
 [('regression inverse-leg-precision 1',
   ({'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDEUR': '0.9231'}, 'EURGBP'), '0.856369'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'CADGBP'),
   '0.582245'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'EURJPY'),
   '164.009395'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: franc aussie',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: usd to euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935')]]
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 inverse-leg-precision 1	`164.015603`	`164.009395`	Failed
regression inverse-leg-precision 2	`1.167489`	`1.167513`	Failed
partial repair guard 2	`1.717521`	`1.717490`	Failed
control: direct usd base	`151.370000`	`151.370000`	Passed
control: usd quote	`0.006606`	`0.006606`	Passed
control: missing leg	`ERR:no-quote`	`ERR:no-quote`	Passed
control: franc aussie	`1.718441`	`1.718443`	Failed

SHA-256 / ce14be340e54b2ec1d341142f36fa5b8862327b17635ec1fc0d2ae2237e29214

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(quotes, target):
    def per_usd(c):
        if c == 'USD': return Decimal(1)
        if 'USD' + c in quotes: return Decimal(quotes['USD' + c])
        if c + 'USD' in quotes: return (1 / Decimal(quotes[c + 'USD'])).quantize(Decimal('0.00000001'))
        return None
    b, q = target[:3], target[3:]
    pb, pq = per_usd(b), per_usd(q)
    if pb is None or pq is None: return 'ERR:no-quote'
    return format((pq / pb).quantize(Decimal('0.000001'), rounding=ROUND_HALF_EVEN), 'f')
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513'),
  ('partial repair guard 2',
   ({'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDCAD': '1.3577'}, 'GBPCAD'),
   '1.717490'),
  ('control: direct usd base',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDJPY'),
   '151.370000'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: franc aussie',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDCAD': '1.3577'}, 'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'USDEUR': '0.9231'},
    'GBPCAD'),
   '1.717490'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: euro yen',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDEUR': '0.9231'}, 'AUDCHF'),
   '0.581922'),
  ('regression inverse-leg-precision 2',
   ({'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'JPYUSD': '0.006610'},
    'CHFGBP'),
   '0.898209'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'USDCAD': '1.3577',
     'JPYUSD': '0.006610'},
    'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'USDEUR': '0.9231'},
    'GBPJPY'),
   '191.483050'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: usd to euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935'),
  ('control: euro yen',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395'),
  ('control: sterling euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'EURAUD'),
   '1.638687'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'USDGBP'),
   '0.790514'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'USDCAD': '1.3577'}, 'EURJPY'),
   '164.009395'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'GBPCHF'),
   '1.113326'),
  ('control: sterling euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513'),
  ('control: direct usd base',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDJPY'),
   '151.370000'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote')],
 [('regression inverse-leg-precision 1',
   ({'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDEUR': '0.9231'}, 'EURGBP'), '0.856369'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'CADGBP'),
   '0.582245'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'EURJPY'),
   '164.009395'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: franc aussie',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: usd to euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935')]]
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 inverse-leg-precision 1	`164.009396`	`164.009395`	Failed
regression inverse-leg-precision 2	`1.167513`	`1.167513`	Passed
partial repair guard 2	`1.717491`	`1.717490`	Failed
control: direct usd base	`151.370000`	`151.370000`	Passed
control: usd quote	`0.006606`	`0.006606`	Passed
control: missing leg	`ERR:no-quote`	`ERR:no-quote`	Passed
control: franc aussie	`1.718443`	`1.718443`	Passed

SHA-256 / 0298320b4aa7779368a6b32884eeb9be413b6405f15a1e11d7586778b7d06beb

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(quotes, target):
    def per_usd(c):
        if c == 'USD': return Decimal(1)
        if 'USD' + c in quotes: return Decimal(quotes['USD' + c])
        if c + 'USD' in quotes: return 1 / Decimal(quotes[c + 'USD'])
        return None
    b, q = target[:3], target[3:]
    pb, pq = per_usd(b), per_usd(q)
    if pb is None or pq is None: return 'ERR:no-quote'
    return format((pq / pb).quantize(Decimal('0.000001'), rounding=ROUND_HALF_EVEN), 'f')
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513'),
  ('partial repair guard 2',
   ({'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDCAD': '1.3577'}, 'GBPCAD'),
   '1.717490'),
  ('control: direct usd base',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDJPY'),
   '151.370000'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: franc aussie',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDCAD': '1.3577'}, 'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'USDEUR': '0.9231'},
    'GBPCAD'),
   '1.717490'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: euro yen',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDEUR': '0.9231'}, 'AUDCHF'),
   '0.581922'),
  ('regression inverse-leg-precision 2',
   ({'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'JPYUSD': '0.006610'},
    'CHFGBP'),
   '0.898209'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'USDCAD': '1.3577',
     'JPYUSD': '0.006610'},
    'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577',
     'USDEUR': '0.9231'},
    'GBPJPY'),
   '191.483050'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: usd to euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935'),
  ('control: euro yen',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURJPY'),
   '164.009395'),
  ('control: sterling euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513')],
 [('regression inverse-leg-precision 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'EURAUD'),
   '1.638687'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'USDGBP'),
   '0.790514'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'USDCAD': '1.3577'}, 'EURJPY'),
   '164.009395'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'GBPCHF'),
   '1.113326'),
  ('control: sterling euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'GBPEUR'),
   '1.167513'),
  ('control: direct usd base',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDJPY'),
   '151.370000'),
  ('control: usd quote',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'JPYUSD'),
   '0.006606'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote')],
 [('regression inverse-leg-precision 1',
   ({'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612', 'USDEUR': '0.9231'}, 'EURGBP'), '0.856369'),
  ('regression inverse-leg-precision 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'CADGBP'),
   '0.582245'),
  ('partial repair guard 1',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'GBPJPY'),
   '191.483050'),
  ('partial repair guard 2',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDCAD': '1.3577'},
    'EURJPY'),
   '164.009395'),
  ('control: missing leg',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'EURSEK'),
   'ERR:no-quote'),
  ('control: franc aussie',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'CHFAUD'),
   '1.718443'),
  ('control: both orientations',
   ({'USDJPY': '151.37',
     'EURUSD': '1.0835',
     'GBPUSD': '1.2650',
     'USDCHF': '0.8801',
     'AUDUSD': '0.6612',
     'USDEUR': '0.9231'},
    'EURCHF'),
   '0.953418'),
  ('control: usd to euro',
   ({'USDJPY': '151.37', 'EURUSD': '1.0835', 'GBPUSD': '1.2650', 'USDCHF': '0.8801', 'AUDUSD': '0.6612'}, 'USDEUR'),
   '0.922935')]]
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 inverse-leg-precision 1	`164.009395`	`164.009395`	Passed
regression inverse-leg-precision 2	`1.167513`	`1.167513`	Passed
partial repair guard 2	`1.717490`	`1.717490`	Passed
control: direct usd base	`151.370000`	`151.370000`	Passed
control: usd quote	`0.006606`	`0.006606`	Passed
control: missing leg	`ERR:no-quote`	`ERR:no-quote`	Passed
control: franc aussie	`1.718443`	`1.718443`	Passed

SHA-256 / e664720a772c1138b6a05e4763b59e54324f04d3d97d035af2a5555adf95bd88

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 2026-09-29T14:47:03.015314+00:00.

Case digest / dd9e26aada6d567e400a3a2f62f18c56b0912ec2ce1af2e28b196f597fada1ab