FA-46426 / Bounded deques / Open access

Rejected block merge increments the directory epoch · case 01

Rejected block merge increments the directory epoch.

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

ROOT CAUSE

Rejected block merge increments the directory epoch.

VERIFIED REPAIR

Restore the documented failed atomicity invariant in block-merge.

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

Case contract

Merge adjacent deque storage blocks if combined occupancy fits one block. Preserve the left block ID, retire the right ID once, and advance the directory epoch only on success.

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,aid,bid,cap,epoch=x
    fits=len(a)+len(b)<=cap
    if not fits:return [a,b,False,aid,[],epoch+1]
    joined=a+b
    right=[]
    identity=aid
    retired=[bid]
    version=epoch+1
    return [joined,right,True,identity,retired,version]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1],[N+2],4,5,3,0]), {1: [[1, 2, 3], [], True, 4, [5], 1], 2: [[2, 3, 4], [], True, 4, [5], 1], 3: [[3, 4, 5], [], True, 4, [5], 1], 4: [[4, 5, 6], [], True, 4, [5], 1], 5: [[5, 6, 7], [], True, 4, [5], 1]}[N])
check('1', solve([[N,N+1],[N+2,N+3],4,5,3,2]), {1: [[1, 2], [3, 4], False, 4, [], 2], 2: [[2, 3], [4, 5], False, 4, [], 2], 3: [[3, 4], [5, 6], False, 4, [], 2], 4: [[4, 5], [6, 7], False, 4, [], 2], 5: [[5, 6], [7, 8], False, 4, [], 2]}[N])
check('2', solve([[],[N,N+1],7,8,4,3]), {1: [[1, 2], [], True, 7, [8], 4], 2: [[2, 3], [], True, 7, [8], 4], 3: [[3, 4], [], True, 7, [8], 4], 4: [[4, 5], [], True, 7, [8], 4], 5: [[5, 6], [], True, 7, [8], 4]}[N])
check('3', solve([[N],[],2,6,3,4]), {1: [[1], [], True, 2, [6], 5], 2: [[2], [], True, 2, [6], 5], 3: [[3], [], True, 2, [6], 5], 4: [[4], [], True, 2, [6], 5], 5: [[5], [], True, 2, [6], 5]}[N])
check('4', solve([[],[],1,3,2,8]), {1: [[], [], True, 1, [3], 9], 2: [[], [], True, 1, [3], 9], 3: [[], [], True, 1, [3], 9], 4: [[], [], True, 1, [3], 9], 5: [[], [], True, 1, [3], 9]}[N])
check('5', solve([[N],[N+1,N+2],6,9,5,1]), {1: [[1, 2, 3], [], True, 6, [9], 2], 2: [[2, 3, 4], [], True, 6, [9], 2], 3: [[3, 4, 5], [], True, 6, [9], 2], 4: [[4, 5, 6], [], True, 6, [9], 2], 5: [[5, 6, 7], [], True, 6, [9], 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
0	`[[1, 2, 3], [], True, 4, [5], 1]`	`[[1, 2, 3], [], True, 4, [5], 1]`	Passed
1	`[[1, 2], [3, 4], False, 4, [], 3]`	`[[1, 2], [3, 4], False, 4, [], 2]`	Failed
2	`[[1, 2], [], True, 7, [8], 4]`	`[[1, 2], [], True, 7, [8], 4]`	Passed
3	`[[1], [], True, 2, [6], 5]`	`[[1], [], True, 2, [6], 5]`	Passed
4	`[[], [], True, 1, [3], 9]`	`[[], [], True, 1, [3], 9]`	Passed
5	`[[1, 2, 3], [], True, 6, [9], 2]`	`[[1, 2, 3], [], True, 6, [9], 2]`	Passed

