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FA-47081 / Bounded deques / Open access

Ring gap insertion fills vacant slots with the inserted payload · case 01

Ring gap insertion fills vacant slots with the inserted payload.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Ring gap insertion fills vacant slots with the inserted payload.

THE FAILURE

Ring gap insertion fills vacant slots with the inserted payload.

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

Case contract

Insert into a valid logical gap by moving the shorter ring side, preferring the right side on equal cost. Left shifts decrement physical head; reconstruct live arc and clear all vacant slots. Full ring rejects atomically.

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):
    slots,head,size,gap,value=x
    cap=len(slots)
    if size==cap:return [slots,head,size,False,0]
    logical=[slots[(head+i)%cap] for i in range(size)]
    left=gap<size-gap
    origin=(head-1)%cap if left else head
    inserted=logical[:gap]+[value]+logical[gap:]
    result=[value]*cap
    for i,v in enumerate(inserted):result[(origin+i)%cap]=v
    count=size+1
    moved=gap if left else size-gap
    return [result,origin,count,True,moved]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1,N+2,None,None],0,3,1,N+3]), {1: [[4, 2, 3, None, 1], 4, 4, True, 1], 2: [[5, 3, 4, None, 2], 4, 4, True, 1], 3: [[6, 4, 5, None, 3], 4, 4, True, 1], 4: [[7, 5, 6, None, 4], 4, 4, True, 1], 5: [[8, 6, 7, None, 5], 4, 4, True, 1]}[N])
check('1', solve([[N+2,None,None,N,N+1],3,3,1,N+3]), {1: [[3, None, 1, 4, 2], 2, 4, True, 1], 2: [[4, None, 2, 5, 3], 2, 4, True, 1], 3: [[5, None, 3, 6, 4], 2, 4, True, 1], 4: [[6, None, 4, 7, 5], 2, 4, True, 1], 5: [[7, None, 5, 8, 6], 2, 4, True, 1]}[N])
check('2', solve([[N,N+1,N+2,N+3,None,None],0,4,2,N+4]), {1: [[1, 2, 5, 3, 4, None], 0, 5, True, 2], 2: [[2, 3, 6, 4, 5, None], 0, 5, True, 2], 3: [[3, 4, 7, 5, 6, None], 0, 5, True, 2], 4: [[4, 5, 8, 6, 7, None], 0, 5, True, 2], 5: [[5, 6, 9, 7, 8, None], 0, 5, True, 2]}[N])
check('3', solve([[None,N,N+1,None],1,2,2,N+2]), {1: [[None, 1, 2, 3], 1, 3, True, 0], 2: [[None, 2, 3, 4], 1, 3, True, 0], 3: [[None, 3, 4, 5], 1, 3, True, 0], 4: [[None, 4, 5, 6], 1, 3, True, 0], 5: [[None, 5, 6, 7], 1, 3, True, 0]}[N])
check('4', solve([[N,N+1],0,2,1,N+2]), {1: [[1, 2], 0, 2, False, 0], 2: [[2, 3], 0, 2, False, 0], 3: [[3, 4], 0, 2, False, 0], 4: [[4, 5], 0, 2, False, 0], 5: [[5, 6], 0, 2, False, 0]}[N])
check('5', solve([[None,None,None],2,0,0,N]), {1: [[None, None, 1], 2, 1, True, 0], 2: [[None, None, 2], 2, 1, True, 0], 3: [[None, None, 3], 2, 1, True, 0], 4: [[None, None, 4], 2, 1, True, 0], 5: [[None, None, 5], 2, 1, True, 0]}[N])
check('6', solve([[N+1,None,None,N],3,2,0,N+2]), {1: [[2, None, 3, 1], 2, 3, True, 0], 2: [[3, None, 4, 2], 2, 3, True, 0], 3: [[4, None, 5, 3], 2, 3, True, 0], 4: [[5, None, 6, 4], 2, 3, True, 0], 5: [[6, None, 7, 5], 2, 3, True, 0]}[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[[4, 2, 3, 4, 1], 4, 4, True, 1][[4, 2, 3, None, 1], 4, 4, True, 1]Failed
1[[3, 4, 1, 4, 2], 2, 4, True, 1][[3, None, 1, 4, 2], 2, 4, True, 1]Failed
2[[1, 2, 5, 3, 4, 5], 0, 5, True, 2][[1, 2, 5, 3, 4, None], 0, 5, True, 2]Failed
3[[3, 1, 2, 3], 1, 3, True, 0][[None, 1, 2, 3], 1, 3, True, 0]Failed
4[[1, 2], 0, 2, False, 0][[1, 2], 0, 2, False, 0]Passed
5[[1, 1, 1], 2, 1, True, 0][[None, None, 1], 2, 1, True, 0]Failed
6[[2, 3, 3, 1], 2, 3, True, 0][[2, None, 3, 1], 2, 3, True, 0]Failed

