FA-13731 / Numerical aggregation / Open access
Tie adjusted concordance squared: X tie correction counts tied pairs rather than varying pairs. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
X tie correction counts tied pairs rather than varying pairs.
VERIFIED REPAIR
Preserve the tie adjusted concordance squared contract at the identified reduction decision.
Unsuccessful approach: Counting every x pair also omits the x tie correction.
Case contract
For paired ordinal observations return sign(tau_b)*tau_b**2 as an exact Fraction string. Every unordered observation pair contributes its coordinate comparison; normalize signed concordance squared by products of non-tied x/y pair counts. Undefined if either coordinate has no varying pairs.
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(points):
concordant=discordant=tx=ty=0
for i in range(len(points)):
for j in range(i+1,len(points)):
dx=points[i][0]-points[j][0]
dy=points[i][1]-points[j][1]
if not dx: tx+=1
if dy: ty+=1
concordant+=int(dx*dy>0)
discordant+=int(dx*dy<0)
if not tx or not ty: return None
d=concordant-discordant
return str(Fraction((1 if d>=0 else -1)*d*d,tx*ty))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 1), (2, 2), (3, 3)],)), '1')
check('regression 2', solve(*([(1, 3), (2, 2), (3, 1)],)), '-1')
check('regression 3', solve(*([(1, 1), (1, 2), (2, 2), (3, 1)],)), '-1/20')
check('regression 4', solve(*([],)), None)
check('regression 5', solve(*([(1, 1), (1, 2)],)), None)
check('regression 6', solve(*([(1, 1), (2, 2), (2, 2), (4, 3)],)), '1')
check('regression 7', solve(*([(1, 2), (3, 1), (4, 4), (2, 5)],)), '0')
check("variable discordance direction",solve([(0,N),(N,0)]),"-1")
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 | None | 1 | Failed |
| regression 2 | None | -1 | Failed |
| regression 3 | -1/4 | -1/20 | Failed |
| regression 4 | None | None | Passed |
| regression 5 | 0 | None | Failed |
| regression 6 | 5 | 1 | Failed |
| regression 7 | None | 0 | Failed |
| variable discordance direction | None | -1 | Failed |
SHA-256 / 1c7fbf0af11acf355da575bc3614b3d1bf2e7770db9dfc8c4786b717df5ffc4a
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(points):
concordant=discordant=tx=ty=0
for i in range(len(points)):
for j in range(i+1,len(points)):
dx=points[i][0]-points[j][0]
dy=points[i][1]-points[j][1]
tx+=1
if dy: ty+=1
concordant+=int(dx*dy>0)
discordant+=int(dx*dy<0)
if not tx or not ty: return None
d=concordant-discordant
return str(Fraction((1 if d>=0 else -1)*d*d,tx*ty))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 1), (2, 2), (3, 3)],)), '1')
check('regression 2', solve(*([(1, 3), (2, 2), (3, 1)],)), '-1')
check('regression 3', solve(*([(1, 1), (1, 2), (2, 2), (3, 1)],)), '-1/20')
check('regression 4', solve(*([],)), None)
check('regression 5', solve(*([(1, 1), (1, 2)],)), None)
check('regression 6', solve(*([(1, 1), (2, 2), (2, 2), (4, 3)],)), '1')
check('regression 7', solve(*([(1, 2), (3, 1), (4, 4), (2, 5)],)), '0')
check("variable discordance direction",solve([(0,N),(N,0)]),"-1")
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 | Passed |
| regression 3 | -1/24 | -1/20 | Failed |
| regression 4 | None | None | Passed |
| regression 5 | 0 | None | Failed |
| regression 6 | 5/6 | 1 | Failed |
| regression 7 | 0 | 0 | Passed |
| variable discordance direction | -1 | -1 | Passed |
SHA-256 / 19c08147003fa53c0d515dc2e7efd21bb58f7908e498b0078392ccb2220d49fb
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(points):
concordant=discordant=tx=ty=0
for i in range(len(points)):
for j in range(i+1,len(points)):
dx=points[i][0]-points[j][0]
dy=points[i][1]-points[j][1]
if dx: tx+=1
if dy: ty+=1
concordant+=int(dx*dy>0)
discordant+=int(dx*dy<0)
if not tx or not ty: return None
d=concordant-discordant
return str(Fraction((1 if d>=0 else -1)*d*d,tx*ty))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(1, 1), (2, 2), (3, 3)],)), '1')
check('regression 2', solve(*([(1, 3), (2, 2), (3, 1)],)), '-1')
check('regression 3', solve(*([(1, 1), (1, 2), (2, 2), (3, 1)],)), '-1/20')
check('regression 4', solve(*([],)), None)
check('regression 5', solve(*([(1, 1), (1, 2)],)), None)
check('regression 6', solve(*([(1, 1), (2, 2), (2, 2), (4, 3)],)), '1')
check('regression 7', solve(*([(1, 2), (3, 1), (4, 4), (2, 5)],)), '0')
check("variable discordance direction",solve([(0,N),(N,0)]),"-1")
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 | Passed |
| regression 3 | -1/20 | -1/20 | Passed |
| regression 4 | None | None | Passed |
| regression 5 | None | None | Passed |
| regression 6 | 1 | 1 | Passed |
| regression 7 | 0 | 0 | Passed |
| variable discordance direction | -1 | -1 | Passed |
SHA-256 / 4af632310cc2bf180cf06298cff0fd8a24e43365131b2d9f51d804bc0b9d6e7b
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 2026-09-29T14:39:10.042233+00:00.
Case digest / 1eb4a42e3e66cc4caacf7e4d37eb0a1ba0ada95fa25b0aa420b13946b19d45e4