FAILURE MAP
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FA-14286 / Numerical aggregation / Open access

Three row count sketch: Queries use each row minimum instead of the key-specific bucket. · case 01

The reduction disagrees with its explicit aggregation oracle.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Queries use each row minimum instead of the key-specific bucket.

VERIFIED REPAIR

Preserve the three row count sketch contract at the identified reduction decision.

Unsuccessful approach: Row totals lose key selectivity and return whole-stream mass.

Case contract

A stipulated nonnegative weighted count-min table has exactly three independent rows of positive width, with bucket functions k%w,(3*k+1)%w,(k//w)%w for nonnegative integer keys. Add all block contributions, then estimate each query by the minimum of its three cells. Return [table,estimates]; no probabilistic error guarantee is claimed.

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(blocks, width, queries):
    table=[[0]*width for _ in range(3)]
    for block in blocks:
        for key,weight in block:
            buckets=[key%width,(3*key+1)%width,(key//width)%width]
            for row,col in enumerate(buckets):
                table[row][col]+=weight
    estimates=[]
    for key in queries:
        buckets=[key%width,(3*key+1)%width,(key//width)%width]
        estimates.append(min(min(row) for row in table))
    return [table,estimates]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[(0, 2), (1, 3)], [(4, 1)]], 4, [0, 1, 4, 8])), [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]])
check('regression 2', solve(*([], 3, [0, 1])), [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]])
check('regression 3', solve(*([[(2, 5)], [], [(2, 2)]], 3, [2, 5])), [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]])
check('regression 4', solve(*([[(0, 1), (0, 1)]], 1, [0, 3])), [[[2], [2], [2]], [2, 2]])
check('regression 5', solve(*([[(7, 0), (2, 4), (5, 1)]], 4, [2, 5, 7])), [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]])
check('regression 6', solve(*([[(1, 2)], [(8, 5), (3, 4)]], 5, [1, 8, 3, 13])), [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]])
check("variable sketch contribution",solve([[(0,N)]],2,[0]),[[[N,0],[0,N],[N,0]],[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[[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [0, 0, 0, 0]][[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]]Failed
regression 2[[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]][[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]]Passed
regression 3[[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [0, 0]][[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]]Failed
regression 4[[[2], [2], [2]], [2, 2]][[[2], [2], [2]], [2, 2]]Passed
regression 5[[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [0, 0, 0]][[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]]Failed
regression 6[[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [0, 0, 0, 0]][[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]]Failed
variable sketch contribution[[[1, 0], [0, 1], [1, 0]], [0]][[[1, 0], [0, 1], [1, 0]], [1]]Failed

SHA-256 / c8b8e4f682d56647b5fe4b241ec25639f7b2ac8fa7a5f094adec0cec9f668444

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(blocks, width, queries):
    table=[[0]*width for _ in range(3)]
    for block in blocks:
        for key,weight in block:
            buckets=[key%width,(3*key+1)%width,(key//width)%width]
            for row,col in enumerate(buckets):
                table[row][col]+=weight
    estimates=[]
    for key in queries:
        buckets=[key%width,(3*key+1)%width,(key//width)%width]
        estimates.append(min(sum(row) for row in table))
    return [table,estimates]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[(0, 2), (1, 3)], [(4, 1)]], 4, [0, 1, 4, 8])), [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]])
check('regression 2', solve(*([], 3, [0, 1])), [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]])
check('regression 3', solve(*([[(2, 5)], [], [(2, 2)]], 3, [2, 5])), [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]])
check('regression 4', solve(*([[(0, 1), (0, 1)]], 1, [0, 3])), [[[2], [2], [2]], [2, 2]])
check('regression 5', solve(*([[(7, 0), (2, 4), (5, 1)]], 4, [2, 5, 7])), [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]])
check('regression 6', solve(*([[(1, 2)], [(8, 5), (3, 4)]], 5, [1, 8, 3, 13])), [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]])
check("variable sketch contribution",solve([[(0,N)]],2,[0]),[[[N,0],[0,N],[N,0]],[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[[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [6, 6, 6, 6]][[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]]Failed
regression 2[[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]][[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]]Passed
regression 3[[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 7]][[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]]Failed
regression 4[[[2], [2], [2]], [2, 2]][[[2], [2], [2]], [2, 2]]Passed
regression 5[[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [5, 5, 5]][[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]]Failed
regression 6[[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [11, 11, 11, 11]][[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]]Failed
variable sketch contribution[[[1, 0], [0, 1], [1, 0]], [1]][[[1, 0], [0, 1], [1, 0]], [1]]Passed

SHA-256 / 4b2c05277bb10a6810c52bbc0effab6267da57f3dc9279bb72bb18858f873041

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(blocks, width, queries):
    table=[[0]*width for _ in range(3)]
    for block in blocks:
        for key,weight in block:
            buckets=[key%width,(3*key+1)%width,(key//width)%width]
            for row,col in enumerate(buckets):
                table[row][col]+=weight
    estimates=[]
    for key in queries:
        buckets=[key%width,(3*key+1)%width,(key//width)%width]
        estimates.append(min(table[row][col] for row,col in enumerate(buckets)))
    return [table,estimates]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[(0, 2), (1, 3)], [(4, 1)]], 4, [0, 1, 4, 8])), [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]])
check('regression 2', solve(*([], 3, [0, 1])), [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]])
check('regression 3', solve(*([[(2, 5)], [], [(2, 2)]], 3, [2, 5])), [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]])
check('regression 4', solve(*([[(0, 1), (0, 1)]], 1, [0, 3])), [[[2], [2], [2]], [2, 2]])
check('regression 5', solve(*([[(7, 0), (2, 4), (5, 1)]], 4, [2, 5, 7])), [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]])
check('regression 6', solve(*([[(1, 2)], [(8, 5), (3, 4)]], 5, [1, 8, 3, 13])), [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]])
check("variable sketch contribution",solve([[(0,N)]],2,[0]),[[[N,0],[0,N],[N,0]],[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[[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]][[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]]Passed
regression 2[[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]][[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]]Passed
regression 3[[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]][[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]]Passed
regression 4[[[2], [2], [2]], [2, 2]][[[2], [2], [2]], [2, 2]]Passed
regression 5[[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]][[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]]Passed
regression 6[[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]][[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]]Passed
variable sketch contribution[[[1, 0], [0, 1], [1, 0]], [1]][[[1, 0], [0, 1], [1, 0]], [1]]Passed

SHA-256 / c6d9eeecd646bee9d90bdbd7c194e3a43e64dc71d005356f968d60d9e621c585

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 2026-09-29T14:39:15.451416+00:00.

Case digest / f7ed3742f01e2ad47f38ae4c6aac831717cc580469bea12f123bd56ba376b913