FA-6331 / Statistics / Open access
Effective sample size weights · case 01
Nominal record count ignores unequal weight concentration.
ROOT CAUSE
Nominal record count ignores unequal weight concentration.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(Fraction(sum(weights)**2,sum(w*w for w in weights))) if sum(w*w for w in weights) else None
Unsuccessful approach: The weight total is not squared, breaking scale invariance.
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. Effective sample size weights. Exact operational definition: str(Fraction(sum(weights)**2,sum(w*w for w in weights))) if sum(w*w for w in weights) 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(weights):
return str(len(weights))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 1, 1],)', solve(*([1, 1, 1],)), '3')
check('fixture 2: ([1, 3],)', solve(*([1, 3],)), '8/5')
check('fixture 3: ([2, 2],)', solve(*([2, 2],)), '2')
check('fixture 4: ([0, 0],)', solve(*([0, 0],)), 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: ([1, 1, 1],) | 3 | 3 | Passed |
| fixture 2: ([1, 3],) | 2 | 8/5 | Failed |
| fixture 3: ([2, 2],) | 2 | 2 | Passed |
| fixture 4: ([0, 0],) | 2 | None | Failed |
SHA-256 / ffe91b435984864c251af15ec16f140fdc8afa777eb3a16b2d063e9650eaf6b8
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(weights):
return str(Fraction(sum(weights),sum(w*w for w in weights))) if sum(w*w for w in weights) else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 1, 1],)', solve(*([1, 1, 1],)), '3')
check('fixture 2: ([1, 3],)', solve(*([1, 3],)), '8/5')
check('fixture 3: ([2, 2],)', solve(*([2, 2],)), '2')
check('fixture 4: ([0, 0],)', solve(*([0, 0],)), 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: ([1, 1, 1],) | 1 | 3 | Failed |
| fixture 2: ([1, 3],) | 2/5 | 8/5 | Failed |
| fixture 3: ([2, 2],) | 1/2 | 2 | Failed |
| fixture 4: ([0, 0],) | None | None | Passed |
SHA-256 / 9cedc0ebc59ee3518e7c939ca3e59da5b8c66e630b69fbc563f6554ddb63d82b
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(weights):
return str(Fraction(sum(weights)**2,sum(w*w for w in weights))) if sum(w*w for w in weights) else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 1, 1],)', solve(*([1, 1, 1],)), '3')
check('fixture 2: ([1, 3],)', solve(*([1, 3],)), '8/5')
check('fixture 3: ([2, 2],)', solve(*([2, 2],)), '2')
check('fixture 4: ([0, 0],)', solve(*([0, 0],)), 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: ([1, 1, 1],) | 3 | 3 | Passed |
| fixture 2: ([1, 3],) | 8/5 | 8/5 | Passed |
| fixture 3: ([2, 2],) | 2 | 2 | Passed |
| fixture 4: ([0, 0],) | None | None | Passed |
SHA-256 / de30c6de879983bcbbb14c751d3de89cc914495aa227febe9b8a437275b68548
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 2026-09-29T14:38:00.516582+00:00.
Case digest / 6e00bab65d2a3776d8c465e76f905f2b8a33fb8af54d67268f991280c540d2b8