SHA-256 / 69192c97f0857d9347a1d15a08746165ab4bbe0b4e25c3986cf50ba9b8561b6e

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    a,b,aid,bid,cap,epoch=x
    fits=len(a)+len(b)<=cap
    if not fits:return [a,b,False,aid,[],epoch+(1 if a else 0)]
    joined=a+b
    right=[]
    identity=aid
    retired=[bid]
    version=epoch+1
    return [joined,right,True,identity,retired,version]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1],[N+2],4,5,3,0]), {1: [[1, 2, 3], [], True, 4, [5], 1], 2: [[2, 3, 4], [], True, 4, [5], 1], 3: [[3, 4, 5], [], True, 4, [5], 1], 4: [[4, 5, 6], [], True, 4, [5], 1], 5: [[5, 6, 7], [], True, 4, [5], 1]}[N])
check('1', solve([[N,N+1],[N+2,N+3],4,5,3,2]), {1: [[1, 2], [3, 4], False, 4, [], 2], 2: [[2, 3], [4, 5], False, 4, [], 2], 3: [[3, 4], [5, 6], False, 4, [], 2], 4: [[4, 5], [6, 7], False, 4, [], 2], 5: [[5, 6], [7, 8], False, 4, [], 2]}[N])
check('2', solve([[],[N,N+1],7,8,4,3]), {1: [[1, 2], [], True, 7, [8], 4], 2: [[2, 3], [], True, 7, [8], 4], 3: [[3, 4], [], True, 7, [8], 4], 4: [[4, 5], [], True, 7, [8], 4], 5: [[5, 6], [], True, 7, [8], 4]}[N])
check('3', solve([[N],[],2,6,3,4]), {1: [[1], [], True, 2, [6], 5], 2: [[2], [], True, 2, [6], 5], 3: [[3], [], True, 2, [6], 5], 4: [[4], [], True, 2, [6], 5], 5: [[5], [], True, 2, [6], 5]}[N])
check('4', solve([[],[],1,3,2,8]), {1: [[], [], True, 1, [3], 9], 2: [[], [], True, 1, [3], 9], 3: [[], [], True, 1, [3], 9], 4: [[], [], True, 1, [3], 9], 5: [[], [], True, 1, [3], 9]}[N])
check('5', solve([[N],[N+1,N+2],6,9,5,1]), {1: [[1, 2, 3], [], True, 6, [9], 2], 2: [[2, 3, 4], [], True, 6, [9], 2], 3: [[3, 4, 5], [], True, 6, [9], 2], 4: [[4, 5, 6], [], True, 6, [9], 2], 5: [[5, 6, 7], [], True, 6, [9], 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
0	`[[1, 2, 3], [], True, 4, [5], 1]`	`[[1, 2, 3], [], True, 4, [5], 1]`	Passed
1	`[[1, 2], [3, 4], False, 4, [], 3]`	`[[1, 2], [3, 4], False, 4, [], 2]`	Failed
2	`[[1, 2], [], True, 7, [8], 4]`	`[[1, 2], [], True, 7, [8], 4]`	Passed
3	`[[1], [], True, 2, [6], 5]`	`[[1], [], True, 2, [6], 5]`	Passed
4	`[[], [], True, 1, [3], 9]`	`[[], [], True, 1, [3], 9]`	Passed
5	`[[1, 2, 3], [], True, 6, [9], 2]`	`[[1, 2, 3], [], True, 6, [9], 2]`	Passed

SHA-256 / 46e53b47f65044bfe8e3bc9ba3f1df98bccbe4d898e78e6e1b0821198017dfad

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    a,b,aid,bid,cap,epoch=x
    fits=len(a)+len(b)<=cap
    if not fits:return [a,b,False,aid,[],epoch]
    joined=a+b
    right=[]
    identity=aid
    retired=[bid]
    version=epoch+1
    return [joined,right,True,identity,retired,version]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1],[N+2],4,5,3,0]), {1: [[1, 2, 3], [], True, 4, [5], 1], 2: [[2, 3, 4], [], True, 4, [5], 1], 3: [[3, 4, 5], [], True, 4, [5], 1], 4: [[4, 5, 6], [], True, 4, [5], 1], 5: [[5, 6, 7], [], True, 4, [5], 1]}[N])
check('1', solve([[N,N+1],[N+2,N+3],4,5,3,2]), {1: [[1, 2], [3, 4], False, 4, [], 2], 2: [[2, 3], [4, 5], False, 4, [], 2], 3: [[3, 4], [5, 6], False, 4, [], 2], 4: [[4, 5], [6, 7], False, 4, [], 2], 5: [[5, 6], [7, 8], False, 4, [], 2]}[N])
check('2', solve([[],[N,N+1],7,8,4,3]), {1: [[1, 2], [], True, 7, [8], 4], 2: [[2, 3], [], True, 7, [8], 4], 3: [[3, 4], [], True, 7, [8], 4], 4: [[4, 5], [], True, 7, [8], 4], 5: [[5, 6], [], True, 7, [8], 4]}[N])
check('3', solve([[N],[],2,6,3,4]), {1: [[1], [], True, 2, [6], 5], 2: [[2], [], True, 2, [6], 5], 3: [[3], [], True, 2, [6], 5], 4: [[4], [], True, 2, [6], 5], 5: [[5], [], True, 2, [6], 5]}[N])
check('4', solve([[],[],1,3,2,8]), {1: [[], [], True, 1, [3], 9], 2: [[], [], True, 1, [3], 9], 3: [[], [], True, 1, [3], 9], 4: [[], [], True, 1, [3], 9], 5: [[], [], True, 1, [3], 9]}[N])
check('5', solve([[N],[N+1,N+2],6,9,5,1]), {1: [[1, 2, 3], [], True, 6, [9], 2], 2: [[2, 3, 4], [], True, 6, [9], 2], 3: [[3, 4, 5], [], True, 6, [9], 2], 4: [[4, 5, 6], [], True, 6, [9], 2], 5: [[5, 6, 7], [], True, 6, [9], 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
0	`[[1, 2, 3], [], True, 4, [5], 1]`	`[[1, 2, 3], [], True, 4, [5], 1]`	Passed
1	`[[1, 2], [3, 4], False, 4, [], 2]`	`[[1, 2], [3, 4], False, 4, [], 2]`	Passed
2	`[[1, 2], [], True, 7, [8], 4]`	`[[1, 2], [], True, 7, [8], 4]`	Passed
3	`[[1], [], True, 2, [6], 5]`	`[[1], [], True, 2, [6], 5]`	Passed
4	`[[], [], True, 1, [3], 9]`	`[[], [], True, 1, [3], 9]`	Passed
5	`[[1, 2, 3], [], True, 6, [9], 2]`	`[[1, 2, 3], [], True, 6, [9], 2]`	Passed

SHA-256 / ef1f2e145a07f4fe64fdf39fd05e748e0110ee157dd8002563a1d74fe7ccac70

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 2026-09-29T14:44:31.883260+00:00.

Case digest / c9c27df51bb56117fa8e99fbb3b4bf35fafd4fed947a189bc470ed27b56dbdfc