FA-46856 / Bounded deques / Open access

Deque block rebalance treats target occupancy as transfer count · case 01

Deque block rebalance treats target occupancy as transfer count.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Deque block rebalance treats target occupancy as transfer count.

VERIFIED REPAIR

Restore the documented left target invariant in block-rebalance.

Unsuccessful approach: The partial repair still applies the incorrect transition to an admitted boundary or multi-element case.

Case contract

Redistribute two adjacent deque blocks to a requested left occupancy without changing element order or block identities. Return signed left-to-right transfer count and new directory lengths.

Why this case matters

Controlled bounded deque implementation model with explicit storage and lifecycle observations.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    a,b,target,aid,bid=x
    joined=a+b
    left=joined[:max(0,len(a)-target)]
    right=joined[target:]
    left_id=aid
    right_id=bid
    transfer=len(a)-target
    directory=[[left_id,len(left)],[right_id,len(right)]]
    return [left,right,left_id,right_id,transfer,directory]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1,N+2],[N+3],2,3,8]), {1: [[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]], 2: [[2, 3], [4, 5], 3, 8, 1, [[3, 2], [8, 2]]], 3: [[3, 4], [5, 6], 3, 8, 1, [[3, 2], [8, 2]]], 4: [[4, 5], [6, 7], 3, 8, 1, [[3, 2], [8, 2]]], 5: [[5, 6], [7, 8], 3, 8, 1, [[3, 2], [8, 2]]]}[N])
check('1', solve([[N],[N+1,N+2,N+3],3,4,9]), {1: [[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]], 2: [[2, 3, 4], [5], 4, 9, -2, [[4, 3], [9, 1]]], 3: [[3, 4, 5], [6], 4, 9, -2, [[4, 3], [9, 1]]], 4: [[4, 5, 6], [7], 4, 9, -2, [[4, 3], [9, 1]]], 5: [[5, 6, 7], [8], 4, 9, -2, [[4, 3], [9, 1]]]}[N])
check('2', solve([[N,N+1],[N+2,N+3],2,5,10]), {1: [[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]], 2: [[2, 3], [4, 5], 5, 10, 0, [[5, 2], [10, 2]]], 3: [[3, 4], [5, 6], 5, 10, 0, [[5, 2], [10, 2]]], 4: [[4, 5], [6, 7], 5, 10, 0, [[5, 2], [10, 2]]], 5: [[5, 6], [7, 8], 5, 10, 0, [[5, 2], [10, 2]]]}[N])
check('3', solve([[],[N,N+1],1,2,7]), {1: [[1], [2], 2, 7, -1, [[2, 1], [7, 1]]], 2: [[2], [3], 2, 7, -1, [[2, 1], [7, 1]]], 3: [[3], [4], 2, 7, -1, [[2, 1], [7, 1]]], 4: [[4], [5], 2, 7, -1, [[2, 1], [7, 1]]], 5: [[5], [6], 2, 7, -1, [[2, 1], [7, 1]]]}[N])
check('4', solve([[N,N+1],[],0,4,6]), {1: [[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]], 2: [[], [2, 3], 4, 6, 2, [[4, 0], [6, 2]]], 3: [[], [3, 4], 4, 6, 2, [[4, 0], [6, 2]]], 4: [[], [4, 5], 4, 6, 2, [[4, 0], [6, 2]]], 5: [[], [5, 6], 4, 6, 2, [[4, 0], [6, 2]]]}[N])
check('5', solve([[N],[N+1],2,1,5]), {1: [[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]], 2: [[2, 3], [], 1, 5, -1, [[1, 2], [5, 0]]], 3: [[3, 4], [], 1, 5, -1, [[1, 2], [5, 0]]], 4: [[4, 5], [], 1, 5, -1, [[1, 2], [5, 0]]], 5: [[5, 6], [], 1, 5, -1, [[1, 2], [5, 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 fixture	Actual	Expected	Outcome
0	`[[1], [3, 4], 3, 8, 1, [[3, 1], [8, 2]]]`	`[[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]]`	Failed
1	`[[], [4], 4, 9, -2, [[4, 0], [9, 1]]]`	`[[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]]`	Failed
2	`[[], [3, 4], 5, 10, 0, [[5, 0], [10, 2]]]`	`[[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]]`	Failed
3	`[[], [2], 2, 7, -1, [[2, 0], [7, 1]]]`	`[[1], [2], 2, 7, -1, [[2, 1], [7, 1]]]`	Failed
4	`[[1, 2], [1, 2], 4, 6, 2, [[4, 2], [6, 2]]]`	`[[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]]`	Failed
5	`[[], [], 1, 5, -1, [[1, 0], [5, 0]]]`	`[[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]]`	Failed

