FA-5986 / Solid geometry / Open access

Cube volume from body diagonal squared · case 01

The body diagonal is used as the cube side.

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

ROOT CAUSE

The body diagonal is used as the cube side.

THE FAILURE

The body diagonal is used as the cube side.

Unsuccessful approach: The face-diagonal relation is used for a body diagonal.

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. diagonal_squared>=0; derive the volume of a cube from the squared body diagonal. Exact operational definition: (diagonal_squared/3)**1.5

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(diagonal_squared):
    return diagonal_squared**1.5
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3,)', solve(*(3,)), 1)
check('fixture 2: (12,)', solve(*(12,)), 8)
check('fixture 3: (27,)', solve(*(27,)), 27)
check('fixture 4: (0,)', solve(*(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 fixture	Actual	Expected	Outcome
fixture 1: (3,)	`5.196152422706632`	`1`	Failed
fixture 2: (12,)	`41.569219381653056`	`8`	Failed
fixture 3: (27,)	`140.29611541307906`	`27`	Failed
fixture 4: (0,)	`0.0`	`0`	Passed

SHA-256 / 75b76ab944ae86752a0dc65aea36e94485ce8d2043dbef8f15bea7a360c9254b

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(diagonal_squared):
    return (diagonal_squared/2)**1.5
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3,)', solve(*(3,)), 1)
check('fixture 2: (12,)', solve(*(12,)), 8)
check('fixture 3: (27,)', solve(*(27,)), 27)
check('fixture 4: (0,)', solve(*(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 fixture	Actual	Expected	Outcome
fixture 1: (3,)	`1.8371173070873836`	`1`	Failed
fixture 2: (12,)	`14.696938456699069`	`8`	Failed
fixture 3: (27,)	`49.60216729135936`	`27`	Failed
fixture 4: (0,)	`0.0`	`0`	Passed

SHA-256 / 49e0e1a0744efee434416e49bdfd93fae5d4bfec28842c31d746e5bfa765bdb4

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 4 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:37:56.196279+00:00.

Case digest / ab8a2266258f958d36da2801bbdd5a57f27d2baa071ad69615fc65f2e1b0be96