FA-6016 / Linear algebra / Open access
Matrix two determinant · case 01
The off-diagonal product is added instead of subtracted.
ROOT CAUSE
The off-diagonal product is added instead of subtracted.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return m[0][0]*m[1][1]-m[0][1]*m[1][0]
Unsuccessful approach: Determinant sign is discarded despite representing orientation.
Case contract
Integer matrix/vector entries, rectangular rows, compatible multiplication dimensions, and square matrices for determinant, trace, inverse, symmetry and characteristic-polynomial operations. Rational matrix outputs are reduced Fraction strings. Matrix two determinant. Exact operational definition: m[0][0]*m[1][1]-m[0][1]*m[1][0]
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Linear algebra 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(m):
return m[0][0]*m[1][1]+m[0][1]*m[1][0]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([[1, 2], [3, 4]],)', solve(*([[1, 2], [3, 4]],)), -2)
check('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), 1)
check('fixture 3: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), 0)
check('fixture 4: ([[0, 1], [1, 0]],)', solve(*([[0, 1], [1, 0]],)), -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, 2], [3, 4]],) | 10 | -2 | Failed |
| fixture 2: ([[1, 0], [0, 1]],) | 1 | 1 | Passed |
| fixture 3: ([[1, 2], [2, 4]],) | 8 | 0 | Failed |
| fixture 4: ([[0, 1], [1, 0]],) | 1 | -1 | Failed |
SHA-256 / 5502633a3846c798d8e4a5e571b54711a59c5c2b15e13a922041483c14d24622
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(m):
return abs(m[0][0]*m[1][1]-m[0][1]*m[1][0])
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([[1, 2], [3, 4]],)', solve(*([[1, 2], [3, 4]],)), -2)
check('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), 1)
check('fixture 3: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), 0)
check('fixture 4: ([[0, 1], [1, 0]],)', solve(*([[0, 1], [1, 0]],)), -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, 2], [3, 4]],) | 2 | -2 | Failed |
| fixture 2: ([[1, 0], [0, 1]],) | 1 | 1 | Passed |
| fixture 3: ([[1, 2], [2, 4]],) | 0 | 0 | Passed |
| fixture 4: ([[0, 1], [1, 0]],) | 1 | -1 | Failed |
SHA-256 / 45d1ea058f8fb1c02ae459abd4b734a90a13b0b46a85d389644da4755abc8136
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(m):
return m[0][0]*m[1][1]-m[0][1]*m[1][0]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([[1, 2], [3, 4]],)', solve(*([[1, 2], [3, 4]],)), -2)
check('fixture 2: ([[1, 0], [0, 1]],)', solve(*([[1, 0], [0, 1]],)), 1)
check('fixture 3: ([[1, 2], [2, 4]],)', solve(*([[1, 2], [2, 4]],)), 0)
check('fixture 4: ([[0, 1], [1, 0]],)', solve(*([[0, 1], [1, 0]],)), -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, 2], [3, 4]],) | -2 | -2 | Passed |
| fixture 2: ([[1, 0], [0, 1]],) | 1 | 1 | Passed |
| fixture 3: ([[1, 2], [2, 4]],) | 0 | 0 | Passed |
| fixture 4: ([[0, 1], [1, 0]],) | -1 | -1 | Passed |
SHA-256 / b0add1fe72d3d322479934a99805faef4dd44da740a04353736977ca9ea907fa
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 2026-09-29T14:37:56.489247+00:00.
Case digest / 182cae5fdb9dac0a0550e4bc1465ffb14d1b78c0b23f32dcb6b4852eeb9342ba