SHA-256 / eaf1e32cab6f29d5eb4be387cfafcd32fb90c32e0d3fedbbd814c0228851a8bb

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    a,b,target,aid,bid=x
    joined=a+b
    left=joined[:target] if not a else joined[:max(0,len(a)-target)]
    right=joined[target:]
    left_id=aid
    right_id=bid
    transfer=len(a)-target
    directory=[[left_id,len(left)],[right_id,len(right)]]
    return [left,right,left_id,right_id,transfer,directory]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1,N+2],[N+3],2,3,8]), {1: [[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]], 2: [[2, 3], [4, 5], 3, 8, 1, [[3, 2], [8, 2]]], 3: [[3, 4], [5, 6], 3, 8, 1, [[3, 2], [8, 2]]], 4: [[4, 5], [6, 7], 3, 8, 1, [[3, 2], [8, 2]]], 5: [[5, 6], [7, 8], 3, 8, 1, [[3, 2], [8, 2]]]}[N])
check('1', solve([[N],[N+1,N+2,N+3],3,4,9]), {1: [[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]], 2: [[2, 3, 4], [5], 4, 9, -2, [[4, 3], [9, 1]]], 3: [[3, 4, 5], [6], 4, 9, -2, [[4, 3], [9, 1]]], 4: [[4, 5, 6], [7], 4, 9, -2, [[4, 3], [9, 1]]], 5: [[5, 6, 7], [8], 4, 9, -2, [[4, 3], [9, 1]]]}[N])
check('2', solve([[N,N+1],[N+2,N+3],2,5,10]), {1: [[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]], 2: [[2, 3], [4, 5], 5, 10, 0, [[5, 2], [10, 2]]], 3: [[3, 4], [5, 6], 5, 10, 0, [[5, 2], [10, 2]]], 4: [[4, 5], [6, 7], 5, 10, 0, [[5, 2], [10, 2]]], 5: [[5, 6], [7, 8], 5, 10, 0, [[5, 2], [10, 2]]]}[N])
check('3', solve([[],[N,N+1],1,2,7]), {1: [[1], [2], 2, 7, -1, [[2, 1], [7, 1]]], 2: [[2], [3], 2, 7, -1, [[2, 1], [7, 1]]], 3: [[3], [4], 2, 7, -1, [[2, 1], [7, 1]]], 4: [[4], [5], 2, 7, -1, [[2, 1], [7, 1]]], 5: [[5], [6], 2, 7, -1, [[2, 1], [7, 1]]]}[N])
check('4', solve([[N,N+1],[],0,4,6]), {1: [[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]], 2: [[], [2, 3], 4, 6, 2, [[4, 0], [6, 2]]], 3: [[], [3, 4], 4, 6, 2, [[4, 0], [6, 2]]], 4: [[], [4, 5], 4, 6, 2, [[4, 0], [6, 2]]], 5: [[], [5, 6], 4, 6, 2, [[4, 0], [6, 2]]]}[N])
check('5', solve([[N],[N+1],2,1,5]), {1: [[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]], 2: [[2, 3], [], 1, 5, -1, [[1, 2], [5, 0]]], 3: [[3, 4], [], 1, 5, -1, [[1, 2], [5, 0]]], 4: [[4, 5], [], 1, 5, -1, [[1, 2], [5, 0]]], 5: [[5, 6], [], 1, 5, -1, [[1, 2], [5, 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 fixture	Actual	Expected	Outcome
0	`[[1], [3, 4], 3, 8, 1, [[3, 1], [8, 2]]]`	`[[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]]`	Failed
1	`[[], [4], 4, 9, -2, [[4, 0], [9, 1]]]`	`[[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]]`	Failed
2	`[[], [3, 4], 5, 10, 0, [[5, 0], [10, 2]]]`	`[[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]]`	Failed
3	`[[1], [2], 2, 7, -1, [[2, 1], [7, 1]]]`	`[[1], [2], 2, 7, -1, [[2, 1], [7, 1]]]`	Passed
4	`[[1, 2], [1, 2], 4, 6, 2, [[4, 2], [6, 2]]]`	`[[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]]`	Failed
5	`[[], [], 1, 5, -1, [[1, 0], [5, 0]]]`	`[[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]]`	Failed

