FA-6131 / Polynomial arithmetic / Open access
Quadratic discriminant · case 01
The product term uses addition instead of subtraction.
ROOT CAUSE
The product term uses addition instead of subtraction.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return b*b-4*a*c
Unsuccessful approach: The discriminant coefficient loses a factor of two.
Case contract
Integer coefficients in ascending power order and integer evaluation bounds; missing high-degree coefficients are zero. Rational outputs are reduced Fraction strings; the zero-polynomial degree is -1. Quadratic discriminant. Exact operational definition: b*b-4*a*c
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Polynomial arithmetic 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(a, b, c):
return b*b+4*a*c
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (1, 0, -1)', solve(*(1, 0, -1)), 4)
check('fixture 2: (1, 2, 1)', solve(*(1, 2, 1)), 0)
check('fixture 3: (1, 0, 1)', solve(*(1, 0, 1)), -4)
check('fixture 4: (2, 3, 1)', solve(*(2, 3, 1)), 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: (1, 0, -1) | -4 | 4 | Failed |
| fixture 2: (1, 2, 1) | 8 | 0 | Failed |
| fixture 3: (1, 0, 1) | 4 | -4 | Failed |
| fixture 4: (2, 3, 1) | 17 | 1 | Failed |
SHA-256 / fa0b46ec5a9ad30762a1432867142e8ffc87d27d23ae1b2747e76962976b20fd
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(a, b, c):
return b*b-2*a*c
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (1, 0, -1)', solve(*(1, 0, -1)), 4)
check('fixture 2: (1, 2, 1)', solve(*(1, 2, 1)), 0)
check('fixture 3: (1, 0, 1)', solve(*(1, 0, 1)), -4)
check('fixture 4: (2, 3, 1)', solve(*(2, 3, 1)), 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: (1, 0, -1) | 2 | 4 | Failed |
| fixture 2: (1, 2, 1) | 2 | 0 | Failed |
| fixture 3: (1, 0, 1) | -2 | -4 | Failed |
| fixture 4: (2, 3, 1) | 5 | 1 | Failed |
SHA-256 / 5f3f5086a1bf776c66b877789040d7da1271e5119385e8dc8897716edd2ed652
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(a, b, c):
return b*b-4*a*c
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (1, 0, -1)', solve(*(1, 0, -1)), 4)
check('fixture 2: (1, 2, 1)', solve(*(1, 2, 1)), 0)
check('fixture 3: (1, 0, 1)', solve(*(1, 0, 1)), -4)
check('fixture 4: (2, 3, 1)', solve(*(2, 3, 1)), 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: (1, 0, -1) | 4 | 4 | Passed |
| fixture 2: (1, 2, 1) | 0 | 0 | Passed |
| fixture 3: (1, 0, 1) | -4 | -4 | Passed |
| fixture 4: (2, 3, 1) | 1 | 1 | Passed |
SHA-256 / b82c92d8abde7c06560e5b5f01a342359cc790ff6fa249223a66e1f4678b06da
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 2026-09-29T14:37:57.853066+00:00.
Case digest / 5a879ce37448883f9830dd3fda058af45507fd5c1b4d6970712a1899881667c0