FA-46366 / Bounded deques / Open access
Block split omits its first right-side value · case 01
Block split omits its first right-side value.
ROOT CAUSE
Block split omits its first right-side value.
VERIFIED REPAIR
Restore the documented right origin invariant in block-split.
Unsuccessful approach: The partial repair still applies the incorrect transition to an admitted boundary or multi-element case.
Case contract
Split a deque storage block at an interior cut, keeping the original identity on the left and assigning a fresh right identity. Publish an incremented directory epoch and ordered block IDs without changing total element count.
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,cut,old,fresh,epoch=x
left=a[:cut]
right=a[cut+1:]
left_id=old
right_id=fresh
version=epoch+1
size=len(left)+len(right)
directory=[left_id,right_id]
return [left,right,left_id,right_id,version,size,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],2,8,9,3]), {1: [[1, 2], [3, 4], 8, 9, 4, 4, [8, 9]], 2: [[2, 3], [4, 5], 8, 9, 4, 4, [8, 9]], 3: [[3, 4], [5, 6], 8, 9, 4, 4, [8, 9]], 4: [[4, 5], [6, 7], 8, 9, 4, 4, [8, 9]], 5: [[5, 6], [7, 8], 8, 9, 4, 4, [8, 9]]}[N])
check('1', solve([[N,N+1,N+2],1,2,4,0]), {1: [[1], [2, 3], 2, 4, 1, 3, [2, 4]], 2: [[2], [3, 4], 2, 4, 1, 3, [2, 4]], 3: [[3], [4, 5], 2, 4, 1, 3, [2, 4]], 4: [[4], [5, 6], 2, 4, 1, 3, [2, 4]], 5: [[5], [6, 7], 2, 4, 1, 3, [2, 4]]}[N])
check('2', solve([[N,N+1],1,7,11,5]), {1: [[1], [2], 7, 11, 6, 2, [7, 11]], 2: [[2], [3], 7, 11, 6, 2, [7, 11]], 3: [[3], [4], 7, 11, 6, 2, [7, 11]], 4: [[4], [5], 7, 11, 6, 2, [7, 11]], 5: [[5], [6], 7, 11, 6, 2, [7, 11]]}[N])
check('3', solve([[N,N+1,N+2,N+3,N+4],3,12,13,4]), {1: [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]], 2: [[2, 3, 4], [5, 6], 12, 13, 5, 5, [12, 13]], 3: [[3, 4, 5], [6, 7], 12, 13, 5, 5, [12, 13]], 4: [[4, 5, 6], [7, 8], 12, 13, 5, 5, [12, 13]], 5: [[5, 6, 7], [8, 9], 12, 13, 5, 5, [12, 13]]}[N])
check('4', solve([[N,N+1,N+2,N+3],1,3,8,2]), {1: [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]], 2: [[2], [3, 4, 5], 3, 8, 3, 4, [3, 8]], 3: [[3], [4, 5, 6], 3, 8, 3, 4, [3, 8]], 4: [[4], [5, 6, 7], 3, 8, 3, 4, [3, 8]], 5: [[5], [6, 7, 8], 3, 8, 3, 4, [3, 8]]}[N])
check('5', solve([[N,N+1,N+2,N+3,N+4],4,5,6,8]), {1: [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]], 2: [[2, 3, 4, 5], [6], 5, 6, 9, 5, [5, 6]], 3: [[3, 4, 5, 6], [7], 5, 6, 9, 5, [5, 6]], 4: [[4, 5, 6, 7], [8], 5, 6, 9, 5, [5, 6]], 5: [[5, 6, 7, 8], [9], 5, 6, 9, 5, [5, 6]]}[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], [4], 8, 9, 4, 3, [8, 9]] | [[1, 2], [3, 4], 8, 9, 4, 4, [8, 9]] | Failed |
| 1 | [[1], [3], 2, 4, 1, 2, [2, 4]] | [[1], [2, 3], 2, 4, 1, 3, [2, 4]] | Failed |
| 2 | [[1], [], 7, 11, 6, 1, [7, 11]] | [[1], [2], 7, 11, 6, 2, [7, 11]] | Failed |
| 3 | [[1, 2, 3], [5], 12, 13, 5, 4, [12, 13]] | [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]] | Failed |