SHA-256 / cd187e2f6c47006317e6df7f024d739875c0afbb594fc9e07ffbb6927350ea92

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    a,b,target,aid,bid=x
    joined=a+b
    left=joined[:target]
    right=joined[target:]
    left_id=aid
    right_id=bid
    transfer=len(a)-target
    directory=[[left_id,len(left)],[right_id,len(right)]]
    return [left,right,left_id,right_id,transfer,directory]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1,N+2],[N+3],2,3,8]), {1: [[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]], 2: [[2, 3], [4, 5], 3, 8, 1, [[3, 2], [8, 2]]], 3: [[3, 4], [5, 6], 3, 8, 1, [[3, 2], [8, 2]]], 4: [[4, 5], [6, 7], 3, 8, 1, [[3, 2], [8, 2]]], 5: [[5, 6], [7, 8], 3, 8, 1, [[3, 2], [8, 2]]]}[N])
check('1', solve([[N],[N+1,N+2,N+3],3,4,9]), {1: [[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]], 2: [[2, 3, 4], [5], 4, 9, -2, [[4, 3], [9, 1]]], 3: [[3, 4, 5], [6], 4, 9, -2, [[4, 3], [9, 1]]], 4: [[4, 5, 6], [7], 4, 9, -2, [[4, 3], [9, 1]]], 5: [[5, 6, 7], [8], 4, 9, -2, [[4, 3], [9, 1]]]}[N])
check('2', solve([[N,N+1],[N+2,N+3],2,5,10]), {1: [[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]], 2: [[2, 3], [4, 5], 5, 10, 0, [[5, 2], [10, 2]]], 3: [[3, 4], [5, 6], 5, 10, 0, [[5, 2], [10, 2]]], 4: [[4, 5], [6, 7], 5, 10, 0, [[5, 2], [10, 2]]], 5: [[5, 6], [7, 8], 5, 10, 0, [[5, 2], [10, 2]]]}[N])
check('3', solve([[],[N,N+1],1,2,7]), {1: [[1], [2], 2, 7, -1, [[2, 1], [7, 1]]], 2: [[2], [3], 2, 7, -1, [[2, 1], [7, 1]]], 3: [[3], [4], 2, 7, -1, [[2, 1], [7, 1]]], 4: [[4], [5], 2, 7, -1, [[2, 1], [7, 1]]], 5: [[5], [6], 2, 7, -1, [[2, 1], [7, 1]]]}[N])
check('4', solve([[N,N+1],[],0,4,6]), {1: [[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]], 2: [[], [2, 3], 4, 6, 2, [[4, 0], [6, 2]]], 3: [[], [3, 4], 4, 6, 2, [[4, 0], [6, 2]]], 4: [[], [4, 5], 4, 6, 2, [[4, 0], [6, 2]]], 5: [[], [5, 6], 4, 6, 2, [[4, 0], [6, 2]]]}[N])
check('5', solve([[N],[N+1],2,1,5]), {1: [[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]], 2: [[2, 3], [], 1, 5, -1, [[1, 2], [5, 0]]], 3: [[3, 4], [], 1, 5, -1, [[1, 2], [5, 0]]], 4: [[4, 5], [], 1, 5, -1, [[1, 2], [5, 0]]], 5: [[5, 6], [], 1, 5, -1, [[1, 2], [5, 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 fixture	Actual	Expected	Outcome
0	`[[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]]`	`[[1, 2], [3, 4], 3, 8, 1, [[3, 2], [8, 2]]]`	Passed
1	`[[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]]`	`[[1, 2, 3], [4], 4, 9, -2, [[4, 3], [9, 1]]]`	Passed
2	`[[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]]`	`[[1, 2], [3, 4], 5, 10, 0, [[5, 2], [10, 2]]]`	Passed
3	`[[1], [2], 2, 7, -1, [[2, 1], [7, 1]]]`	`[[1], [2], 2, 7, -1, [[2, 1], [7, 1]]]`	Passed
4	`[[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]]`	`[[], [1, 2], 4, 6, 2, [[4, 0], [6, 2]]]`	Passed
5	`[[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]]`	`[[1, 2], [], 1, 5, -1, [[1, 2], [5, 0]]]`	Passed

SHA-256 / 11d0b7614a186d9f7d2caf833d429e69c852dffcab5bdba2b6c8814051bd71fb

Verification & scope

Offline finite deterministic model; no claim of production implementation or concurrent memory-model conformance. 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 2026-09-29T14:44:35.999874+00:00.

Case digest / 2c280fda850bcb14638a14f6f787d04e08383342bdc0b0cce10a7b238d010485