{"abstract":"The bounded pairing cut splice certificate reports an incorrect predecessor next.","category":"Heap invariants","checks":7,"contract":"A pairing-heap cut input contains parent id, ordered child ids, selected child, and preexisting roots. Remove the child while preserving sibling order. Return remaining children, new first child, successor previous pointer (parent if selected was first), predecessor next pointer, promoted root list, and detached child links [parent,previous,next] all None.","evaluation_group":"s3-heap-model-pairing-cut-splice","failed_approach":"The local patch uses None if not before else [before[-1],None] and still violates the stated relation.","family":"s3-heap-pairing-cut-splice-predecessor_next","id":"FA-40726","implementations":{"attempt":{"sha256":"04fac7096672446c37d611d86ee20db0c513a6e2dbcb9cd43e62d7f4f2a62d81","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    p=d['parent']; cs=d['children']; c=d['child']; k=cs.index(c); before=cs[:k]; after=cs[k+1:]; kept=before+after\n    return {'children': kept,\n    'first': kept[0] if kept else None,\n    'successor_previous': None if not after else [after[0],before[-1] if before else p],\n    'predecessor_next': None if not before else [before[-1],None],\n    'roots': d[\"roots\"]+[c],\n    'detached': [None,None,None]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100], 'child': 100, 'roots': [9, 8]}, {'children': [1, 2, 3], 'first': 1, 'successor_previous': None, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101], 'child': 101, 'roots': [9, 8]}, {'children': [1, 2, 3, 100], 'first': 1, 'successor_previous': None, 'predecessor_next': [100, None], 'roots': [9, 8, 101], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102], 'child': 102, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101], 'first': 1, 'successor_previous': None, 'predecessor_next': [101, None], 'roots': [9, 8, 102], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103], 'child': 103, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102], 'first': 1, 'successor_previous': None, 'predecessor_next': [102, None], 'roots': [9, 8, 103], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103, 104], 'child': 104, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102, 103], 'first': 1, 'successor_previous': None, 'predecessor_next': [103, None], 'roots': [9, 8, 104], 'detached': [None, None, None]})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\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":"8804d8ac99e74aef4e4e7832f994c8de55c4e77253ea1860fab5c3b2231529fb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    p=d['parent']; cs=d['children']; c=d['child']; k=cs.index(c); before=cs[:k]; after=cs[k+1:]; kept=before+after\n    return {'children': kept,\n    'first': kept[0] if kept else None,\n    'successor_previous': None if not after else [after[0],before[-1] if before else p],\n    'predecessor_next': None if not before else [before[-1],c],\n    'roots': d[\"roots\"]+[c],\n    'detached': [None,None,None]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100], 'child': 100, 'roots': [9, 8]}, {'children': [1, 2, 3], 'first': 1, 'successor_previous': None, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101], 'child': 101, 'roots': [9, 8]}, {'children': [1, 2, 3, 100], 'first': 1, 'successor_previous': None, 'predecessor_next': [100, None], 'roots': [9, 8, 101], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102], 'child': 102, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101], 'first': 1, 'successor_previous': None, 'predecessor_next': [101, None], 'roots': [9, 8, 102], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103], 'child': 103, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102], 'first': 1, 'successor_previous': None, 'predecessor_next': [102, None], 'roots': [9, 8, 103], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103, 104], 'child': 104, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102, 103], 'first': 1, 'successor_previous': None, 'predecessor_next': [103, None], 'roots': [9, 8, 104], 'detached': [None, None, None]})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\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":"bb56ccd20fdc1c76ac210d3b9601c108b672b1ada81a4401ef60947955785779","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    p=d['parent']; cs=d['children']; c=d['child']; k=cs.index(c); before=cs[:k]; after=cs[k+1:]; kept=before+after\n    return {'children': kept,\n    'first': kept[0] if kept else None,\n    'successor_previous': None if not after else [after[0],before[-1] if before else p],\n    'predecessor_next': None if not before else [before[-1],after[0] if after else None],\n    'roots': d[\"roots\"]+[c],\n    'detached': [None,None,None]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100], 'child': 100, 'roots': [9, 8]}, {'children': [1, 2, 3], 'first': 1, 'successor_previous': None, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101], 'child': 101, 'roots': [9, 8]}, {'children': [1, 2, 3, 100], 'first': 1, 'successor_previous': None, 'predecessor_next': [100, None], 'roots': [9, 8, 101], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102], 'child': 102, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101], 'first': 1, 'successor_previous': None, 'predecessor_next': [101, None], 'roots': [9, 8, 102], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103], 'child': 103, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102], 'first': 1, 'successor_previous': None, 'predecessor_next': [102, None], 'roots': [9, 8, 103], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103, 104], 'child': 104, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102, 103], 'first': 1, 'successor_previous': None, 'predecessor_next': [103, None], 'roots': [9, 8, 104], 'detached': [None, None, None]})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\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":"A stipulated offline diagnostic model; it does not implement a production allocator, concurrency protocol, or complete heap library. 