FA-13121 / Numerical aggregation / Open access
Frequency left quantile: Support values are sorted descending for a lower-tail quantile. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Support values are sorted descending for a lower-tail quantile.
VERIFIED REPAIR
Preserve the frequency left quantile contract at the identified reduction decision.
Unsuccessful approach: Magnitude order is not signed numerical order.
Case contract
Rows are integer [value, nonnegative frequency]; 0<=p<=q, q>0. Return the smallest supported value whose cumulative positive frequency reaches p/q of total. At p=0 return minimum positive support. No positive mass 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(rows, p, q):
rows=sorted(((x,w) for x,w in rows if w>0),reverse=True)
if not rows: return None
total=sum(w for x,w in rows)
threshold=Fraction(p,q)*total
running=0
for x,w in rows:
running+=w
if running>=threshold: return x
return rows[-1][0]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(-8, 1), (-2, 1), (3, 1)], 2, 5)), -2)
check('regression 2', solve(*([(1, 2), (8, 5)], 1, 2)), 8)
check('regression 3', solve(*([(1, 1), (8, 2)], 2, 5)), 8)
check('regression 4', solve(*([(9, 1), (1, 3), (5, 2)], 1, 2)), 1)
check('regression 5', solve(*([(8, 0), (2, 1)], 0, 1)), 2)
check('regression 6', solve(*([], 1, 2)), None)
check('regression 7', solve(*([(1, 0), (5, 0)], 1, 2)), None)
check('regression 8', solve(*([(1, 1), (4, 2), (8, 1)], 3, 4)), 4)
check('regression 9', solve(*([(9, 4), (2, 1)], 1, 1)), 9)
check('regression 10', solve(*([(3, 2), (3, 1), (1, 1)], 1, 2)), 3)
check('regression 11', solve(*([(2, 2), (7, 2)], 1, 2)), 2)
check("variable rank",solve([(N,2),(N+4,1)],1,2),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 | -2 | -2 | Passed |
| regression 2 | 8 | 8 | Passed |
| regression 3 | 8 | 8 | Passed |
| regression 4 | 5 | 1 | Failed |
| regression 5 | 2 | 2 | Passed |
| regression 6 | None | None | Passed |
| regression 7 | None | None | Passed |
| regression 8 | 4 | 4 | Passed |
| regression 9 | 2 | 9 | Failed |
| regression 10 | 3 | 3 | Passed |
| regression 11 | 7 | 2 | Failed |
| variable rank | 1 | 1 | Passed |
SHA-256 / 33a91d9ee9b1db882d9cb1721974f281d11b3d600ea552264a43b5deb0a91253
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, p, q):
rows=sorted(((x,w) for x,w in rows if w>0),key=lambda r:abs(r[0]))
if not rows: return None
total=sum(w for x,w in rows)
threshold=Fraction(p,q)*total
running=0
for x,w in rows:
running+=w
if running>=threshold: return x
return rows[-1][0]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(-8, 1), (-2, 1), (3, 1)], 2, 5)), -2)
check('regression 2', solve(*([(1, 2), (8, 5)], 1, 2)), 8)
check('regression 3', solve(*([(1, 1), (8, 2)], 2, 5)), 8)
check('regression 4', solve(*([(9, 1), (1, 3), (5, 2)], 1, 2)), 1)
check('regression 5', solve(*([(8, 0), (2, 1)], 0, 1)), 2)
check('regression 6', solve(*([], 1, 2)), None)
check('regression 7', solve(*([(1, 0), (5, 0)], 1, 2)), None)
check('regression 8', solve(*([(1, 1), (4, 2), (8, 1)], 3, 4)), 4)
check('regression 9', solve(*([(9, 4), (2, 1)], 1, 1)), 9)
check('regression 10', solve(*([(3, 2), (3, 1), (1, 1)], 1, 2)), 3)
check('regression 11', solve(*([(2, 2), (7, 2)], 1, 2)), 2)
check("variable rank",solve([(N,2),(N+4,1)],1,2),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 | 3 | -2 | Failed |
| regression 2 | 8 | 8 | Passed |
| regression 3 | 8 | 8 | Passed |
| regression 4 | 1 | 1 | Passed |
| regression 5 | 2 | 2 | Passed |
| regression 6 | None | None | Passed |
| regression 7 | None | None | Passed |
| regression 8 | 4 | 4 | Passed |
| regression 9 | 9 | 9 | Passed |
| regression 10 | 3 | 3 | Passed |
| regression 11 | 2 | 2 | Passed |
| variable rank | 1 | 1 | Passed |
SHA-256 / 285beb40a0150aab857220fc717de96c502151a354b5b08139a5d147c4ec0533
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, p, q):
rows=sorted((x,w) for x,w in rows if w>0)
if not rows: return None
total=sum(w for x,w in rows)
threshold=Fraction(p,q)*total
running=0
for x,w in rows:
running+=w
if running>=threshold: return x
return rows[-1][0]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(-8, 1), (-2, 1), (3, 1)], 2, 5)), -2)
check('regression 2', solve(*([(1, 2), (8, 5)], 1, 2)), 8)
check('regression 3', solve(*([(1, 1), (8, 2)], 2, 5)), 8)
check('regression 4', solve(*([(9, 1), (1, 3), (5, 2)], 1, 2)), 1)
check('regression 5', solve(*([(8, 0), (2, 1)], 0, 1)), 2)
check('regression 6', solve(*([], 1, 2)), None)
check('regression 7', solve(*([(1, 0), (5, 0)], 1, 2)), None)
check('regression 8', solve(*([(1, 1), (4, 2), (8, 1)], 3, 4)), 4)
check('regression 9', solve(*([(9, 4), (2, 1)], 1, 1)), 9)
check('regression 10', solve(*([(3, 2), (3, 1), (1, 1)], 1, 2)), 3)
check('regression 11', solve(*([(2, 2), (7, 2)], 1, 2)), 2)
check("variable rank",solve([(N,2),(N+4,1)],1,2),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 | -2 | -2 | Passed |
| regression 2 | 8 | 8 | Passed |
| regression 3 | 8 | 8 | Passed |
| regression 4 | 1 | 1 | Passed |
| regression 5 | 2 | 2 | Passed |
| regression 6 | None | None | Passed |
| regression 7 | None | None | Passed |
| regression 8 | 4 | 4 | Passed |
| regression 9 | 9 | 9 | Passed |
| regression 10 | 3 | 3 | Passed |
| regression 11 | 2 | 2 | Passed |
| variable rank | 1 | 1 | Passed |
SHA-256 / 551bcdb223f6329978a6042ae9bafef33f637bb02ab4034980f21b6095458761
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 2026-09-29T14:39:03.835859+00:00.
Case digest / 41d76e22a096666e2d4738247c25efc42ab2c50db1db9b16041dcaa5d67c908f