FA-46621 / Bounded deques / Open access
Deque borrow uses the live count as its physical contiguous span · case 01
Deque borrow uses the live count as its physical contiguous span.
ROOT CAUSE
Deque borrow uses the live count as its physical contiguous span.
VERIFIED REPAIR
Restore the documented first span bound invariant in range-borrow.
Unsuccessful approach: The partial repair still applies the incorrect transition to an admitted boundary or multi-element case.
Case contract
Borrow a valid logical subrange from a bounded ring as at most two physical spans. Reject negative or out-of-live-range requests. Borrow captures the current epoch and pins storage only for nonempty ranges.
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):
cap,head,size,start,count,epoch=x
if start<0 or count<0 or start+count>size:return [False,[],epoch,0,False]
origin=(head+start)%cap
first=min(count,size)
spans=[[origin,first]] if first else []
if count>first:spans.append([0,count-first])
captured=epoch
pin=count>0
return [True,spans,captured,count,pin]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([8,6,5,1,3,N]), {1: [True, [[7, 1], [0, 2]], 1, 3, True], 2: [True, [[7, 1], [0, 2]], 2, 3, True], 3: [True, [[7, 1], [0, 2]], 3, 3, True], 4: [True, [[7, 1], [0, 2]], 4, 3, True], 5: [True, [[7, 1], [0, 2]], 5, 3, True]}[N])
check('1', solve([8,2,4,1,2,N]), {1: [True, [[3, 2]], 1, 2, True], 2: [True, [[3, 2]], 2, 2, True], 3: [True, [[3, 2]], 3, 2, True], 4: [True, [[3, 2]], 4, 2, True], 5: [True, [[3, 2]], 5, 2, True]}[N])
check('2', solve([7,5,4,0,4,N]), {1: [True, [[5, 2], [0, 2]], 1, 4, True], 2: [True, [[5, 2], [0, 2]], 2, 4, True], 3: [True, [[5, 2], [0, 2]], 3, 4, True], 4: [True, [[5, 2], [0, 2]], 4, 4, True], 5: [True, [[5, 2], [0, 2]], 5, 4, True]}[N])
check('3', solve([8,3,2,2,0,N]), {1: [True, [], 1, 0, False], 2: [True, [], 2, 0, False], 3: [True, [], 3, 0, False], 4: [True, [], 4, 0, False], 5: [True, [], 5, 0, False]}[N])
check('4', solve([8,3,2,1,2,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[N])
check('5', solve([6,2,3,-1,2,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[N])
check('6', solve([7,1,5,3,-1,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[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 | [True, [[7, 3]], 1, 3, True] | [True, [[7, 1], [0, 2]], 1, 3, True] | Failed |
| 1 | [True, [[3, 2]], 1, 2, True] | [True, [[3, 2]], 1, 2, True] | Passed |
| 2 | [True, [[5, 4]], 1, 4, True] | [True, [[5, 2], [0, 2]], 1, 4, True] | Failed |
| 3 | [True, [], 1, 0, False] | [True, [], 1, 0, False] | Passed |
| 4 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
| 5 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
| 6 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
SHA-256 / 6260dda25c9bea563d4cbcc315f189a842b67978d4dcd9f64cb0698d4708e3be
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
cap,head,size,start,count,epoch=x
if start<0 or count<0 or start+count>size:return [False,[],epoch,0,False]
origin=(head+start)%cap
first=min(count,cap-origin) if origin==0 else min(count,size)
spans=[[origin,first]] if first else []
if count>first:spans.append([0,count-first])
captured=epoch
pin=count>0
return [True,spans,captured,count,pin]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([8,6,5,1,3,N]), {1: [True, [[7, 1], [0, 2]], 1, 3, True], 2: [True, [[7, 1], [0, 2]], 2, 3, True], 3: [True, [[7, 1], [0, 2]], 3, 3, True], 4: [True, [[7, 1], [0, 2]], 4, 3, True], 5: [True, [[7, 1], [0, 2]], 5, 3, True]}[N])
check('1', solve([8,2,4,1,2,N]), {1: [True, [[3, 2]], 1, 2, True], 2: [True, [[3, 2]], 2, 2, True], 3: [True, [[3, 2]], 3, 2, True], 4: [True, [[3, 2]], 4, 2, True], 5: [True, [[3, 2]], 5, 2, True]}[N])
