FA-46026 / Bounded deques / Open access

Cross-splice inserts after the designated gap · case 01

Cross-splice inserts after the designated gap.

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

ROOT CAUSE

Cross-splice inserts after the designated gap.

VERIFIED REPAIR

Restore the documented insertion gap invariant in cross-splice.

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

Case contract

Move a half-open slice from one deque to another at a valid gap. Reject overflow atomically. Return [source,destination,accepted,moved].

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,start,stop,gap,cap = x
    piece = a[start:stop]
    if len(b)+len(piece)>cap: return [a,b,False,0]
    left = a[:start]+a[stop:]
    right = b[:gap+1]+piece+b[gap+1:]
    return [left,right,True,len(piece)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior', solve([[N,N+1,N+2,N+3],[N+10,N+11],1,3,1,5]), {1: [[1, 4], [11, 2, 3, 12], True, 2], 2: [[2, 5], [12, 3, 4, 13], True, 2], 3: [[3, 6], [13, 4, 5, 14], True, 2], 4: [[4, 7], [14, 5, 6, 15], True, 2], 5: [[5, 8], [15, 6, 7, 16], True, 2]}[N])
check('overflow', solve([[N,N+1,N+2],[N+10],0,3,0,3]), {1: [[1, 2, 3], [11], False, 0], 2: [[2, 3, 4], [12], False, 0], 3: [[3, 4, 5], [13], False, 0], 4: [[4, 5, 6], [14], False, 0], 5: [[5, 6, 7], [15], False, 0]}[N])
check('empty slice', solve([[N,N+1],[N+10],1,1,0,2]), {1: [[1, 2], [11], True, 0], 2: [[2, 3], [12], True, 0], 3: [[3, 4], [13], True, 0], 4: [[4, 5], [14], True, 0], 5: [[5, 6], [15], True, 0]}[N])
check('whole source', solve([[N,N+1],[],0,2,0,2]), {1: [[], [1, 2], True, 2], 2: [[], [2, 3], True, 2], 3: [[], [3, 4], True, 2], 4: [[], [4, 5], True, 2], 5: [[], [5, 6], True, 2]}[N])
check('append splice', solve([[N,N+1,N+2],[N+10],0,2,1,4]), {1: [[3], [11, 1, 2], True, 2], 2: [[4], [12, 2, 3], True, 2], 3: [[5], [13, 3, 4], True, 2], 4: [[6], [14, 4, 5], True, 2], 5: [[7], [15, 5, 6], True, 2]}[N])
check('tail slice', solve([[N,N+1,N+2],[N+10],2,3,0,3]), {1: [[1, 2], [3, 11], True, 1], 2: [[2, 3], [4, 12], True, 1], 3: [[3, 4], [5, 13], True, 1], 4: [[4, 5], [6, 14], True, 1], 5: [[5, 6], [7, 15], True, 1]}[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
interior	`[[1, 4], [11, 12, 2, 3], True, 2]`	`[[1, 4], [11, 2, 3, 12], True, 2]`	Failed
overflow	`[[1, 2, 3], [11], False, 0]`	`[[1, 2, 3], [11], False, 0]`	Passed
empty slice	`[[1, 2], [11], True, 0]`	`[[1, 2], [11], True, 0]`	Passed
whole source	`[[], [1, 2], True, 2]`	`[[], [1, 2], True, 2]`	Passed
append splice	`[[3], [11, 1, 2], True, 2]`	`[[3], [11, 1, 2], True, 2]`	Passed
tail slice	`[[1, 2], [11, 3], True, 1]`	`[[1, 2], [3, 11], True, 1]`	Failed

