FA-14041 / Numerical aggregation / Open access

Bucket extrema downsampling: Selected points report bucket-local rather than global indices. · case 01

The reduction disagrees with its explicit aggregation oracle.

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

ROOT CAUSE

Selected points report bucket-local rather than global indices.

THE FAILURE

Selected points report bucket-local rather than global indices.

Unsuccessful approach: Using the bucket start for every extremum loses its local location.

Case contract

For positive integer width, partition numeric observations into consecutive buckets including a final short bucket. Emit each bucket first-occurring minimum and first-occurring maximum once, in original observation order, as [global index,value]. Flat buckets emit one point.

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(xs, width):
    out=[]
    for start in range(0,len(xs),width):
        bucket=xs[start:start+width]
        low=min(range(len(bucket)),key=lambda i:(bucket[i],i))
        high=max(range(len(bucket)),key=lambda i:(bucket[i],-i))
        for i in sorted(set([low,high])):
            out.append([i,bucket[i]])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([8, 1, 6, 2, 9, 3, 4], 3)), [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]])
check('regression 2', solve(*([], 2)), [])
check('regression 3', solve(*([3, 3, 3, 1, 1], 3)), [[0, 3], [3, 1]])
check('regression 4', solve(*([-4, -1, -8, 0], 2)), [[0, -4], [1, -1], [2, -8], [3, 0]])
check('regression 5', solve(*([9, 1, 5], 1)), [[0, 9], [1, 1], [2, 5]])
check('regression 6', solve(*([4, 2, 8, 3], 9)), [[1, 2], [2, 8]])
check('regression 7', solve(*([5, 5, 1, 1, 9, 9], 6)), [[2, 1], [4, 9]])
check("variable bucket amplitude",solve([N,0,2*N],3),[[1,0],[2,2*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	`[[0, 8], [1, 1], [0, 2], [1, 9], [0, 4]]`	`[[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]]`	Failed
regression 2	`[]`	`[]`	Passed
regression 3	`[[0, 3], [0, 1]]`	`[[0, 3], [3, 1]]`	Failed
regression 4	`[[0, -4], [1, -1], [0, -8], [1, 0]]`	`[[0, -4], [1, -1], [2, -8], [3, 0]]`	Failed
regression 5	`[[0, 9], [0, 1], [0, 5]]`	`[[0, 9], [1, 1], [2, 5]]`	Failed
regression 6	`[[1, 2], [2, 8]]`	`[[1, 2], [2, 8]]`	Passed
regression 7	`[[2, 1], [4, 9]]`	`[[2, 1], [4, 9]]`	Passed
variable bucket amplitude	`[[1, 0], [2, 2]]`	`[[1, 0], [2, 2]]`	Passed

SHA-256 / 64c2d4f8aadaa9565567d3c595387933d62fd40def302a0643caa39c8ec0cfe0

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(xs, width):
    out=[]
    for start in range(0,len(xs),width):
        bucket=xs[start:start+width]
        low=min(range(len(bucket)),key=lambda i:(bucket[i],i))
        high=max(range(len(bucket)),key=lambda i:(bucket[i],-i))
        for i in sorted(set([low,high])):
            out.append([start,bucket[i]])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([8, 1, 6, 2, 9, 3, 4], 3)), [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]])
check('regression 2', solve(*([], 2)), [])
check('regression 3', solve(*([3, 3, 3, 1, 1], 3)), [[0, 3], [3, 1]])
check('regression 4', solve(*([-4, -1, -8, 0], 2)), [[0, -4], [1, -1], [2, -8], [3, 0]])
check('regression 5', solve(*([9, 1, 5], 1)), [[0, 9], [1, 1], [2, 5]])
check('regression 6', solve(*([4, 2, 8, 3], 9)), [[1, 2], [2, 8]])
check('regression 7', solve(*([5, 5, 1, 1, 9, 9], 6)), [[2, 1], [4, 9]])
check("variable bucket amplitude",solve([N,0,2*N],3),[[1,0],[2,2*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	`[[0, 8], [0, 1], [3, 2], [3, 9], [6, 4]]`	`[[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]]`	Failed
regression 2	`[]`	`[]`	Passed
regression 3	`[[0, 3], [3, 1]]`	`[[0, 3], [3, 1]]`	Passed
regression 4	`[[0, -4], [0, -1], [2, -8], [2, 0]]`	`[[0, -4], [1, -1], [2, -8], [3, 0]]`	Failed
regression 5	`[[0, 9], [1, 1], [2, 5]]`	`[[0, 9], [1, 1], [2, 5]]`	Passed
regression 6	`[[0, 2], [0, 8]]`	`[[1, 2], [2, 8]]`	Failed
regression 7	`[[0, 1], [0, 9]]`	`[[2, 1], [4, 9]]`	Failed
variable bucket amplitude	`[[0, 0], [0, 2]]`	`[[1, 0], [2, 2]]`	Failed

SHA-256 / 7d19a452654be0cc875e0527482b7bc5e08fb8203bd84e0b3084fe1e0bb84832

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:13.142290+00:00.

Case digest / 9853b6d6c245fb60cb6ca61cd4538d19f3b1016829b1914d346da744a5ea65e4