FA-13176 / Numerical aggregation / Open access
Maximum subarray block summary: The crossing candidate combines the old prefix with incoming suffix. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The crossing candidate combines the old prefix with incoming suffix.
VERIFIED REPAIR
Preserve the maximum subarray block summary contract at the identified reduction decision.
Unsuccessful approach: Two suffixes still skip the beginning of the incoming block.
Case contract
Merge ordered disjoint integer blocks, preserving concatenation order. Return [total, maximum prefix sum, maximum suffix sum, maximum contiguous subarray sum]; empty subarrays are allowed and have sum zero.
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):
total=prefix=suffix=best=0
for block in blocks:
t=sum(block)
p=max([0]+[sum(block[:i]) for i in range(1,len(block)+1)])
s=max([0]+[sum(block[i:]) for i in range(len(block))])
b=max([0]+[sum(block[i:j]) for i in range(len(block)) for j in range(i+1,len(block)+1)])
new_best=max(best,b,prefix+s)
new_prefix=max(prefix,total+p)
new_suffix=max(s,suffix+t)
total=total+t
prefix,suffix,best=new_prefix,new_suffix,new_best
return [total,prefix,suffix,best]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[-100, 5]],)), [-95, 0, 5, 5])
check('regression 2', solve(*([[2, -7, 4], [3, -1]],)), [1, 2, 6, 7])
check('regression 3', solve(*([[-8, -2], [-3]],)), [-13, 0, 0, 0])
check('regression 4', solve(*([],)), [0, 0, 0, 0])
check('regression 5', solve(*([[4, -2], [], [3, -9, 6]],)), [2, 5, 6, 6])
check('regression 6', solve(*([[-2, 7], [-3, 5, -9], [2]],)), [0, 7, 2, 9])
check('regression 7', solve(*([[8, -9], [1, -4, 9]],)), [5, 8, 9, 9])
check('regression 8', solve(*([[1, 2], [3, 4]],)), [10, 10, 10, 10])
check("variable cross block peak",solve([[-N,2*N],[N,-4*N]]),[-2*N,2*N,0,3*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 | [-95, 0, 5, 5] | [-95, 0, 5, 5] | Passed |
| regression 2 | [1, 2, 6, 4] | [1, 2, 6, 7] | Failed |
| regression 3 | [-13, 0, 0, 0] | [-13, 0, 0, 0] | Passed |
| regression 4 | [0, 0, 0, 0] | [0, 0, 0, 0] | Passed |
| regression 5 | [2, 5, 6, 10] | [2, 5, 6, 6] | Failed |
| regression 6 | [0, 7, 2, 9] | [0, 7, 2, 9] | Passed |
| regression 7 | [5, 8, 9, 17] | [5, 8, 9, 9] | Failed |
| regression 8 | [10, 10, 10, 10] | [10, 10, 10, 10] | Passed |
| variable cross block peak | [-2, 2, 0, 2] | [-2, 2, 0, 3] | Failed |
SHA-256 / b22d6ee34f183370514b6b5e0d554c9e49e618c9cb1ce7e1dac2f747efd17c72
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):
total=prefix=suffix=best=0
for block in blocks:
t=sum(block)
p=max([0]+[sum(block[:i]) for i in range(1,len(block)+1)])
s=max([0]+[sum(block[i:]) for i in range(len(block))])
b=max([0]+[sum(block[i:j]) for i in range(len(block)) for j in range(i+1,len(block)+1)])
new_best=max(best,b,suffix+s)
new_prefix=max(prefix,total+p)
new_suffix=max(s,suffix+t)
total=total+t
prefix,suffix,best=new_prefix,new_suffix,new_best
return [total,prefix,suffix,best]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[-100, 5]],)), [-95, 0, 5, 5])
check('regression 2', solve(*([[2, -7, 4], [3, -1]],)), [1, 2, 6, 7])
