FA-14336 / Numerical aggregation / Open access
Capped weight effective size: Zero weight population is assigned a zero measured effective size. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Zero weight population is assigned a zero measured effective size.
THE FAILURE
Zero weight population is assigned a zero measured effective size.
Unsuccessful approach: A unit effective size also invents an observation for an undefined normalization.
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(w*w for w in ws)
return str(Fraction(s*s,q)) if q else "0"
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 | 0 | None | Failed |
| regression 3 | 0 | None | Failed |
| 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 / b0828f488b607f7b2485e5c78c827d3e4687503eb26f8dd51c58cece14e812ec
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(w*w for w in ws)
return str(Fraction(s*s,q)) if q else "1"
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 | 1 | None | Failed |
| regression 3 | 1 | None | Failed |
| 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 / 6a84aa08a7187ffbf71e2c567115a42883ed3154a9350171a347dad616f285b9
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 9 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.
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Sign in to the archive ↗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 2026-09-29T14:39:15.814592+00:00.
Case digest / e49193d8a9c616589695dafe1153cea9c72e3f900a79cb526aee4bfe57d266c1