FA-5996 / Solid geometry / Open access

Right cone slant length squared · case 01

The legs are added before squaring.

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

ROOT CAUSE

The legs are added before squaring.

VERIFIED REPAIR

Apply the specified mathematical contract directly, preserving all terms and boundary cases: return r*r+h*h

Unsuccessful approach: Subtracting squares treats height as the hypotenuse.

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. Right cone slant length squared. Exact operational definition: r*r+h*h

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+h)**2
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 4)', solve(*(3, 4)), 25)
check('fixture 2: (0, 5)', solve(*(0, 5)), 25)
check('fixture 3: (2, 0)', solve(*(2, 0)), 4)
check('fixture 4: (1, 1)', solve(*(1, 1)), 2)
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)	`49`	`25`	Failed
fixture 2: (0, 5)	`25`	`25`	Passed
fixture 3: (2, 0)	`4`	`4`	Passed
fixture 4: (1, 1)	`4`	`2`	Failed

SHA-256 / 9fdc08ca0b5bc4eee00cc165d92a15907d35c74a0aac47bd6b8d51b8301b76fa

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 h*h-r*r
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 4)', solve(*(3, 4)), 25)
check('fixture 2: (0, 5)', solve(*(0, 5)), 25)
check('fixture 3: (2, 0)', solve(*(2, 0)), 4)
check('fixture 4: (1, 1)', solve(*(1, 1)), 2)
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)	`7`	`25`	Failed
fixture 2: (0, 5)	`25`	`25`	Passed
fixture 3: (2, 0)	`-4`	`4`	Failed
fixture 4: (1, 1)	`0`	`2`	Failed

SHA-256 / c336cd19ca433cb1b58ca9d06df823de9bc492143d9551b7aed5dc824ec7e0ac

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*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)), 25)
check('fixture 2: (0, 5)', solve(*(0, 5)), 25)
check('fixture 3: (2, 0)', solve(*(2, 0)), 4)
check('fixture 4: (1, 1)', solve(*(1, 1)), 2)
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)	`25`	`25`	Passed
fixture 2: (0, 5)	`25`	`25`	Passed
fixture 3: (2, 0)	`4`	`4`	Passed
fixture 4: (1, 1)	`2`	`2`	Passed

SHA-256 / c591d099ac4d8e08c7c1fb1fbe299cac3a7f5d7660e4983917ddacb468f27da1

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 2026-09-29T14:37:56.203506+00:00.

Case digest / 72610b84ce097c69c852bcf03a7854f1895e01373211cd73a078131789df41b7