SHA-256 / fc03b95fa145c9e0044e28525f0764a75650063272477d4649d5ee5d944e67cf

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    slots,head,size,gap,value=x
    cap=len(slots)
    if size==cap:return [slots,head,size,False,0]
    logical=[slots[(head+i)%cap] for i in range(size)]
    left=gap<size-gap
    origin=(head-1)%cap if left else head
    inserted=logical[:gap]+[value]+logical[gap:]
    result=[None]*cap if size==0 else [value]*cap
    for i,v in enumerate(inserted):result[(origin+i)%cap]=v
    count=size+1
    moved=gap if left else size-gap
    return [result,origin,count,True,moved]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('0', solve([[N,N+1,N+2,None,None],0,3,1,N+3]), {1: [[4, 2, 3, None, 1], 4, 4, True, 1], 2: [[5, 3, 4, None, 2], 4, 4, True, 1], 3: [[6, 4, 5, None, 3], 4, 4, True, 1], 4: [[7, 5, 6, None, 4], 4, 4, True, 1], 5: [[8, 6, 7, None, 5], 4, 4, True, 1]}[N])
check('1', solve([[N+2,None,None,N,N+1],3,3,1,N+3]), {1: [[3, None, 1, 4, 2], 2, 4, True, 1], 2: [[4, None, 2, 5, 3], 2, 4, True, 1], 3: [[5, None, 3, 6, 4], 2, 4, True, 1], 4: [[6, None, 4, 7, 5], 2, 4, True, 1], 5: [[7, None, 5, 8, 6], 2, 4, True, 1]}[N])
check('2', solve([[N,N+1,N+2,N+3,None,None],0,4,2,N+4]), {1: [[1, 2, 5, 3, 4, None], 0, 5, True, 2], 2: [[2, 3, 6, 4, 5, None], 0, 5, True, 2], 3: [[3, 4, 7, 5, 6, None], 0, 5, True, 2], 4: [[4, 5, 8, 6, 7, None], 0, 5, True, 2], 5: [[5, 6, 9, 7, 8, None], 0, 5, True, 2]}[N])
check('3', solve([[None,N,N+1,None],1,2,2,N+2]), {1: [[None, 1, 2, 3], 1, 3, True, 0], 2: [[None, 2, 3, 4], 1, 3, True, 0], 3: [[None, 3, 4, 5], 1, 3, True, 0], 4: [[None, 4, 5, 6], 1, 3, True, 0], 5: [[None, 5, 6, 7], 1, 3, True, 0]}[N])
check('4', solve([[N,N+1],0,2,1,N+2]), {1: [[1, 2], 0, 2, False, 0], 2: [[2, 3], 0, 2, False, 0], 3: [[3, 4], 0, 2, False, 0], 4: [[4, 5], 0, 2, False, 0], 5: [[5, 6], 0, 2, False, 0]}[N])
check('5', solve([[None,None,None],2,0,0,N]), {1: [[None, None, 1], 2, 1, True, 0], 2: [[None, None, 2], 2, 1, True, 0], 3: [[None, None, 3], 2, 1, True, 0], 4: [[None, None, 4], 2, 1, True, 0], 5: [[None, None, 5], 2, 1, True, 0]}[N])
check('6', solve([[N+1,None,None,N],3,2,0,N+2]), {1: [[2, None, 3, 1], 2, 3, True, 0], 2: [[3, None, 4, 2], 2, 3, True, 0], 3: [[4, None, 5, 3], 2, 3, True, 0], 4: [[5, None, 6, 4], 2, 3, True, 0], 5: [[6, None, 7, 5], 2, 3, True, 0]}[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[[4, 2, 3, 4, 1], 4, 4, True, 1][[4, 2, 3, None, 1], 4, 4, True, 1]Failed
1[[3, 4, 1, 4, 2], 2, 4, True, 1][[3, None, 1, 4, 2], 2, 4, True, 1]Failed
2[[1, 2, 5, 3, 4, 5], 0, 5, True, 2][[1, 2, 5, 3, 4, None], 0, 5, True, 2]Failed
3[[3, 1, 2, 3], 1, 3, True, 0][[None, 1, 2, 3], 1, 3, True, 0]Failed
4[[1, 2], 0, 2, False, 0][[1, 2], 0, 2, False, 0]Passed
5[[None, None, 1], 2, 1, True, 0][[None, None, 1], 2, 1, True, 0]Passed
6[[2, 3, 3, 1], 2, 3, True, 0][[2, None, 3, 1], 2, 3, True, 0]Failed

SHA-256 / aaa8d9f1ce79a330a377696e045fc8bf10fbedeb4cfbb8bc8eb1d22624b1297e

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:44:38.239408+00:00.

Case digest / 5814ece94cd8a1e77a4220c47d29ee3aad89b9ca764f3384dbd7be3e4bb47089