FA-13666 / Numerical aggregation / Open access
Contingency pearson reduction: The product of marginals is not divided by the grand total. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The product of marginals is not divided by the grand total.
VERIFIED REPAIR
Preserve the contingency pearson reduction contract at the identified reduction decision.
Unsuccessful approach: Probability normalization divides by total twice instead of yielding an expected count.
Case contract
For a rectangular nonnegative integer count table, return the Pearson sum of (observed-expected)^2/expected under independence, with expected=row marginal*column marginal/grand total. Zero expected cells contribute zero; empty or zero-total tables return "0". Exact Fraction string; no inferential p-value claim.
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(table):
n=len(table)
m=len(table[0]) if n else 0
rows=[sum(r) for r in table]
cols=[sum(table[i][j] for i in range(n)) for j in range(m)]
total=sum(rows)
if not total: return "0"
stat=Fraction(0)
for i in range(n):
for j in range(m):
expected=Fraction(rows[i]*cols[j])
if expected==0: continue
stat+=(table[i][j]-expected)**2/expected
return str(stat)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[4, 0], [0, 4]],)), '8')
check('regression 2', solve(*([[2, 3], [4, 6]],)), '0')
check('regression 3', solve(*([],)), '0')
check('regression 4', solve(*([[0, 0], [0, 0]],)), '0')
check('regression 5', solve(*([[2, 0, 1], [3, 4, 0]],)), '30/7')
check('regression 6', solve(*([[0, 0, 0], [1, 2, 3]],)), '0')
check('regression 7', solve(*([[1, 2], [3, 0], [2, 4]],)), '4')
check("variable diagonal mass",solve([[N,0],[0,N]]),str(2*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 | 50 | 8 | Failed |
| regression 2 | 196 | 0 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | 570/7 | 30/7 | Failed |
| regression 6 | 25 | 0 | Failed |
| regression 7 | 364/3 | 4 | Failed |
| variable diagonal mass | 2 | 2 | Passed |
SHA-256 / 2da4876a127cebcb326b788b942e1dcebe1835a4db62102990b6004e36514b6e
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(table):
n=len(table)
m=len(table[0]) if n else 0
rows=[sum(r) for r in table]
cols=[sum(table[i][j] for i in range(n)) for j in range(m)]
total=sum(rows)
if not total: return "0"
stat=Fraction(0)
for i in range(n):
for j in range(m):
expected=Fraction(rows[i]*cols[j],total*total)
if expected==0: continue
stat+=(table[i][j]-expected)**2/expected
return str(stat)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[4, 0], [0, 4]],)), '8')
check('regression 2', solve(*([[2, 3], [4, 6]],)), '0')
check('regression 3', solve(*([],)), '0')
check('regression 4', solve(*([[0, 0], [0, 0]],)), '0')
check('regression 5', solve(*([[2, 0, 1], [3, 4, 0]],)), '30/7')
check('regression 6', solve(*([[0, 0, 0], [1, 2, 3]],)), '0')
check('regression 7', solve(*([[1, 2], [3, 0], [2, 4]],)), '4')
check("variable diagonal mass",solve([[N,0],[0,N]]),str(2*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 | 113 | 8 | Failed |
| regression 2 | 196 | 0 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | 867/7 | 30/7 | Failed |
| regression 6 | 25 | 0 | Failed |
| regression 7 | 169 | 4 | Failed |
| variable diagonal mass | 5 | 2 | Failed |
SHA-256 / 730cb90b875047c1e1b9aff3676d49b9f054987ede7b530ead314ba7abc9479f
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(table):
n=len(table)
m=len(table[0]) if n else 0
rows=[sum(r) for r in table]
cols=[sum(table[i][j] for i in range(n)) for j in range(m)]
total=sum(rows)
if not total: return "0"
stat=Fraction(0)
for i in range(n):
for j in range(m):
expected=Fraction(rows[i]*cols[j],total)
if expected==0: continue
stat+=(table[i][j]-expected)**2/expected
return str(stat)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[4, 0], [0, 4]],)), '8')
check('regression 2', solve(*([[2, 3], [4, 6]],)), '0')
check('regression 3', solve(*([],)), '0')
check('regression 4', solve(*([[0, 0], [0, 0]],)), '0')
check('regression 5', solve(*([[2, 0, 1], [3, 4, 0]],)), '30/7')
check('regression 6', solve(*([[0, 0, 0], [1, 2, 3]],)), '0')
check('regression 7', solve(*([[1, 2], [3, 0], [2, 4]],)), '4')
check("variable diagonal mass",solve([[N,0],[0,N]]),str(2*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 | 8 | 8 | Passed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | 30/7 | 30/7 | Passed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 4 | 4 | Passed |
| variable diagonal mass | 2 | 2 | Passed |
SHA-256 / a542bad753b06822356152fad5fc9b485291a2b7e3697bb4d919b633d8619773
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 2026-09-29T14:39:09.402345+00:00.
Case digest / 33e632008215fa9a37bd81612555cc2ef7a275dc5fbde56973e0189993b6a7f3