FA-5926 / Solid geometry / Open access
Cone volume divided by pi · case 01
A cone is assigned the volume of its bounding cylinder.
ROOT CAUSE
A cone is assigned the volume of its bounding cylinder.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return r*r*h/3
Unsuccessful approach: The base radius is not squared.
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. Cone volume divided by pi. Exact operational definition: r*r*h/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, h):
return r*r*h
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 4)', solve(*(3, 4)), 12)
check('fixture 2: (1, 3)', solve(*(1, 3)), 1)
check('fixture 3: (0, 5)', solve(*(0, 5)), 0)
check('fixture 4: (2, 6)', solve(*(2, 6)), 8)
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: (3, 4) | 36 | 12 | Failed |
| fixture 2: (1, 3) | 3 | 1 | Failed |
| fixture 3: (0, 5) | 0 | 0 | Passed |
| fixture 4: (2, 6) | 24 | 8 | Failed |
SHA-256 / e204d5c2c67a6935bc0330c671a2e4f5f0b9ec70dfbb889e8dfd9f3fd0132750
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, h):
return r*h/3
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 4)', solve(*(3, 4)), 12)
check('fixture 2: (1, 3)', solve(*(1, 3)), 1)
check('fixture 3: (0, 5)', solve(*(0, 5)), 0)
check('fixture 4: (2, 6)', solve(*(2, 6)), 8)
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: (3, 4) | 4.0 | 12 | Failed |
| fixture 2: (1, 3) | 1.0 | 1 | Passed |
| fixture 3: (0, 5) | 0.0 | 0 | Passed |
| fixture 4: (2, 6) | 4.0 | 8 | Failed |
SHA-256 / 275ea221cfef2dcff9e1e9722a5e1cd8f53c9b9fc52e6777ae263c85fb75d913
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, h):
return r*r*h/3
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 4)', solve(*(3, 4)), 12)
check('fixture 2: (1, 3)', solve(*(1, 3)), 1)
check('fixture 3: (0, 5)', solve(*(0, 5)), 0)
check('fixture 4: (2, 6)', solve(*(2, 6)), 8)
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: (3, 4) | 12.0 | 12 | Passed |
| fixture 2: (1, 3) | 1.0 | 1 | Passed |
| fixture 3: (0, 5) | 0.0 | 0 | Passed |
| fixture 4: (2, 6) | 8.0 | 8 | Passed |
SHA-256 / 39c555528ebb53661464dda16b31def596b382db22ec031424b98d7213095aa0
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 2026-09-29T14:37:55.383174+00:00.
Case digest / ea2d95a273c8d006df81f24cd7196c034e207c0e45cd5b3bab82275339b0fd40