FA-13371 / Numerical aggregation / Open access
Empirical distinct draw collision: All label frequencies are summed before squaring. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
All label frequencies are summed before squaring.
THE FAILURE
All label frequencies are summed before squaring.
Unsuccessful approach: Subtracting label count rather than observation count retains self-pairs.
Case contract
Return probability that two distinct uniformly chosen observation indices carry equal integer labels, as an exact Fraction string. Fewer than two observations returns None. Labels themselves are nominal; repeated indices are excluded.
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(xs):
counts=Counter(xs)
n=len(xs)
if n<2: return None
return str(Fraction(sum(counts.values())*(sum(counts.values())-1),n*(n-1)))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 1, 2],)), '1/3')
check('regression 2', solve(*([1, 2, 3],)), '0')
check('regression 3', solve(*([],)), None)
check('regression 4', solve(*([9],)), None)
check('regression 5', solve(*([2, 2, 2, 2],)), '1')
check('regression 6', solve(*([0, 0, 1, 1, 1, 2],)), '4/15')
check('regression 7', solve(*([-1, -1, 0, 0],)), '1/3')
check("variable collision multiplicity",solve([0]*N+[1]),str(Fraction(N*(N-1),(N+1)*N)))
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 | 1/3 | Failed |
| regression 2 | 1 | 0 | Failed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | 1 | 4/15 | Failed |
| regression 7 | 1 | 1/3 | Failed |
| variable collision multiplicity | 1 | 0 | Failed |
SHA-256 / 712eb75eca110cd9a1e7e4da52d1b7ff7093b2b1f40724cfd9839e881c9e2d8f
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(xs):
counts=Counter(xs)
n=len(xs)
if n<2: return None
return str(Fraction(sum(v*v for v in counts.values())-len(counts),n*(n-1)))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([1, 1, 2],)), '1/3')
check('regression 2', solve(*([1, 2, 3],)), '0')
check('regression 3', solve(*([],)), None)
check('regression 4', solve(*([9],)), None)
check('regression 5', solve(*([2, 2, 2, 2],)), '1')
check('regression 6', solve(*([0, 0, 1, 1, 1, 2],)), '4/15')
check('regression 7', solve(*([-1, -1, 0, 0],)), '1/3')
check("variable collision multiplicity",solve([0]*N+[1]),str(Fraction(N*(N-1),(N+1)*N)))
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 | 1/2 | 1/3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 5/4 | 1 | Failed |
| regression 6 | 11/30 | 4/15 | Failed |
| regression 7 | 1/2 | 1/3 | Failed |
| variable collision multiplicity | 0 | 0 | Passed |
SHA-256 / 9b7a41fd230fc124575bf51cee4aa22c657a641ff1b409edb73a0d800ff441bd
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 2026-09-29T14:39:06.394231+00:00.
Case digest / 09d556cdb1f54225e6978136e50655ebed97d9a6c5f5e5e6f7dffd0ab8af4ceb