FA-5951 / Solid geometry / Open access

Tetrahedron axis intercept volume · case 01

The triangular base factor of one half is omitted.

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

ROOT CAUSE

The triangular base factor of one half is omitted.

THE FAILURE

The triangular base factor of one half is omitted.

Unsuccessful approach: The containing cuboid is mistaken for the tetrahedron.

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. Tetrahedron axis intercept volume. Exact operational definition: a*b*c/6

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(a, b, c):
    return a*b*c/3
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (2, 3, 4)', solve(*(2, 3, 4)), 4)
check('fixture 2: (1, 1, 1)', solve(*(1, 1, 1)), 0.16666666666666666)
check('fixture 3: (0, 2, 3)', solve(*(0, 2, 3)), 0)
check('fixture 4: (6, 6, 6)', solve(*(6, 6, 6)), 36)
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: (2, 3, 4)	`8.0`	`4`	Failed
fixture 2: (1, 1, 1)	`0.3333333333333333`	`0.16666666666666666`	Failed
fixture 3: (0, 2, 3)	`0.0`	`0`	Passed
fixture 4: (6, 6, 6)	`72.0`	`36`	Failed

SHA-256 / c63261cb99032cc18e356a7ef7190922ca6b0f81474f6a578da9877dc3b1ce92

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(a, b, c):
    return a*b*c
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (2, 3, 4)', solve(*(2, 3, 4)), 4)
check('fixture 2: (1, 1, 1)', solve(*(1, 1, 1)), 0.16666666666666666)
check('fixture 3: (0, 2, 3)', solve(*(0, 2, 3)), 0)
check('fixture 4: (6, 6, 6)', solve(*(6, 6, 6)), 36)
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: (2, 3, 4)	`24`	`4`	Failed
fixture 2: (1, 1, 1)	`1`	`0.16666666666666666`	Failed
fixture 3: (0, 2, 3)	`0`	`0`	Passed
fixture 4: (6, 6, 6)	`216`	`36`	Failed

SHA-256 / 9d0030c1502ea5897ad0136857d567a09362cdcd9d2a0a456a8d7fb48075b63a

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:37:55.676913+00:00.

Case digest / b51dbbb77eae7949af026c8276980df3985e9a6e540d1887c9cbe0227a0f5bc5