FA-5911 / Solid geometry / Open access
Sphere volume divided by pi · case 01
Radius is squared instead of cubed for volume.
ROOT CAUSE
Radius is squared instead of cubed for volume.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return 4*r**3/3
Unsuccessful approach: The sphere coefficient loses its factor of four.
Case contract
Nonnegative integer dimensions; exact products and ordinary Python real division. Quantities named divided by pi or pi-squared deliberately omit that factor from the returned result. Sphere volume divided by pi. Exact operational definition: 4*r**3/3
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Solid geometry 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(r):
return 4*r*r/3
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (0,)', solve(*(0,)), 0)
check('fixture 2: (3,)', solve(*(3,)), 36)
check('fixture 3: (6,)', solve(*(6,)), 288)
check('fixture 4: (1,)', solve(*(1,)), 1.3333333333333333)
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: (0,) | 0.0 | 0 | Passed |
| fixture 2: (3,) | 12.0 | 36 | Failed |
| fixture 3: (6,) | 48.0 | 288 | Failed |
| fixture 4: (1,) | 1.3333333333333333 | 1.3333333333333333 | Passed |
SHA-256 / a00638b8c7e4fa72a370d89cbff360d558d4071e7af3c2ccd8794805ffcf538a
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(r):
return r**3/3
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (0,)', solve(*(0,)), 0)
check('fixture 2: (3,)', solve(*(3,)), 36)
check('fixture 3: (6,)', solve(*(6,)), 288)
check('fixture 4: (1,)', solve(*(1,)), 1.3333333333333333)
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: (0,) | 0.0 | 0 | Passed |
| fixture 2: (3,) | 9.0 | 36 | Failed |
| fixture 3: (6,) | 72.0 | 288 | Failed |
| fixture 4: (1,) | 0.3333333333333333 | 1.3333333333333333 | Failed |
SHA-256 / 888873edae1a9105090fb118262e844c2bce926fbc086d2628ac8851c3af8954
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(r):
return 4*r**3/3
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (0,)', solve(*(0,)), 0)
check('fixture 2: (3,)', solve(*(3,)), 36)
check('fixture 3: (6,)', solve(*(6,)), 288)
check('fixture 4: (1,)', solve(*(1,)), 1.3333333333333333)
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: (0,) | 0.0 | 0 | Passed |
| fixture 2: (3,) | 36.0 | 36 | Passed |
| fixture 3: (6,) | 288.0 | 288 | Passed |
| fixture 4: (1,) | 1.3333333333333333 | 1.3333333333333333 | Passed |
SHA-256 / c67bd876330b74256c81ce947e4dc170ae55d781a4b1df2147a9f06a3a1640be
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 2026-09-29T14:37:55.338575+00:00.
Case digest / 997dce11f5083bf07d1f86549be64275a40e3cbf44581743160ae803b20c9591