FA-13356 / Numerical aggregation / Open access
Empirical distinct draw collision: Only the numerator is converted to unordered pairs. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Only the numerator is converted to unordered pairs.
VERIFIED REPAIR
Preserve the empirical distinct draw collision contract at the identified reduction decision.
Unsuccessful approach: Doubling the ordered numerator creates the opposite normalization error.
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(v*(v-1)//2 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 | 1/6 | 1/3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 1/2 | 1 | Failed |
| regression 6 | 2/15 | 4/15 | Failed |
| regression 7 | 1/6 | 1/3 | Failed |
| variable collision multiplicity | 0 | 0 | Passed |
SHA-256 / f512cd83653137d0fc9cf4f205e6dbeda7dc01f03caa614a54cf70a76c3f0c27
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(2*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 | 2/3 | 1/3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | None | None | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 2 | 1 | Failed |
| regression 6 | 8/15 | 4/15 | Failed |
| regression 7 | 2/3 | 1/3 | Failed |
| variable collision multiplicity | 0 | 0 | Passed |
SHA-256 / 01c5762b296f4297ab672311383f18b90865a6aedb2aa49b13163c896838fd64
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(xs):
counts=Counter(xs)
n=len(xs)
if n<2: return None
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 | None | None | Passed |
| regression 4 | None | None | Passed |
| 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 / 1a4fae3a590539025dd4b2a652d158dbbd99f79868cffa8a0ba14904108f78f5
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 2026-09-29T14:39:06.057496+00:00.
Case digest / 744af57f8712debe60b9eed8de61715cbf77215de281ce63a33fbcb3a2cf09ae