FA-14176 / Numerical aggregation / Open access
Jointly observed pair summary: Cross-product sum is replaced by the product of coordinate sums. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Cross-product sum is replaced by the product of coordinate sums.
VERIFIED REPAIR
Preserve the jointly observed pair summary contract at the identified reduction decision.
Unsuccessful approach: Adding paired coordinates also does not preserve cross-products.
Case contract
Each row holds two integer values or None. Include a row only when both values are observed; zero is observed. Return [paired count, x sum, y sum, cross-product sum, squared-distance sum]. No imputation and no marginal-only contributions.
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(rows):
pairs=[(x,y) for x,y in rows if x is not None and y is not None]
return [len(pairs),sum(x for x,y in pairs),sum(y for x,y in pairs),sum(x for x,y in pairs)*sum(y for x,y in pairs),sum((x-y)**2 for x,y in pairs)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 2), (None, 9), (3, None), (0, 4)],)), [2, 1, 6, 2, 17])
check('regression 2', solve(*([],)), [0, 0, 0, 0, 0])
check('regression 3', solve(*([(None, None)],)), [0, 0, 0, 0, 0])
check('regression 4', solve(*([(-2, 3), (4, -1), (0, 0)],)), [3, 2, 2, -10, 50])
check('regression 5', solve(*([(3, 3), (3, 3), (None, 4)],)), [2, 6, 6, 18, 0])
check('regression 6', solve(*([(0, 2), (2, 0)],)), [2, 2, 2, 0, 8])
check('regression 7', solve(*([(5, None), (None, 6)],)), [0, 0, 0, 0, 0])
check("variable complete pair",solve([(N,2*N),(None,N),(0,N)]),[2,N,3*N,2*N*N,2*N*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, 1, 6, 6, 17] | [2, 1, 6, 2, 17] | Failed |
| regression 2 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| regression 3 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| regression 4 | [3, 2, 2, 4, 50] | [3, 2, 2, -10, 50] | Failed |
| regression 5 | [2, 6, 6, 36, 0] | [2, 6, 6, 18, 0] | Failed |
| regression 6 | [2, 2, 2, 4, 8] | [2, 2, 2, 0, 8] | Failed |
| regression 7 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| variable complete pair | [2, 1, 3, 3, 2] | [2, 1, 3, 2, 2] | Failed |
SHA-256 / 44d1af965a17a02f29fa3fd80c5ab88fed82f49393bb3d729ba7295940f2a525
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(rows):
pairs=[(x,y) for x,y in rows if x is not None and y is not None]
return [len(pairs),sum(x for x,y in pairs),sum(y for x,y in pairs),sum(x+y for x,y in pairs),sum((x-y)**2 for x,y in pairs)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 2), (None, 9), (3, None), (0, 4)],)), [2, 1, 6, 2, 17])
check('regression 2', solve(*([],)), [0, 0, 0, 0, 0])
check('regression 3', solve(*([(None, None)],)), [0, 0, 0, 0, 0])
check('regression 4', solve(*([(-2, 3), (4, -1), (0, 0)],)), [3, 2, 2, -10, 50])
check('regression 5', solve(*([(3, 3), (3, 3), (None, 4)],)), [2, 6, 6, 18, 0])
check('regression 6', solve(*([(0, 2), (2, 0)],)), [2, 2, 2, 0, 8])
check('regression 7', solve(*([(5, None), (None, 6)],)), [0, 0, 0, 0, 0])
check("variable complete pair",solve([(N,2*N),(None,N),(0,N)]),[2,N,3*N,2*N*N,2*N*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, 1, 6, 7, 17] | [2, 1, 6, 2, 17] | Failed |
| regression 2 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| regression 3 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| regression 4 | [3, 2, 2, 4, 50] | [3, 2, 2, -10, 50] | Failed |
| regression 5 | [2, 6, 6, 12, 0] | [2, 6, 6, 18, 0] | Failed |
| regression 6 | [2, 2, 2, 4, 8] | [2, 2, 2, 0, 8] | Failed |
| regression 7 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| variable complete pair | [2, 1, 3, 4, 2] | [2, 1, 3, 2, 2] | Failed |
SHA-256 / 9e33ba2e915869dc0e0cd1c3a9d2e3bbc0f6c49228e2cc0f9b89f0dd54675a70
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(rows):
pairs=[(x,y) for x,y in rows if x is not None and y is not None]
return [len(pairs),sum(x for x,y in pairs),sum(y for x,y in pairs),sum(x*y for x,y in pairs),sum((x-y)**2 for x,y in pairs)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 2), (None, 9), (3, None), (0, 4)],)), [2, 1, 6, 2, 17])
check('regression 2', solve(*([],)), [0, 0, 0, 0, 0])
check('regression 3', solve(*([(None, None)],)), [0, 0, 0, 0, 0])
check('regression 4', solve(*([(-2, 3), (4, -1), (0, 0)],)), [3, 2, 2, -10, 50])
check('regression 5', solve(*([(3, 3), (3, 3), (None, 4)],)), [2, 6, 6, 18, 0])
check('regression 6', solve(*([(0, 2), (2, 0)],)), [2, 2, 2, 0, 8])
check('regression 7', solve(*([(5, None), (None, 6)],)), [0, 0, 0, 0, 0])
check("variable complete pair",solve([(N,2*N),(None,N),(0,N)]),[2,N,3*N,2*N*N,2*N*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, 1, 6, 2, 17] | [2, 1, 6, 2, 17] | Passed |
| regression 2 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| regression 3 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| regression 4 | [3, 2, 2, -10, 50] | [3, 2, 2, -10, 50] | Passed |
| regression 5 | [2, 6, 6, 18, 0] | [2, 6, 6, 18, 0] | Passed |
| regression 6 | [2, 2, 2, 0, 8] | [2, 2, 2, 0, 8] | Passed |
| regression 7 | [0, 0, 0, 0, 0] | [0, 0, 0, 0, 0] | Passed |
| variable complete pair | [2, 1, 3, 2, 2] | [2, 1, 3, 2, 2] | Passed |
SHA-256 / 60c442955b5ed4ca674217effef5b7c2d93fe8155f1f2af49686d10e0ebe6143
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 2026-09-29T14:39:14.390711+00:00.
Case digest / b732f1d32edb760b86355a58fe4a27efd4a0291ecb41faa10544a211fc01f92f