FA-13431 / Numerical aggregation / Open access
Empirical transport distance: Signed CDF differences cancel before absolute value. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Signed CDF differences cancel before absolute value.
THE FAILURE
Signed CDF differences cancel before absolute value.
Unsuccessful approach: Leaving the signed result computes mean displacement rather than transport cost.
Case contract
For nonempty integer samples with equal total probability after separate normalization, return integral of absolute CDF difference over the real line 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)
points=sorted(set(ca)|set(cb))
pa=pb=Fraction(0)
area=Fraction(0)
for i,x in enumerate(points[:-1]):
pa+=Fraction(ca[x],len(a))
pb+=Fraction(cb[x],len(b))
area+=(pa-pb)*(points[i+1]-x)
return str(abs(area))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([0, 0, 9], [1, 4])), '17/6')
check('regression 2', solve(*([2], [7])), '5')
check('regression 3', solve(*([1, 2], [1, 2])), '0')
check('regression 4', solve(*([], [1])), None)
check('regression 5', solve(*([-8, -1, 4], [-3, 9, 9])), '20/3')
check('regression 6', solve(*([0, 2, 8], [0, 8])), '4/3')
check('regression 7', solve(*([0, 10], [4, 6])), '4')
check("variable transport span",solve([0],[N]),str(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 | 17/6 | Failed |
| regression 2 | 5 | 5 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 20/3 | 20/3 | Passed |
| regression 6 | 2/3 | 4/3 | Failed |
| regression 7 | 0 | 4 | Failed |
| variable transport span | 1 | 1 | Passed |
SHA-256 / d8c90b320be13499d6e950ae79d88f301f16e8b3e9c04d25178f6f4558f69a23
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)
points=sorted(set(ca)|set(cb))
pa=pb=Fraction(0)
area=Fraction(0)
for i,x in enumerate(points[:-1]):
pa+=Fraction(ca[x],len(a))
pb+=Fraction(cb[x],len(b))
area+=(pa-pb)*(points[i+1]-x)
return str(area)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([0, 0, 9], [1, 4])), '17/6')
check('regression 2', solve(*([2], [7])), '5')
check('regression 3', solve(*([1, 2], [1, 2])), '0')
check('regression 4', solve(*([], [1])), None)
check('regression 5', solve(*([-8, -1, 4], [-3, 9, 9])), '20/3')
check('regression 6', solve(*([0, 2, 8], [0, 8])), '4/3')
check('regression 7', solve(*([0, 10], [4, 6])), '4')
check("variable transport span",solve([0],[N]),str(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 | 17/6 | Failed |
| regression 2 | 5 | 5 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | 20/3 | 20/3 | Passed |
| regression 6 | 2/3 | 4/3 | Failed |
| regression 7 | 0 | 4 | Failed |
| variable transport span | 1 | 1 | Passed |
SHA-256 / f239be0f7b93673c4baefedba9691d667b64d0cff503d0b5aef0b9e62d8ed75f
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 2026-09-29T14:39:07.201975+00:00.
Case digest / 71954716431ad78f099649ba5d44f04f25c5ec121c24c139d9f15dbafb2dc50c