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FA-45981 / Bounded deques / Open access

Cursor after an erased node retains its old index · case 01

Cursor after an erased node retains its old index.

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

ROOT CAUSE

Only the immediate successor cursor gets its ordinal corrected.

THE FAILURE

Only the immediate successor cursor gets its ordinal corrected.

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

Case contract

Erase a selected position while updating independent stable cursors. A cursor at the erased element moves to its successor, or end; later cursors shift left, earlier cursors stay. Return values, cursor positions, and cursor-observed values; None denotes end.

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):
    items, at, cursors = x
    remaining = items[:at] + items[at+1:]
    updated = []
    for position in cursors:
        if position is None:
            next_position = None
        elif position < at:
            next_position = position
        elif position == at:
            next_position = at if at < len(remaining) else None
        else:
            next_position = position
        updated.append(next_position)
    observed = [remaining[p] if p is not None and 0 <= p < len(remaining) else None for p in updated]
    return [remaining,updated,observed]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior cursors', solve([[N,N+1,N+2,N+3],1,[0,1,2,3,None]]), [[N,N+2,N+3],[0,1,1,2,None],[N,N+2,N+2,N+3,None]])
check('erased last cursor', solve([[N,N+1],1,[0,1,None]]), [[N],[0,None,None],[N,None,None]])
check('all point at head', solve([[N,N+1,N+2],0,[0,0,2]]), [[N+1,N+2],[0,0,1],[N+1,N+1,N+2]])
check('single node erased', solve([[N],0,[0,None]]), [[],[None,None],[None,None]])
check('no cursors', solve([[N,N+1],0,[]]), [[N+1],[],[]])
check('unaffected cursors', solve([[N,N+1,N+2,N+3],3,[0,1,2]]), [[N,N+1,N+2],[0,1,2],[N,N+1,N+2]])
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
interior cursors[[1, 3, 4], [0, 1, 2, 3, None], [1, 3, 4, None, None]][[1, 3, 4], [0, 1, 1, 2, None], [1, 3, 3, 4, None]]Failed
erased last cursor[[1], [0, None, None], [1, None, None]][[1], [0, None, None], [1, None, None]]Passed
all point at head[[2, 3], [0, 0, 2], [2, 2, None]][[2, 3], [0, 0, 1], [2, 2, 3]]Failed
single node erased[[], [None, None], [None, None]][[], [None, None], [None, None]]Passed
no cursors[[2], [], []][[2], [], []]Passed
unaffected cursors[[1, 2, 3], [0, 1, 2], [1, 2, 3]][[1, 2, 3], [0, 1, 2], [1, 2, 3]]Passed

SHA-256 / c46a16aba034a2f046bc5357392e13f583d158c19fa75765f8434f05cfe67d2a

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    items, at, cursors = x
    remaining = items[:at] + items[at+1:]
    updated = []
    for position in cursors:
        if position is None:
            next_position = None
        elif position < at:
            next_position = position
        elif position == at:
            next_position = at if at < len(remaining) else None
        else:
            next_position = position - 1 if position == at + 1 else position
        updated.append(next_position)
    observed = [remaining[p] if p is not None and 0 <= p < len(remaining) else None for p in updated]
    return [remaining,updated,observed]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior cursors', solve([[N,N+1,N+2,N+3],1,[0,1,2,3,None]]), [[N,N+2,N+3],[0,1,1,2,None],[N,N+2,N+2,N+3,None]])
check('erased last cursor', solve([[N,N+1],1,[0,1,None]]), [[N],[0,None,None],[N,None,None]])
check('all point at head', solve([[N,N+1,N+2],0,[0,0,2]]), [[N+1,N+2],[0,0,1],[N+1,N+1,N+2]])
check('single node erased', solve([[N],0,[0,None]]), [[],[None,None],[None,None]])
check('no cursors', solve([[N,N+1],0,[]]), [[N+1],[],[]])
check('unaffected cursors', solve([[N,N+1,N+2,N+3],3,[0,1,2]]), [[N,N+1,N+2],[0,1,2],[N,N+1,N+2]])
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
interior cursors[[1, 3, 4], [0, 1, 1, 3, None], [1, 3, 3, None, None]][[1, 3, 4], [0, 1, 1, 2, None], [1, 3, 3, 4, None]]Failed
erased last cursor[[1], [0, None, None], [1, None, None]][[1], [0, None, None], [1, None, None]]Passed
all point at head[[2, 3], [0, 0, 2], [2, 2, None]][[2, 3], [0, 0, 1], [2, 2, 3]]Failed
single node erased[[], [None, None], [None, None]][[], [None, None], [None, None]]Passed
no cursors[[2], [], []][[2], [], []]Passed
unaffected cursors[[1, 2, 3], [0, 1, 2], [1, 2, 3]][[1, 2, 3], [0, 1, 2], [1, 2, 3]]Passed

SHA-256 / 0ac8e734c3ca9ea3423d1459560bfd759902e48cc1bbd6f245e9badfdae9f0b7

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 6 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 2026-09-29T14:44:27.673350+00:00.

Case digest / c38c05c8f00301d567e8f5dc807db418c8b08a88ea0e5657998b9ab5d7b13222