check('2', solve([7,5,4,0,4,N]), {1: [True, [[5, 2], [0, 2]], 1, 4, True], 2: [True, [[5, 2], [0, 2]], 2, 4, True], 3: [True, [[5, 2], [0, 2]], 3, 4, True], 4: [True, [[5, 2], [0, 2]], 4, 4, True], 5: [True, [[5, 2], [0, 2]], 5, 4, True]}[N])
check('3', solve([8,3,2,2,0,N]), {1: [True, [], 1, 0, False], 2: [True, [], 2, 0, False], 3: [True, [], 3, 0, False], 4: [True, [], 4, 0, False], 5: [True, [], 5, 0, False]}[N])
check('4', solve([8,3,2,1,2,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[N])
check('5', solve([6,2,3,-1,2,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[N])
check('6', solve([7,1,5,3,-1,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[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 | [True, [[7, 3]], 1, 3, True] | [True, [[7, 1], [0, 2]], 1, 3, True] | Failed |
| 1 | [True, [[3, 2]], 1, 2, True] | [True, [[3, 2]], 1, 2, True] | Passed |
| 2 | [True, [[5, 4]], 1, 4, True] | [True, [[5, 2], [0, 2]], 1, 4, True] | Failed |
| 3 | [True, [], 1, 0, False] | [True, [], 1, 0, False] | Passed |
| 4 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
| 5 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
| 6 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
SHA-256 / 90d1052e3ee5d889516bc94ffc1f53d0682815917b75722bbc3e59b71ecb297e
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
cap,head,size,start,count,epoch=x
if start<0 or count<0 or start+count>size:return [False,[],epoch,0,False]
origin=(head+start)%cap
first=min(count,cap-origin)
spans=[[origin,first]] if first else []
if count>first:spans.append([0,count-first])
captured=epoch
pin=count>0
return [True,spans,captured,count,pin]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([8,6,5,1,3,N]), {1: [True, [[7, 1], [0, 2]], 1, 3, True], 2: [True, [[7, 1], [0, 2]], 2, 3, True], 3: [True, [[7, 1], [0, 2]], 3, 3, True], 4: [True, [[7, 1], [0, 2]], 4, 3, True], 5: [True, [[7, 1], [0, 2]], 5, 3, True]}[N])
check('1', solve([8,2,4,1,2,N]), {1: [True, [[3, 2]], 1, 2, True], 2: [True, [[3, 2]], 2, 2, True], 3: [True, [[3, 2]], 3, 2, True], 4: [True, [[3, 2]], 4, 2, True], 5: [True, [[3, 2]], 5, 2, True]}[N])
check('2', solve([7,5,4,0,4,N]), {1: [True, [[5, 2], [0, 2]], 1, 4, True], 2: [True, [[5, 2], [0, 2]], 2, 4, True], 3: [True, [[5, 2], [0, 2]], 3, 4, True], 4: [True, [[5, 2], [0, 2]], 4, 4, True], 5: [True, [[5, 2], [0, 2]], 5, 4, True]}[N])
check('3', solve([8,3,2,2,0,N]), {1: [True, [], 1, 0, False], 2: [True, [], 2, 0, False], 3: [True, [], 3, 0, False], 4: [True, [], 4, 0, False], 5: [True, [], 5, 0, False]}[N])
check('4', solve([8,3,2,1,2,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[N])
check('5', solve([6,2,3,-1,2,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[N])
check('6', solve([7,1,5,3,-1,N]), {1: [False, [], 1, 0, False], 2: [False, [], 2, 0, False], 3: [False, [], 3, 0, False], 4: [False, [], 4, 0, False], 5: [False, [], 5, 0, False]}[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 | [True, [[7, 1], [0, 2]], 1, 3, True] | [True, [[7, 1], [0, 2]], 1, 3, True] | Passed |
| 1 | [True, [[3, 2]], 1, 2, True] | [True, [[3, 2]], 1, 2, True] | Passed |
| 2 | [True, [[5, 2], [0, 2]], 1, 4, True] | [True, [[5, 2], [0, 2]], 1, 4, True] | Passed |
| 3 | [True, [], 1, 0, False] | [True, [], 1, 0, False] | Passed |
| 4 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
| 5 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
| 6 | [False, [], 1, 0, False] | [False, [], 1, 0, False] | Passed |
SHA-256 / 2851c069034c3cd8ddb5cb61b343f334ab5207d9976d03a0d84ae21cb23960e7
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 2026-09-29T14:44:33.864033+00:00.
Case digest / e2d11bb68fed43ef12786edd9798812f48cf47b1a6e4a5b863cb8c560ac2c5a9