FA-14291 / Numerical aggregation / Open access
Capped weight effective size: The denominator squares total weight instead of summing squares. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The denominator squares total weight instead of summing squares.
VERIFIED REPAIR
Preserve the capped weight effective size contract at the identified reduction decision.
Unsuccessful approach: Using linear total weight computes a mass rather than a concentration correction.
Case contract
For nonnegative integer importance weights and positive integer cap, clip each weight to cap, then return Kish effective size (sum clipped weights)**2/sum squared clipped weights as exact Fraction string. Negative weight, invalid cap, or zero total yields None.
Why this case matters
Exact bounded examples isolate a reduction defect without floating-point or external-service effects.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(weights, cap):
if cap<=0 or any(w<0 for w in weights): return None
ws=[min(w,cap) for w in weights]
s=sum(ws)
q=sum(ws)**2
return str(Fraction(s*s,q)) if q else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 2, 4], 3)), '18/7')
check('regression 2', solve(*([0, 0], 3)), None)
check('regression 3', solve(*([], 4)), None)
check('regression 4', solve(*([2, 2, 2], 9)), '3')
check('regression 5', solve(*([10, 1], 2)), '9/5')
check('regression 6', solve(*([-1, 2], 3)), None)
check('regression 7', solve(*([1, 3], 0)), None)
check('regression 8', solve(*([0, 2, 5, 1], 4)), '7/3')
check("variable effective-size imbalance",solve([N,1],N+1),str(Fraction((N+1)**2,N*N+1)))
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 |
|---|---|---|---|
| regression 1 | 1 | 18/7 | Failed |
| regression 2 | None | None | Passed |
| regression 3 | None | None | Passed |
| regression 4 | 1 | 3 | Failed |
| regression 5 | 1 | 9/5 | Failed |
| regression 6 | None | None | Passed |
| regression 7 | None | None | Passed |
| regression 8 | 1 | 7/3 | Failed |
| variable effective-size imbalance | 1 | 2 | Failed |
SHA-256 / cb9cf1f4412418b6ee21f5aa9bb5b6a6b2529a4dbf8d77eb60fa607979e07f2d
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(weights, cap):
if cap<=0 or any(w<0 for w in weights): return None
ws=[min(w,cap) for w in weights]
s=sum(ws)
q=sum(ws)
return str(Fraction(s*s,q)) if q else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 2, 4], 3)), '18/7')
check('regression 2', solve(*([0, 0], 3)), None)
check('regression 3', solve(*([], 4)), None)
check('regression 4', solve(*([2, 2, 2], 9)), '3')
check('regression 5', solve(*([10, 1], 2)), '9/5')
check('regression 6', solve(*([-1, 2], 3)), None)
check('regression 7', solve(*([1, 3], 0)), None)
check('regression 8', solve(*([0, 2, 5, 1], 4)), '7/3')
check("variable effective-size imbalance",solve([N,1],N+1),str(Fraction((N+1)**2,N*N+1)))
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 |
|---|---|---|---|
| regression 1 | 6 | 18/7 | Failed |
| regression 2 | None | None | Passed |
| regression 3 | None | None | Passed |
| regression 4 | 6 | 3 | Failed |
| regression 5 | 3 | 9/5 | Failed |
| regression 6 | None | None | Passed |
| regression 7 | None | None | Passed |
| regression 8 | 7 | 7/3 | Failed |
| variable effective-size imbalance | 2 | 2 | Passed |
SHA-256 / 4e1371b9a2ecbad7a2430803846ed1a8935758dc4f3461447c58d739fd82f85d
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(weights, cap):
if cap<=0 or any(w<0 for w in weights): return None
ws=[min(w,cap) for w in weights]
s=sum(ws)
q=sum(w*w for w in ws)
return str(Fraction(s*s,q)) if q else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 2, 4], 3)), '18/7')
check('regression 2', solve(*([0, 0], 3)), None)
check('regression 3', solve(*([], 4)), None)
check('regression 4', solve(*([2, 2, 2], 9)), '3')
check('regression 5', solve(*([10, 1], 2)), '9/5')
check('regression 6', solve(*([-1, 2], 3)), None)
check('regression 7', solve(*([1, 3], 0)), None)
check('regression 8', solve(*([0, 2, 5, 1], 4)), '7/3')
check("variable effective-size imbalance",solve([N,1],N+1),str(Fraction((N+1)**2,N*N+1)))
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 |
|---|---|---|---|
| regression 1 | 18/7 | 18/7 | Passed |
| regression 2 | None | None | Passed |
| regression 3 | None | None | Passed |
| regression 4 | 3 | 3 | Passed |
| regression 5 | 9/5 | 9/5 | Passed |
| regression 6 | None | None | Passed |
| regression 7 | None | None | Passed |
| regression 8 | 7/3 | 7/3 | Passed |
| variable effective-size imbalance | 2 | 2 | Passed |
SHA-256 / 61f806a746d3e9cfa531358801637470e6812ee5f41e519561133d31baa04b6e
Verification & scope
Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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 2026-09-29T14:39:15.493489+00:00.
Case digest / 17d261e3fd147e19a46c52d10ec283149a04832c88f83331ae71b0d033727ba9