FA-14106 / Numerical aggregation / Open access
Multiset overlap similarity: The largest single-label overlap replaces total shared mass. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The largest single-label overlap replaces total shared mass.
THE FAILURE
The largest single-label overlap replaces total shared mass.
Unsuccessful approach: The least shared label also ignores accumulated overlap.
Case contract
Return multiset Jaccard similarity: sum of per-label minimum frequencies divided by sum of per-label maximum frequencies, as exact Fraction string. Both empty returns "1". Integer labels are nominal.
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(a, b):
ca,cb=Counter(a),Counter(b)
keys=set(ca)|set(cb)
intersection=max([min(ca[k],cb[k]) for k in keys] or [0])
union=sum(max(ca[k],cb[k]) for k in keys)
return str(Fraction(intersection,union)) if union else "1"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 1, 1, 2], [1, 2, 2])), '2/5')
check('regression 2', solve(*([], [])), '1')
check('regression 3', solve(*([1, 2], [])), '0')
check('regression 4', solve(*([2, 2], [2, 2])), '1')
check('regression 5', solve(*([-1, 0, 0], [0, 1])), '1/4')
check('regression 6', solve(*([3, 3, 4], [3, 3, 3, 4, 4])), '3/5')
check('regression 7', solve(*([0], [1])), '0')
check("variable overlap mass",solve([0]*N,[0]*(N+1)),str(Fraction(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 | 1/5 | 2/5 | Failed |
| regression 2 | 1 | 1 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 1 | 1 | Passed |
| regression 5 | 1/4 | 1/4 | Passed |
| regression 6 | 2/5 | 3/5 | Failed |
| regression 7 | 0 | 0 | Passed |
| variable overlap mass | 1/2 | 1/2 | Passed |
SHA-256 / 8a391f050117dd3f4441b45294909998568021b0d26834f9aa01ccf000b60548
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(a, b):
ca,cb=Counter(a),Counter(b)
keys=set(ca)|set(cb)
intersection=min([min(ca[k],cb[k]) for k in keys] or [0])
union=sum(max(ca[k],cb[k]) for k in keys)
return str(Fraction(intersection,union)) if union else "1"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 1, 1, 2], [1, 2, 2])), '2/5')
check('regression 2', solve(*([], [])), '1')
check('regression 3', solve(*([1, 2], [])), '0')
check('regression 4', solve(*([2, 2], [2, 2])), '1')
check('regression 5', solve(*([-1, 0, 0], [0, 1])), '1/4')
check('regression 6', solve(*([3, 3, 4], [3, 3, 3, 4, 4])), '3/5')
check('regression 7', solve(*([0], [1])), '0')
check("variable overlap mass",solve([0]*N,[0]*(N+1)),str(Fraction(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 | 1/5 | 2/5 | Failed |
| regression 2 | 1 | 1 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 1 | 1 | Passed |
| regression 5 | 0 | 1/4 | Failed |
| regression 6 | 1/5 | 3/5 | Failed |
| regression 7 | 0 | 0 | Passed |
| variable overlap mass | 1/2 | 1/2 | Passed |
SHA-256 / 2e0576be8870761c2cac781a24add203c7b17483143c88cc00df1e614300f19e
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 8 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 2026-09-29T14:39:13.705442+00:00.
Case digest / 5b5732f14755d1c8f4bba7dc603c1fd9007b108d809ef9690c17075f93e11af8