{"abstract":"Ring gap insertion reads backing array order as logical order.","category":"Bounded deques","checks":7,"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.","evaluation_group":"s3-bounded-deques-ring-gap-insert","failed_approach":"The partial repair still applies the incorrect transition to an admitted boundary or multi-element case.","family":"s3-bounded-deques-ring-gap-insert-logical-gather","id":"FA-47061","implementations":{"attempt":{"sha256":"4a6cac0a825a4597887aa3b14a0b5c7159c58634392bb1617a4e5f23364d3734","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    slots,head,size,gap,value=x\n    cap=len(slots)\n    if size==cap:return [slots,head,size,False,0]\n    logical=[slots[(head+i)%cap] for i in range(size)] if head==0 else slots[:size]\n    left=gap<size-gap\n    origin=(head-1)%cap if left else head\n    inserted=logical[:gap]+[value]+logical[gap:]\n    result=[None]*cap\n    for i,v in enumerate(inserted):result[(origin+i)%cap]=v\n    count=size+1\n    moved=gap if left else size-gap\n    return [result,origin,count,True,moved]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"520388e7262bc72f683c610d77eb6fdffe2c90ec98aab54fb0087acbc222dfa6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    slots,head,size,gap,value=x\n    cap=len(slots)\n    if size==cap:return [slots,head,size,False,0]\n    logical=slots[:size]\n    left=gap<size-gap\n    origin=(head-1)%cap if left else head\n    inserted=logical[:gap]+[value]+logical[gap:]\n    result=[None]*cap\n    for i,v in enumerate(inserted):result[(origin+i)%cap]=v\n    count=size+1\n    moved=gap if left else size-gap\n    return [result,origin,count,True,moved]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"d1f9a30d28beb8d9c00c662342ed9547e57ee692af4106f83e6850829d0d4fad","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    slots,head,size,gap,value=x\n    cap=len(slots)\n    if size==cap:return [slots,head,size,False,0]\n    logical=[slots[(head+i)%cap] for i in range(size)]\n    left=gap<size-gap\n    origin=(head-1)%cap if left else head\n    inserted=logical[:gap]+[value]+logical[gap:]\n    result=[None]*cap\n    for i,v in enumerate(inserted):result[(origin+i)%cap]=v\n    count=size+1\n    moved=gap if left else size-gap\n    return [result,origin,count,True,moved]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\ncheck('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])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-bounded-deques-ring-gap-insert-logical-gather","generated_at":"2026-09-29T14:44:37.866307+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Controlled bounded deque implementation model with explicit storage and lifecycle observations.","repair":"Restore the documented logical gather invariant in ring-gap-insert.","root_cause":"Ring gap insertion reads backing array order as logical order.","sha256":"b3ac9626605c2975db1d5b08e7abd53eac6cc0ae1604cd22bba6bcbb0092ec0d","title":"Ring gap insertion reads backing array order as logical order · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.753,"exit_code":1,"observations":[{"actual":[[4,2,3,null,1],4,4,true,1],"check":"0","expected":[[4,2,3,null,1],4,4,true,1],"passed":true},{"actual":[[null,null,3,4,null],2,4,true,1],"check":"1","expected":[[3,null,1,4,2],2,4,true,1],"passed":false},{"actual":[[1,2,5,3,4,null],0,5,true,2],"check":"2","expected":[[1,2,5,3,4,null],0,5,true,2],"passed":true},{"actual":[[null,null,1,3],1,3,true,0],"check":"3","expected":[[null,1,2,3],1,3,true,0],"passed":false},{"actual":[[1,2],0,2,false,0],"check":"4","expected":[[1,2],0,2,false,0],"passed":true},{"actual":[[null,null,1],2,1,true,0],"check":"5","expected":[[null,null,1],2,1,true,0],"passed":true},{"actual":[[null,null,3,2],2,3,true,0],"check":"6","expected":[[2,null,3,1],2,3,true,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"0\", \"actual\": [[4, 2, 3, null, 1], 4, 4, true, 1], \"expected\": [[4, 2, 3, null, 1], 4, 4, true, 1], \"passed\": true}, {\"check\": \"1\", \"actual\": [[null, null, 3, 4, null], 2, 4, true, 1], \"expected\": [[3, null, 1, 4, 2], 2, 4, true, 1], \"passed\": false}, {\"check\": \"2\", \"actual\": [[1, 