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FA-5931 / Solid geometry / Open access

Conical frustum volume divided by pi · case 01

Subtracting same-height cones omits the mixed-radius term.

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

ROOT CAUSE

Subtracting same-height cones omits the mixed-radius term.

VERIFIED REPAIR

Apply the specified mathematical contract directly, preserving all terms and boundary cases: return h*(r*r+r*R+R*R)/3

Unsuccessful approach: Averaging endpoint disk areas is not exact for a conical frustum.

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. Conical frustum volume divided by pi. Exact operational definition: h*(r*r+r*R+R*R)/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, R, h):
    return h*(R*R-r*r)/3
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (1, 2, 3)', solve(*(1, 2, 3)), 7)
check('fixture 2: (2, 2, 3)', solve(*(2, 2, 3)), 12)
check('fixture 3: (0, 3, 4)', solve(*(0, 3, 4)), 12)
check('fixture 4: (1, 3, 0)', solve(*(1, 3, 0)), 0)
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 fixtureActualExpectedOutcome
fixture 1: (1, 2, 3)3.07Failed
fixture 2: (2, 2, 3)0.012Failed
fixture 3: (0, 3, 4)12.012Passed
fixture 4: (1, 3, 0)0.00Passed

SHA-256 / eebcf8167f4e2bfd77dfe8753aeba2e799952279fff0e938e0c7e4f61be48173

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, R, h):
    return h*(r*r+R*R)/2
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (1, 2, 3)', solve(*(1, 2, 3)), 7)
check('fixture 2: (2, 2, 3)', solve(*(2, 2, 3)), 12)
check('fixture 3: (0, 3, 4)', solve(*(0, 3, 4)), 12)
check('fixture 4: (1, 3, 0)', solve(*(1, 3, 0)), 0)
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 fixtureActualExpectedOutcome
fixture 1: (1, 2, 3)7.57Failed
fixture 2: (2, 2, 3)12.012Passed
fixture 3: (0, 3, 4)18.012Failed
fixture 4: (1, 3, 0)0.00Passed

SHA-256 / 59dc6d7664258844c5d7e691b479aebba83effe7525e629d2a8ae73c20a5d1d9

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, R, h):
    return h*(r*r+r*R+R*R)/3
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (1, 2, 3)', solve(*(1, 2, 3)), 7)
check('fixture 2: (2, 2, 3)', solve(*(2, 2, 3)), 12)
check('fixture 3: (0, 3, 4)', solve(*(0, 3, 4)), 12)
check('fixture 4: (1, 3, 0)', solve(*(1, 3, 0)), 0)
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 fixtureActualExpectedOutcome
fixture 1: (1, 2, 3)7.07Passed
fixture 2: (2, 2, 3)12.012Passed
fixture 3: (0, 3, 4)12.012Passed
fixture 4: (1, 3, 0)0.00Passed

SHA-256 / 9fd91c3886011ca23fb4e9b05b85378399bbb220e32f1cf21af3d5eb5afb6500

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 2026-09-29T14:37:55.405214+00:00.

Case digest / c2c88b54fcb553ef5628d2f8f951bf36da6ab492124b338846fb0e86f8313605