| 4 | [[1], [3, 4], 3, 8, 3, 3, [3, 8]] | [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]] | Failed |
| 5 | [[1, 2, 3, 4], [], 5, 6, 9, 4, [5, 6]] | [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]] | Failed |
SHA-256 / 8af355ee889df6f58905d09086a6ec23e00730a039e1cdcaab09d19065ca8593
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
a,cut,old,fresh,epoch=x
left=a[:cut]
right=a[cut:] if cut==1 else a[cut+1:]
left_id=old
right_id=fresh
version=epoch+1
size=len(left)+len(right)
directory=[left_id,right_id]
return [left,right,left_id,right_id,version,size,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],2,8,9,3]), {1: [[1, 2], [3, 4], 8, 9, 4, 4, [8, 9]], 2: [[2, 3], [4, 5], 8, 9, 4, 4, [8, 9]], 3: [[3, 4], [5, 6], 8, 9, 4, 4, [8, 9]], 4: [[4, 5], [6, 7], 8, 9, 4, 4, [8, 9]], 5: [[5, 6], [7, 8], 8, 9, 4, 4, [8, 9]]}[N])
check('1', solve([[N,N+1,N+2],1,2,4,0]), {1: [[1], [2, 3], 2, 4, 1, 3, [2, 4]], 2: [[2], [3, 4], 2, 4, 1, 3, [2, 4]], 3: [[3], [4, 5], 2, 4, 1, 3, [2, 4]], 4: [[4], [5, 6], 2, 4, 1, 3, [2, 4]], 5: [[5], [6, 7], 2, 4, 1, 3, [2, 4]]}[N])
check('2', solve([[N,N+1],1,7,11,5]), {1: [[1], [2], 7, 11, 6, 2, [7, 11]], 2: [[2], [3], 7, 11, 6, 2, [7, 11]], 3: [[3], [4], 7, 11, 6, 2, [7, 11]], 4: [[4], [5], 7, 11, 6, 2, [7, 11]], 5: [[5], [6], 7, 11, 6, 2, [7, 11]]}[N])
check('3', solve([[N,N+1,N+2,N+3,N+4],3,12,13,4]), {1: [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]], 2: [[2, 3, 4], [5, 6], 12, 13, 5, 5, [12, 13]], 3: [[3, 4, 5], [6, 7], 12, 13, 5, 5, [12, 13]], 4: [[4, 5, 6], [7, 8], 12, 13, 5, 5, [12, 13]], 5: [[5, 6, 7], [8, 9], 12, 13, 5, 5, [12, 13]]}[N])
check('4', solve([[N,N+1,N+2,N+3],1,3,8,2]), {1: [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]], 2: [[2], [3, 4, 5], 3, 8, 3, 4, [3, 8]], 3: [[3], [4, 5, 6], 3, 8, 3, 4, [3, 8]], 4: [[4], [5, 6, 7], 3, 8, 3, 4, [3, 8]], 5: [[5], [6, 7, 8], 3, 8, 3, 4, [3, 8]]}[N])
check('5', solve([[N,N+1,N+2,N+3,N+4],4,5,6,8]), {1: [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]], 2: [[2, 3, 4, 5], [6], 5, 6, 9, 5, [5, 6]], 3: [[3, 4, 5, 6], [7], 5, 6, 9, 5, [5, 6]], 4: [[4, 5, 6, 7], [8], 5, 6, 9, 5, [5, 6]], 5: [[5, 6, 7, 8], [9], 5, 6, 9, 5, [5, 6]]}[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], [4], 8, 9, 4, 3, [8, 9]] | [[1, 2], [3, 4], 8, 9, 4, 4, [8, 9]] | Failed |
| 1 | [[1], [2, 3], 2, 4, 1, 3, [2, 4]] | [[1], [2, 3], 2, 4, 1, 3, [2, 4]] | Passed |
| 2 | [[1], [2], 7, 11, 6, 2, [7, 11]] | [[1], [2], 7, 11, 6, 2, [7, 11]] | Passed |
| 3 | [[1, 2, 3], [5], 12, 13, 5, 4, [12, 13]] | [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]] | Failed |
| 4 | [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]] | [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]] | Passed |
| 5 | [[1, 2, 3, 4], [], 5, 6, 9, 4, [5, 6]] | [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]] | Failed |