SHA-256 / ecb9abcc07b4162e6aaf278f5ee800102654354589782f401447a48e38adc1b9

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    a,b,start,stop,gap,cap = x
    piece = a[start:stop]
    if len(b)+len(piece)>cap: return [a,b,False,0]
    left = a[:start]+a[stop:]
    right = b[:gap]+piece+b[gap:] if gap==len(b) else b[:gap+1]+piece+b[gap+1:]
    return [left,right,True,len(piece)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior', solve([[N,N+1,N+2,N+3],[N+10,N+11],1,3,1,5]), {1: [[1, 4], [11, 2, 3, 12], True, 2], 2: [[2, 5], [12, 3, 4, 13], True, 2], 3: [[3, 6], [13, 4, 5, 14], True, 2], 4: [[4, 7], [14, 5, 6, 15], True, 2], 5: [[5, 8], [15, 6, 7, 16], True, 2]}[N])
check('overflow', solve([[N,N+1,N+2],[N+10],0,3,0,3]), {1: [[1, 2, 3], [11], False, 0], 2: [[2, 3, 4], [12], False, 0], 3: [[3, 4, 5], [13], False, 0], 4: [[4, 5, 6], [14], False, 0], 5: [[5, 6, 7], [15], False, 0]}[N])
check('empty slice', solve([[N,N+1],[N+10],1,1,0,2]), {1: [[1, 2], [11], True, 0], 2: [[2, 3], [12], True, 0], 3: [[3, 4], [13], True, 0], 4: [[4, 5], [14], True, 0], 5: [[5, 6], [15], True, 0]}[N])
check('whole source', solve([[N,N+1],[],0,2,0,2]), {1: [[], [1, 2], True, 2], 2: [[], [2, 3], True, 2], 3: [[], [3, 4], True, 2], 4: [[], [4, 5], True, 2], 5: [[], [5, 6], True, 2]}[N])
check('append splice', solve([[N,N+1,N+2],[N+10],0,2,1,4]), {1: [[3], [11, 1, 2], True, 2], 2: [[4], [12, 2, 3], True, 2], 3: [[5], [13, 3, 4], True, 2], 4: [[6], [14, 4, 5], True, 2], 5: [[7], [15, 5, 6], True, 2]}[N])
check('tail slice', solve([[N,N+1,N+2],[N+10],2,3,0,3]), {1: [[1, 2], [3, 11], True, 1], 2: [[2, 3], [4, 12], True, 1], 3: [[3, 4], [5, 13], True, 1], 4: [[4, 5], [6, 14], True, 1], 5: [[5, 6], [7, 15], True, 1]}[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
interior	`[[1, 4], [11, 12, 2, 3], True, 2]`	`[[1, 4], [11, 2, 3, 12], True, 2]`	Failed
overflow	`[[1, 2, 3], [11], False, 0]`	`[[1, 2, 3], [11], False, 0]`	Passed
empty slice	`[[1, 2], [11], True, 0]`	`[[1, 2], [11], True, 0]`	Passed
whole source	`[[], [1, 2], True, 2]`	`[[], [1, 2], True, 2]`	Passed
append splice	`[[3], [11, 1, 2], True, 2]`	`[[3], [11, 1, 2], True, 2]`	Passed
tail slice	`[[1, 2], [11, 3], True, 1]`	`[[1, 2], [3, 11], True, 1]`	Failed

SHA-256 / 295845bc3a129c198e54144f458795c6eed15c0015d0337c194c7a0fa9f5de3b

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    a,b,start,stop,gap,cap = x
    piece = a[start:stop]
    if len(b)+len(piece)>cap: return [a,b,False,0]
    left = a[:start]+a[stop:]
    right = b[:gap]+piece+b[gap:]
    return [left,right,True,len(piece)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior', solve([[N,N+1,N+2,N+3],[N+10,N+11],1,3,1,5]), {1: [[1, 4], [11, 2, 3, 12], True, 2], 2: [[2, 5], [12, 3, 4, 13], True, 2], 3: [[3, 6], [13, 4, 5, 14], True, 2], 4: [[4, 7], [14, 5, 6, 15], True, 2], 5: [[5, 8], [15, 6, 7, 16], True, 2]}[N])
check('overflow', solve([[N,N+1,N+2],[N+10],0,3,0,3]), {1: [[1, 2, 3], [11], False, 0], 2: [[2, 3, 4], [12], False, 0], 3: [[3, 4, 5], [13], False, 0], 4: [[4, 5, 6], [14], False, 0], 5: [[5, 6, 7], [15], False, 0]}[N])
check('empty slice', solve([[N,N+1],[N+10],1,1,0,2]), {1: [[1, 2], [11], True, 0], 2: [[2, 3], [12], True, 0], 3: [[3, 4], [13], True, 0], 4: [[4, 5], [14], True, 0], 5: [[5, 6], [15], True, 0]}[N])
check('whole source', solve([[N,N+1],[],0,2,0,2]), {1: [[], [1, 2], True, 2], 2: [[], [2, 3], True, 2], 3: [[], [3, 4], True, 2], 4: [[], [4, 5], True, 2], 5: [[], [5, 6], True, 2]}[N])
check('append splice', solve([[N,N+1,N+2],[N+10],0,2,1,4]), {1: [[3], [11, 1, 2], True, 2], 2: [[4], [12, 2, 3], True, 2], 3: [[5], [13, 3, 4], True, 2], 4: [[6], [14, 4, 5], True, 2], 5: [[7], [15, 5, 6], True, 2]}[N])
check('tail slice', solve([[N,N+1,N+2],[N+10],2,3,0,3]), {1: [[1, 2], [3, 11], True, 1], 2: [[2, 3], [4, 12], True, 1], 3: [[3, 4], [5, 13], True, 1], 4: [[4, 5], [6, 14], True, 1], 5: [[5, 6], [7, 15], True, 1]}[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
interior	`[[1, 4], [11, 2, 3, 12], True, 2]`	`[[1, 4], [11, 2, 3, 12], True, 2]`	Passed
overflow	`[[1, 2, 3], [11], False, 0]`	`[[1, 2, 3], [11], False, 0]`	Passed
empty slice	`[[1, 2], [11], True, 0]`	`[[1, 2], [11], True, 0]`	Passed
whole source	`[[], [1, 2], True, 2]`	`[[], [1, 2], True, 2]`	Passed
append splice	`[[3], [11, 1, 2], True, 2]`	`[[3], [11, 1, 2], True, 2]`	Passed
tail slice	`[[1, 2], [3, 11], True, 1]`	`[[1, 2], [3, 11], True, 1]`	Passed

SHA-256 / a60b552814b1f3988246cfa74e81c14c34ee1ab7f492bf291a1fa02e23d6ead7

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 2026-09-29T14:44:28.148114+00:00.

Case digest / 3340052c4cbea4628b53b71eca5216d3cfe4b4a0d1df2a5c4b3fdf89a74a9082