FAILURE MAP
← Case archive

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.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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