2, 5, 3, 4, null], 0, 5, true, 2], \"expected\": [[1, 2, 5, 3, 4, null], 0, 5, true, 2], \"passed\": true}, {\"check\": \"3\", \"actual\": [[null, null, 1, 3], 1, 3, true, 0], \"expected\": [[null, 1, 2, 3], 1, 3, true, 0], \"passed\": false}, {\"check\": \"4\", \"actual\": [[1, 2], 0, 2, false, 0], \"expected\": [[1, 2], 0, 2, false, 0], \"passed\": true}, {\"check\": \"5\", \"actual\": [[null, null, 1], 2, 1, true, 0], \"expected\": [[null, null, 1], 2, 1, true, 0], \"passed\": true}, {\"check\": \"6\", \"actual\": [[null, null, 3, 2], 2, 3, true, 0], \"expected\": [[2, null, 3, 1], 2, 3, true, 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.551,"exit_code":1,"observations":[{"actual":[[4,2,3,null,1],4,4,true,1],"check":"0","expected":[[4,2,3,null,1],4,4,true,1],"passed":true},{"actual":[[null,null,3,4,null],2,4,true,1],"check":"1","expected":[[3,null,1,4,2],2,4,true,1],"passed":false},{"actual":[[1,2,5,3,4,null],0,5,true,2],"check":"2","expected":[[1,2,5,3,4,null],0,5,true,2],"passed":true},{"actual":[[null,null,1,3],1,3,true,0],"check":"3","expected":[[null,1,2,3],1,3,true,0],"passed":false},{"actual":[[1,2],0,2,false,0],"check":"4","expected":[[1,2],0,2,false,0],"passed":true},{"actual":[[null,null,1],2,1,true,0],"check":"5","expected":[[null,null,1],2,1,true,0],"passed":true},{"actual":[[null,null,3,2],2,3,true,0],"check":"6","expected":[[2,null,3,1],2,3,true,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"0\", \"actual\": [[4, 2, 3, null, 1], 4, 4, true, 1], \"expected\": [[4, 2, 3, null, 1], 4, 4, true, 1], \"passed\": true}, {\"check\": \"1\", \"actual\": [[null, null, 3, 4, null], 2, 4, true, 1], \"expected\": [[3, null, 1, 4, 2], 2, 4, true, 1], \"passed\": false}, {\"check\": \"2\", \"actual\": [[1, 2, 5, 3, 4, null], 0, 5, true, 2], \"expected\": [[1, 2, 5, 3, 4, null], 0, 5, true, 2], \"passed\": true}, {\"check\": \"3\", \"actual\": [[null, null, 1, 3], 1, 3, true, 0], \"expected\": [[null, 1, 2, 3], 1, 3, true, 0], \"passed\": false}, {\"check\": \"4\", \"actual\": [[1, 2], 0, 2, false, 0], \"expected\": [[1, 2], 0, 2, false, 0], \"passed\": true}, {\"check\": \"5\", \"actual\": [[null, null, 1], 2, 1, true, 0], \"expected\": [[null, null, 1], 2, 1, true, 0], \"passed\": true}, {\"check\": \"6\", \"actual\": [[null, null, 3, 2], 2, 3, true, 0], \"expected\": [[2, null, 3, 1], 2, 3, true, 0], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.046,"exit_code":0,"observations":[{"actual":[[4,2,3,null,1],4,4,true,1],"check":"0","expected":[[4,2,3,null,1],4,4,true,1],"passed":true},{"actual":[[3,null,1,4,2],2,4,true,1],"check":"1","expected":[[3,null,1,4,2],2,4,true,1],"passed":true},{"actual":[[1,2,5,3,4,null],0,5,true,2],"check":"2","expected":[[1,2,5,3,4,null],0,5,true,2],"passed":true},{"actual":[[null,1,2,3],1,3,true,0],"check":"3","expected":[[null,1,2,3],1,3,true,0],"passed":true},{"actual":[[1,2],0,2,false,0],"check":"4","expected":[[1,2],0,2,false,0],"passed":true},{"actual":[[null,null,1],2,1,true,0],"check":"5","expected":[[null,null,1],2,1,true,0],"passed":true},{"actual":[[2,null,3,1],2,3,true,0],"check":"6","expected":[[2,null,3,1],2,3,true,0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"0\", \"actual\": [[4, 2, 3, null, 1], 4, 4, true, 1], \"expected\": [[4, 2, 3, null, 1], 4, 4, true, 1], \"passed\": true}, {\"check\": \"1\", \"actual\": [[3, null, 1, 4, 2], 2, 4, true, 1], \"expected\": [[3, null, 1, 4, 2], 2, 4, true, 1], \"passed\": true}, {\"check\": \"2\", \"actual\": [[1, 2, 5, 3, 4, null], 0, 5, true, 2], \"expected\": [[1, 2, 5, 3, 4, null], 0, 5, true, 2], \"passed\": true}, {\"check\": \"3\", \"actual\": [[null, 1, 2, 3], 1, 3, true, 0], \"expected\": [[null, 1, 2, 3], 1, 3, true, 0], \"passed\": true}, {\"check\": \"4\", \"actual\": [[1, 2], 0, 2, false, 0], \"expected\": [[1, 2], 0, 2, false, 0], \"passed\": true}, {\"check\": \"5\", \"actual\": [[null, null, 1], 2, 1, true, 0], \"expected\": [[null, null, 1], 2, 1, true, 0], \"passed\": true}, {\"check\": \"6\", \"actual\": [[2, null, 3, 1], 2, 3, true, 0], \"expected\": [[2, null, 3, 1], 2, 3, true, 0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}