FA-13396 / Numerical aggregation / Open access
Empirical cdf supremum: The scan omits positions appearing in only one sample. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The scan omits positions appearing in only one sample.
VERIFIED REPAIR
Preserve the empirical cdf supremum contract at the identified reduction decision.
Unsuccessful approach: Scanning only the first support can miss a maximum after a second-only jump.
Case contract
Return the maximum absolute difference between the right-continuous empirical cumulative distributions of two nonempty integer samples as a Fraction string. Empty either side returns 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(a, b):
if not a or not b: return None
ca,cb=Counter(a),Counter(b)
pa=pb=Fraction(0)
best=Fraction(0)
for x in sorted(set(ca)&set(cb)):
pa+=Fraction(ca[x],len(a))
pb+=Fraction(cb[x],len(b))
best=max(best,abs(pa-pb))
return str(best)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([3], [0])), '1')
check('regression 2', solve(*([-5, 3], [-2, 1])), '1/2')
check('regression 3', solve(*([1, 1, 4], [2, 3])), '2/3')
check('regression 4', solve(*([0, 0, 0], [0])), '0')
check('regression 5', solve(*([], [1])), None)
check('regression 6', solve(*([1, 2], [1, 2])), '0')
check('regression 7', solve(*([-5, 0, 8], [-2, 8, 8, 8])), '5/12')
check('regression 8', solve(*([0, 4], [0, 1, 2, 3, 4])), '3/10')
check('regression 9', solve(*([2, 2], [1, 1, 3, 3])), '1/2')
check("variable support",solve([0,N],[N,N]),"1/2")
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 | 0 | 1 | Failed |
| regression 2 | 0 | 1/2 | Failed |
| regression 3 | 0 | 2/3 | Failed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 5/12 | 5/12 | Passed |
| regression 8 | 3/5 | 3/10 | Failed |
| regression 9 | 0 | 1/2 | Failed |
| variable support | 1/2 | 1/2 | Passed |
SHA-256 / 93ee9594917e5f640308e5d798247a04e73303f90e35248792ef21bfe5d8f211
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):
if not a or not b: return None
ca,cb=Counter(a),Counter(b)
pa=pb=Fraction(0)
best=Fraction(0)
for x in sorted(set(ca)):
pa+=Fraction(ca[x],len(a))
pb+=Fraction(cb[x],len(b))
best=max(best,abs(pa-pb))
return str(best)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([3], [0])), '1')
check('regression 2', solve(*([-5, 3], [-2, 1])), '1/2')
check('regression 3', solve(*([1, 1, 4], [2, 3])), '2/3')
check('regression 4', solve(*([0, 0, 0], [0])), '0')
check('regression 5', solve(*([], [1])), None)
check('regression 6', solve(*([1, 2], [1, 2])), '0')
check('regression 7', solve(*([-5, 0, 8], [-2, 8, 8, 8])), '5/12')
check('regression 8', solve(*([0, 4], [0, 1, 2, 3, 4])), '3/10')
check('regression 9', solve(*([2, 2], [1, 1, 3, 3])), '1/2')
check("variable support",solve([0,N],[N,N]),"1/2")
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 | Passed |
| regression 2 | 1 | 1/2 | Failed |
| regression 3 | 1 | 2/3 | Failed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 2/3 | 5/12 | Failed |
| regression 8 | 3/5 | 3/10 | Failed |
| regression 9 | 1 | 1/2 | Failed |
| variable support | 1/2 | 1/2 | Passed |
SHA-256 / c0782a52453310188c11a7aff04dde0877fcac8177afc64c8e4a1bbb431e50cd
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(a, b):
if not a or not b: return None
ca,cb=Counter(a),Counter(b)
pa=pb=Fraction(0)
best=Fraction(0)
for x in sorted(set(ca)|set(cb)):
pa+=Fraction(ca[x],len(a))
pb+=Fraction(cb[x],len(b))
best=max(best,abs(pa-pb))
return str(best)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([3], [0])), '1')
check('regression 2', solve(*([-5, 3], [-2, 1])), '1/2')
check('regression 3', solve(*([1, 1, 4], [2, 3])), '2/3')
check('regression 4', solve(*([0, 0, 0], [0])), '0')
check('regression 5', solve(*([], [1])), None)
check('regression 6', solve(*([1, 2], [1, 2])), '0')
check('regression 7', solve(*([-5, 0, 8], [-2, 8, 8, 8])), '5/12')
check('regression 8', solve(*([0, 4], [0, 1, 2, 3, 4])), '3/10')
check('regression 9', solve(*([2, 2], [1, 1, 3, 3])), '1/2')
check("variable support",solve([0,N],[N,N]),"1/2")
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 | Passed |
| regression 2 | 1/2 | 1/2 | Passed |
| regression 3 | 2/3 | 2/3 | Passed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 5/12 | 5/12 | Passed |
| regression 8 | 3/10 | 3/10 | Passed |
| regression 9 | 1/2 | 1/2 | Passed |
| variable support | 1/2 | 1/2 | Passed |
SHA-256 / ddf4ebc36608e574c462ed740eefb855c4c46abcb901c6a609803ce88ef84dbe
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 2026-09-29T14:39:06.620472+00:00.
Case digest / ebd125605593ca01e0416c2bc7facdc9dff5c349363920fdcb78f12f1fe3c44d