FAILURE MAP
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FA-46366 / Bounded deques / Open access

Block split omits its first right-side value · case 01

Block split omits its first right-side value.

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

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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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