FA-6196 / Statistics / Open access
Mode smallest tie · case 01
The largest tied mode is selected instead of the smallest.
ROOT CAUSE
The largest tied mode is selected instead of the smallest.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return min(set(values),key=lambda x:(-values.count(x),x)) if values else None
Unsuccessful approach: Input order replaces frequency comparison.
Case contract
Integer finite observations and equal lengths for paired samples. Counts and weights are nonnegative. Rational results use reduced Fraction strings. Empty or undefined statistics return None where shown. Return the smallest observation among tied highest-frequency values, or None for empty input. Exact operational definition: min(set(values),key=lambda x:(-values.count(x),x)) if values else None
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Statistical estimators 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(values):
return max(set(values),key=lambda x:(values.count(x),x)) if values else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([3, 3, 1, 1],)', solve(*([3, 3, 1, 1],)), 1)
check('fixture 2: ([2, 1, 2],)', solve(*([2, 1, 2],)), 2)
check('fixture 3: ([7],)', solve(*([7],)), 7)
check('fixture 4: ([],)', solve(*([],)), None)
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, 3, 1, 1],) | 3 | 1 | Failed |
| fixture 2: ([2, 1, 2],) | 2 | 2 | Passed |
| fixture 3: ([7],) | 7 | 7 | Passed |
| fixture 4: ([],) | None | None | Passed |
SHA-256 / a6c87e6271b0da942f8ceeb5a2a24efab702cd9f98da607c56a758473626959c
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(values):
return values[0] if values else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([3, 3, 1, 1],)', solve(*([3, 3, 1, 1],)), 1)
check('fixture 2: ([2, 1, 2],)', solve(*([2, 1, 2],)), 2)
check('fixture 3: ([7],)', solve(*([7],)), 7)
check('fixture 4: ([],)', solve(*([],)), None)
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, 3, 1, 1],) | 3 | 1 | Failed |
| fixture 2: ([2, 1, 2],) | 2 | 2 | Passed |
| fixture 3: ([7],) | 7 | 7 | Passed |
| fixture 4: ([],) | None | None | Passed |
SHA-256 / fe0cf2de2078a2f4d25e4fec41d448c2780b4e4bf05808207b8abe500759e403
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(values):
return min(set(values),key=lambda x:(-values.count(x),x)) if values else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([3, 3, 1, 1],)', solve(*([3, 3, 1, 1],)), 1)
check('fixture 2: ([2, 1, 2],)', solve(*([2, 1, 2],)), 2)
check('fixture 3: ([7],)', solve(*([7],)), 7)
check('fixture 4: ([],)', solve(*([],)), None)
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, 3, 1, 1],) | 1 | 1 | Passed |
| fixture 2: ([2, 1, 2],) | 2 | 2 | Passed |
| fixture 3: ([7],) | 7 | 7 | Passed |
| fixture 4: ([],) | None | None | Passed |
SHA-256 / 243df2a8948b6f8379a29c6d31a98c5c2dd05c7a5520e517896a1971f63b9689
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 2026-09-29T14:37:58.692544+00:00.
Case digest / d7333ab499675fc54727378099fa9bb84d88ef5e7748c1de1013939842e77789