FA-5606 / Combinatorics / Open access
Binary subsets count · case 01
Squaring the size does not enumerate include/exclude choices.
ROOT CAUSE
Squaring the size does not enumerate include/exclude choices.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return 2**n
Unsuccessful approach: Doubling the size grows linearly rather than by independent choices.
Case contract
Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. Binary subsets count. Exact operational definition: 2**n
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics 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 n*n
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (0,)', solve(*(0,)), 1)
check('fixture 2: (1,)', solve(*(1,)), 2)
check('fixture 3: (3,)', solve(*(3,)), 8)
check('fixture 4: (5,)', solve(*(5,)), 32)
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: (0,) | 0 | 1 | Failed |
| fixture 2: (1,) | 1 | 2 | Failed |
| fixture 3: (3,) | 9 | 8 | Failed |
| fixture 4: (5,) | 25 | 32 | Failed |
SHA-256 / e6b5153ac93f3e75133246d7b3d9cef899730566d65fc10b44278b84a6c0ffdd
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 2*n
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (0,)', solve(*(0,)), 1)
check('fixture 2: (1,)', solve(*(1,)), 2)
check('fixture 3: (3,)', solve(*(3,)), 8)
check('fixture 4: (5,)', solve(*(5,)), 32)
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: (0,) | 0 | 1 | Failed |
| fixture 2: (1,) | 2 | 2 | Passed |
| fixture 3: (3,) | 6 | 8 | Failed |
| fixture 4: (5,) | 10 | 32 | Failed |
SHA-256 / 501cb594103b86b1a85ec07ef0ef65886685dd6fc00888dbc03ac741b478a44e
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(n):
return 2**n
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (0,)', solve(*(0,)), 1)
check('fixture 2: (1,)', solve(*(1,)), 2)
check('fixture 3: (3,)', solve(*(3,)), 8)
check('fixture 4: (5,)', solve(*(5,)), 32)
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: (0,) | 1 | 1 | Passed |
| fixture 2: (1,) | 2 | 2 | Passed |
| fixture 3: (3,) | 8 | 8 | Passed |
| fixture 4: (5,) | 32 | 32 | Passed |
SHA-256 / 811f0ee5e27262e459b92d5336b8e5ee7853bff94dd4637ac51199ba91c3f502
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 2026-09-29T14:37:51.438681+00:00.
Case digest / 94f716c1716afbbb7d44f3f446a208952e528c86e77d9e3d2251dbc8aa193fb8