FA-5991 / Solid geometry / Open access

Cavalieri prism volume · case 01

Area and height are added instead of multiplied.

Verified by executionVariant 1 · 4 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Area and height are added instead of multiplied.

VERIFIED REPAIR

Apply the specified mathematical contract directly, preserving all terms and boundary cases: return base_area*perpendicular_height

Unsuccessful approach: A pyramid coefficient incorrectly reduces the prism volume.

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. Cavalieri prism volume. Exact operational definition: base_area*perpendicular_height

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(base_area, perpendicular_height):
    return base_area+perpendicular_height
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 3)', solve(*(4, 3)), 12)
check('fixture 2: (0, 5)', solve(*(0, 5)), 0)
check('fixture 3: (7, 0)', solve(*(7, 0)), 0)
check('fixture 4: (5, 5)', solve(*(5, 5)), 25)
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: (4, 3)	`7`	`12`	Failed
fixture 2: (0, 5)	`5`	`0`	Failed
fixture 3: (7, 0)	`7`	`0`	Failed
fixture 4: (5, 5)	`10`	`25`	Failed

SHA-256 / 6ec91dd2f588215554271dc7f70d25b7e4b652ee521b06105023941da9437a3f

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(base_area, perpendicular_height):
    return base_area*perpendicular_height/3
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 3)', solve(*(4, 3)), 12)
check('fixture 2: (0, 5)', solve(*(0, 5)), 0)
check('fixture 3: (7, 0)', solve(*(7, 0)), 0)
check('fixture 4: (5, 5)', solve(*(5, 5)), 25)
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: (4, 3)	`4.0`	`12`	Failed
fixture 2: (0, 5)	`0.0`	`0`	Passed
fixture 3: (7, 0)	`0.0`	`0`	Passed
fixture 4: (5, 5)	`8.333333333333334`	`25`	Failed

SHA-256 / b4473b3c2d120ed5b586c390a906ac74a72ce236c593174aba28ecdb45c5ebc4

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(base_area, perpendicular_height):
    return base_area*perpendicular_height
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 3)', solve(*(4, 3)), 12)
check('fixture 2: (0, 5)', solve(*(0, 5)), 0)
check('fixture 3: (7, 0)', solve(*(7, 0)), 0)
check('fixture 4: (5, 5)', solve(*(5, 5)), 25)
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: (4, 3)	`12`	`12`	Passed
fixture 2: (0, 5)	`0`	`0`	Passed
fixture 3: (7, 0)	`0`	`0`	Passed
fixture 4: (5, 5)	`25`	`25`	Passed

SHA-256 / 6ab322be2235ff2777fbfe8a6b2b7c2e81889af4843ac09ef325ad1ed90977b5

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 2026-09-29T14:37:56.203151+00:00.

Case digest / daf537220e48c9aeffe0fdf97f20dd43836ca94b3d1850034cbe3d824b9f0cd0