FA-13366 / Numerical aggregation / Open access
Empirical distinct draw collision: A singleton is assigned zero rather than an undefined distinct-draw probability. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
A singleton is assigned zero rather than an undefined distinct-draw probability.
THE FAILURE
A singleton is assigned zero rather than an undefined distinct-draw probability.
Unsuccessful approach: A singleton does not provide two distinct draw indices even if its label would match itself.
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 "0"
return str(Fraction(sum(v*(v-1) for v in counts.values()),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 | 1/3 | 1/3 | Passed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | None | Failed |
| regression 4 | 0 | None | Failed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | 4/15 | 4/15 | Passed |
| regression 7 | 1/3 | 1/3 | Passed |
| variable collision multiplicity | 0 | 0 | Passed |
SHA-256 / 9712f951d4b4a5ace585e643620b8dd9003d823ad5e5323df1832a2c1ebd46f5
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 "1"
return str(Fraction(sum(v*(v-1) for v in counts.values()),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 | 1/3 | 1/3 | Passed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 1 | None | Failed |
| regression 4 | 1 | None | Failed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | 4/15 | 4/15 | Passed |
| regression 7 | 1/3 | 1/3 | Passed |
| variable collision multiplicity | 0 | 0 | Passed |
SHA-256 / f042191be172429405f4231f647c6f62d6a7e47b01e8ad99c63c500f0b330359
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 / 40fb871b1db740766c5d0ef825a81799f110238a705224b3efa3de7b9cb55cf9