SHA-256 / 50c8fc4d6cd3c0841c9c650517f3c3672b697cbe68efaa913014d3d197d70d7d
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
a,cut,old,fresh,epoch=x
left=a[:cut]
right=a[cut:]
left_id=old
right_id=fresh
version=epoch+1
size=len(left)+len(right)
directory=[left_id,right_id]
return [left,right,left_id,right_id,version,size,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],2,8,9,3]), {1: [[1, 2], [3, 4], 8, 9, 4, 4, [8, 9]], 2: [[2, 3], [4, 5], 8, 9, 4, 4, [8, 9]], 3: [[3, 4], [5, 6], 8, 9, 4, 4, [8, 9]], 4: [[4, 5], [6, 7], 8, 9, 4, 4, [8, 9]], 5: [[5, 6], [7, 8], 8, 9, 4, 4, [8, 9]]}[N])
check('1', solve([[N,N+1,N+2],1,2,4,0]), {1: [[1], [2, 3], 2, 4, 1, 3, [2, 4]], 2: [[2], [3, 4], 2, 4, 1, 3, [2, 4]], 3: [[3], [4, 5], 2, 4, 1, 3, [2, 4]], 4: [[4], [5, 6], 2, 4, 1, 3, [2, 4]], 5: [[5], [6, 7], 2, 4, 1, 3, [2, 4]]}[N])
check('2', solve([[N,N+1],1,7,11,5]), {1: [[1], [2], 7, 11, 6, 2, [7, 11]], 2: [[2], [3], 7, 11, 6, 2, [7, 11]], 3: [[3], [4], 7, 11, 6, 2, [7, 11]], 4: [[4], [5], 7, 11, 6, 2, [7, 11]], 5: [[5], [6], 7, 11, 6, 2, [7, 11]]}[N])
check('3', solve([[N,N+1,N+2,N+3,N+4],3,12,13,4]), {1: [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]], 2: [[2, 3, 4], [5, 6], 12, 13, 5, 5, [12, 13]], 3: [[3, 4, 5], [6, 7], 12, 13, 5, 5, [12, 13]], 4: [[4, 5, 6], [7, 8], 12, 13, 5, 5, [12, 13]], 5: [[5, 6, 7], [8, 9], 12, 13, 5, 5, [12, 13]]}[N])
check('4', solve([[N,N+1,N+2,N+3],1,3,8,2]), {1: [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]], 2: [[2], [3, 4, 5], 3, 8, 3, 4, [3, 8]], 3: [[3], [4, 5, 6], 3, 8, 3, 4, [3, 8]], 4: [[4], [5, 6, 7], 3, 8, 3, 4, [3, 8]], 5: [[5], [6, 7, 8], 3, 8, 3, 4, [3, 8]]}[N])
check('5', solve([[N,N+1,N+2,N+3,N+4],4,5,6,8]), {1: [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]], 2: [[2, 3, 4, 5], [6], 5, 6, 9, 5, [5, 6]], 3: [[3, 4, 5, 6], [7], 5, 6, 9, 5, [5, 6]], 4: [[4, 5, 6, 7], [8], 5, 6, 9, 5, [5, 6]], 5: [[5, 6, 7, 8], [9], 5, 6, 9, 5, [5, 6]]}[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], 8, 9, 4, 4, [8, 9]] | [[1, 2], [3, 4], 8, 9, 4, 4, [8, 9]] | Passed |
| 1 | [[1], [2, 3], 2, 4, 1, 3, [2, 4]] | [[1], [2, 3], 2, 4, 1, 3, [2, 4]] | Passed |
| 2 | [[1], [2], 7, 11, 6, 2, [7, 11]] | [[1], [2], 7, 11, 6, 2, [7, 11]] | Passed |
| 3 | [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]] | [[1, 2, 3], [4, 5], 12, 13, 5, 5, [12, 13]] | Passed |
| 4 | [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]] | [[1], [2, 3, 4], 3, 8, 3, 4, [3, 8]] | Passed |
| 5 | [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]] | [[1, 2, 3, 4], [5], 5, 6, 9, 5, [5, 6]] | Passed |
SHA-256 / 622e42f183f79baae6194f3cf57a2939b574f69d3a1ba4d652141be3efd3f8c4
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 2026-09-29T14:44:31.300138+00:00.
Case digest / 79e38ae43c848bbdc9cd330d5997dc98cf3aae873510edab64c4368117b14f80