FA-5586 / Number theory / Open access

Integer cube root floor · case 01

Nearest root differs from a floor root between cubes.

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

ROOT CAUSE

Nearest root differs from a floor root between cubes.

THE FAILURE

Nearest root differs from a floor root between cubes.

Unsuccessful approach: Truncating the magnitude rounds negative noncubes toward zero.

Case contract

Integer inputs; n is positive unless a zero or negative fixture explicitly extends that operation. A modulus is greater than one; p is prime; exponent k may be signed when an inverse exists. n is any integer in the small bounded fixture domain; return greatest r with r**3<=n. The linear search is an illustrative algorithm, not a large-input performance claim. Exact operational definition: next(k-1 for k in range(abs(n)+2) if k**3>n) if n>=0 else -next(k for k in range(abs(n)+1) if k**3>=-n)

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Number theory 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(n):
    return round(abs(n)**(1/3))*(1 if n>=0 else -1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (26,)', solve(*(26,)), 2)
check('fixture 2: (27,)', solve(*(27,)), 3)
check('fixture 3: (-9,)', solve(*(-9,)), -3)
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: (26,)	`3`	`2`	Failed
fixture 2: (27,)	`3`	`3`	Passed
fixture 3: (-9,)	`-2`	`-3`	Failed
fixture 4: (0,)	`0`	`0`	Passed

SHA-256 / 94560392e8e4e1ab8bbb9a611f59130a221e64e2fb0ec5f2dedace9b0197657c

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(n):
    return int(abs(n)**(1/3))*(1 if n>=0 else -1)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (26,)', solve(*(26,)), 2)
check('fixture 2: (27,)', solve(*(27,)), 3)
check('fixture 3: (-9,)', solve(*(-9,)), -3)
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: (26,)	`2`	`2`	Passed
fixture 2: (27,)	`3`	`3`	Passed
fixture 3: (-9,)	`-2`	`-3`	Failed
fixture 4: (0,)	`0`	`0`	Passed

SHA-256 / e0174cbc218664ddc4afdad4047ba265f367a4bfe4dee835b21f2017aced2501

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 2026-09-29T14:37:51.024487+00:00.

Case digest / 6ccfb67bf3480d461633e0b747ef95a76fb6ecc6ad9cb411843917e6460da458