check('regression 3', solve(*([[-8, -2], [-3]],)), [-13, 0, 0, 0])
check('regression 4', solve(*([],)), [0, 0, 0, 0])
check('regression 5', solve(*([[4, -2], [], [3, -9, 6]],)), [2, 5, 6, 6])
check('regression 6', solve(*([[-2, 7], [-3, 5, -9], [2]],)), [0, 7, 2, 9])
check('regression 7', solve(*([[8, -9], [1, -4, 9]],)), [5, 8, 9, 9])
check('regression 8', solve(*([[1, 2], [3, 4]],)), [10, 10, 10, 10])
check("variable cross block peak",solve([[-N,2*N],[N,-4*N]]),[-2*N,2*N,0,3*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 | [-95, 0, 5, 5] | [-95, 0, 5, 5] | Passed |
| regression 2 | [1, 2, 6, 6] | [1, 2, 6, 7] | Failed |
| regression 3 | [-13, 0, 0, 0] | [-13, 0, 0, 0] | Passed |
| regression 4 | [0, 0, 0, 0] | [0, 0, 0, 0] | Passed |
| regression 5 | [2, 5, 6, 8] | [2, 5, 6, 6] | Failed |
| regression 6 | [0, 7, 2, 7] | [0, 7, 2, 9] | Failed |
| regression 7 | [5, 8, 9, 9] | [5, 8, 9, 9] | Passed |
| regression 8 | [10, 10, 10, 10] | [10, 10, 10, 10] | Passed |
| variable cross block peak | [-2, 2, 0, 2] | [-2, 2, 0, 3] | Failed |
SHA-256 / 220693615fb571a235dd0e457a7a11dd092383343f453a55b4094e11720986cd
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):
total=prefix=suffix=best=0
for block in blocks:
t=sum(block)
p=max([0]+[sum(block[:i]) for i in range(1,len(block)+1)])
s=max([0]+[sum(block[i:]) for i in range(len(block))])
b=max([0]+[sum(block[i:j]) for i in range(len(block)) for j in range(i+1,len(block)+1)])
new_best=max(best,b,suffix+p)
new_prefix=max(prefix,total+p)
new_suffix=max(s,suffix+t)
total=total+t
prefix,suffix,best=new_prefix,new_suffix,new_best
return [total,prefix,suffix,best]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[-100, 5]],)), [-95, 0, 5, 5])
check('regression 2', solve(*([[2, -7, 4], [3, -1]],)), [1, 2, 6, 7])
check('regression 3', solve(*([[-8, -2], [-3]],)), [-13, 0, 0, 0])
check('regression 4', solve(*([],)), [0, 0, 0, 0])
check('regression 5', solve(*([[4, -2], [], [3, -9, 6]],)), [2, 5, 6, 6])
check('regression 6', solve(*([[-2, 7], [-3, 5, -9], [2]],)), [0, 7, 2, 9])
check('regression 7', solve(*([[8, -9], [1, -4, 9]],)), [5, 8, 9, 9])
check('regression 8', solve(*([[1, 2], [3, 4]],)), [10, 10, 10, 10])
check("variable cross block peak",solve([[-N,2*N],[N,-4*N]]),[-2*N,2*N,0,3*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 | [-95, 0, 5, 5] | [-95, 0, 5, 5] | Passed |
| regression 2 | [1, 2, 6, 7] | [1, 2, 6, 7] | Passed |
| regression 3 | [-13, 0, 0, 0] | [-13, 0, 0, 0] | Passed |
| regression 4 | [0, 0, 0, 0] | [0, 0, 0, 0] | Passed |
| regression 5 | [2, 5, 6, 6] | [2, 5, 6, 6] | Passed |
| regression 6 | [0, 7, 2, 9] | [0, 7, 2, 9] | Passed |
| regression 7 | [5, 8, 9, 9] | [5, 8, 9, 9] | Passed |
| regression 8 | [10, 10, 10, 10] | [10, 10, 10, 10] | Passed |
| variable cross block peak | [-2, 2, 0, 3] | [-2, 2, 0, 3] | Passed |
SHA-256 / e4797b1147c92336e8b898e2f3d32f1b5c7446b40369599781886673d584e95d
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 2026-09-29T14:39:04.320399+00:00.
Case digest / dcf065b42cb882b4808645c18f95dfb8be6a32e8dc4de427a22384d349bc290a