FA-5436 / Integer arithmetic / Open access
Integer signum · case 01
Zero is assigned a positive direction.
ROOT CAUSE
Zero is assigned a positive direction.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return (n>0)-(n<0)
Unsuccessful approach: Floating sign transfer also treats zero as positive.
Case contract
Integer arguments; denominators, steps, moduli, and bit widths are positive. Unsigned word inputs fit the specified width except where masking is explicitly the operation. Sequence sizes are nonnegative. Integer signum. Exact operational definition: (n>0)-(n<0)
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Integer mathematics results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n):
return 1 if n>=0 else -1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (-5,)', solve(*(-5,)), -1)
check('fixture 2: (0,)', solve(*(0,)), 0)
check('fixture 3: (7,)', solve(*(7,)), 1)
check('fixture 4: (1606938044258990275541962092341162602522202993782792835301376,)', solve(*(1606938044258990275541962092341162602522202993782792835301376,)), 1)
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 |
|---|---|---|---|
| fixture 1: (-5,) | -1 | -1 | Passed |
| fixture 2: (0,) | 1 | 0 | Failed |
| fixture 3: (7,) | 1 | 1 | Passed |
| fixture 4: (1606938044258990275541962092341162602522202993782792835301376,) | 1 | 1 | Passed |
SHA-256 / 2dc8ce3bfe48bb387218b01045092d875ee273e52820043694a40c4db0184064
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n):
return int(math.copysign(1,n))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (-5,)', solve(*(-5,)), -1)
check('fixture 2: (0,)', solve(*(0,)), 0)
check('fixture 3: (7,)', solve(*(7,)), 1)
check('fixture 4: (1606938044258990275541962092341162602522202993782792835301376,)', solve(*(1606938044258990275541962092341162602522202993782792835301376,)), 1)
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 |
|---|---|---|---|
| fixture 1: (-5,) | -1 | -1 | Passed |
| fixture 2: (0,) | 1 | 0 | Failed |
| fixture 3: (7,) | 1 | 1 | Passed |
| fixture 4: (1606938044258990275541962092341162602522202993782792835301376,) | 1 | 1 | Passed |
SHA-256 / 65f4c2142169daca6042026386e17d62132153102ff861c6e7b2d7928db3f173
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n):
return (n>0)-(n<0)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (-5,)', solve(*(-5,)), -1)
check('fixture 2: (0,)', solve(*(0,)), 0)
check('fixture 3: (7,)', solve(*(7,)), 1)
check('fixture 4: (1606938044258990275541962092341162602522202993782792835301376,)', solve(*(1606938044258990275541962092341162602522202993782792835301376,)), 1)
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 |
|---|---|---|---|
| fixture 1: (-5,) | -1 | -1 | Passed |
| fixture 2: (0,) | 0 | 0 | Passed |
| fixture 3: (7,) | 1 | 1 | Passed |
| fixture 4: (1606938044258990275541962092341162602522202993782792835301376,) | 1 | 1 | Passed |
SHA-256 / 9926356ad12a20518881da051e3ea99ba2fe90682643595de32aed3ba4a953ce
Verification & scope
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 2026-09-29T14:37:49.473567+00:00.
Case digest / 7baef65b4070d9a131954c7f21e706df4a2af62c45349e024bf9a5ee8acc7d4b