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-heap-pairing-cut-splice-predecessor_next","generated_at":"2026-09-29T14:43:33.857923+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"This isolates an internal heap representation or priority-structure invariant using deterministic finite records.","repair":"Derive predecessor next using None if not before else [before[-1],after[0] if after else None] under the stated bounded certificate contract.","root_cause":"Pairing cut predecessor bypasses the removed child to its successor.","sha256":"036d0dd6751e18f8d644a09735700b261d7609028cc86a2f41565ffdeddddc6d","title":"Pairing cut predecessor bypasses the removed child to its successor · case 01","variant":1,"variant_policy":"Six explicit regression certificates are retained; a seventh changes structural size, position, priority, or bounds with N.","verification":{"attempt":{"elapsed_ms":39.425,"exit_code":1,"observations":[{"actual":{"children":[],"detached":[null,null,null],"first":null,"predecessor_next":null,"roots":[9,8,1],"successor_previous":null},"check":"regression certificate 1","expected":{"children":[],"detached":[null,null,null],"first":null,"predecessor_next":null,"roots":[9,8,1],"successor_previous":null},"passed":true},{"actual":{"children":[2],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"check":"regression certificate 2","expected":{"children":[2],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"passed":true},{"actual":{"children":[1],"detached":[null,null,null],"first":1,"predecessor_next":[1,null],"roots":[9,8,2],"successor_previous":null},"check":"regression certificate 3","expected":{"children":[1],"detached":[null,null,null],"first":1,"predecessor_next":[1,null],"roots":[9,8,2],"successor_previous":null},"passed":true},{"actual":{"children":[1,3],"detached":[null,null,null],"first":1,"predecessor_next":[1,null],"roots":[9,8,2],"successor_previous":[3,1]},"check":"regression certificate 4","expected":{"children":[1,3],"detached":[null,null,null],"first":1,"predecessor_next":[1,3],"roots":[9,8,2],"successor_previous":[3,1]},"passed":false},{"actual":{"children":[1,2,4],"detached":[null,null,null],"first":1,"predecessor_next":[2,null],"roots":[9,8,3],"successor_previous":[4,2]},"check":"regression certificate 5","expected":{"children":[1,2,4],"detached":[null,null,null],"first":1,"predecessor_next":[2,4],"roots":[9,8,3],"successor_previous":[4,2]},"passed":false},{"actual":{"children":[2,3],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"check":"regression certificate 6","expected":{"children":[2,3],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"passed":true},{"actual":{"children":[1,2,3],"detached":[null,null,null],"first":1,"predecessor_next":[3,null],"roots":[9,8,100],"successor_previous":null},"check":"variant-dependent certificate","expected":{"children":[1,2,3],"detached":[null,null,null],"first":1,"predecessor_next":[3,null],"roots":[9,8,100],"successor_previous":null},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"children\": [], \"first\": null, \"successor_previous\": null, \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"expected\": {\"children\": [], \"first\": null, \"successor_previous\": null, \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"children\": [2], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"expected\": {\"children\": [2], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"children\": [1], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [1, null], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [1, null], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"children\": [1, 3], \"first\": 1, \"successor_previous\": [3, 1], \"predecessor_next\": [1, null], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1, 3], \"first\": 1, \"successor_previous\": [3, 1], \"predecessor_next\": [1, 3], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"children\": [1, 2, 4], \"first\": 1, \"successor_previous\": [4, 2], \"predecessor_next\": [2, null], \"roots\": [9, 8, 3], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1, 2, 4], \"first\": 1, \"successor_previous\": [4, 2], \"predecessor_next\": [2, 4], \"roots\": [9, 8, 3], \"detached\": [null, null, null]}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"children\": [2, 3], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"expected\": {\"children\": [2, 3], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"children\": [1, 2, 3], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [3, null], \"roots\": [9, 8, 100], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1, 2, 3], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [3, null], \"roots\": [9, 8, 100], \"detached\": [null, null, null]}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.623,"exit_code":1,"observations":[{"actual":{"children":[],"detached":[null,null,null],"first":null,"predecessor_next":null,"roots":[9,8,1],"successor_previous":null},"check":"regression certificate 1","expected":{"children":[],"detached":[null,null,null],"first":null,"predecessor_next":null,"roots":[9,8,1],"successor_previous":null},"passed":true},{"actual":{"children":[2],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"check":"regression certificate 2","expected":{"children":[2],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"passed":true},{"actual":{"children":[1],"detached":[null,null,null],"first":1,"predecessor_next":[1,2],"roots":[9,8,2],"successor_previous":null},"check":"regression certificate 3","expected":{"children":[1],"detached":[null,null,null],"first":1,"predecessor_next":[1,null],"roots":[9,8,2],"successor_previous":null},"passed":false},{"actual":{"children":[1,3],"detached":[null,null,null],"first":1,"predecessor_next":[1,2],"roots":[9,8,2],"successor_previous":[3,1]},"check":"regression certificate 4","expected":{"children":[1,3],"detached":[null,null,null],"first":1,"predecessor_next":[1,3],"roots":[9,8,2],"successor_previous":[3,1]},"passed":false},{"actual":{"children":[1,2,4],"detached":[null,null,null],"first":1,"predecessor_next":[2,3],"roots":[9,8,3],"successor_previous":[4,2]},"check":"regression certificate 5","expected":{"children":[1,2,4],"detached":[null,null,null],"first":1,"predecessor_next":[2,4],"roots":[9,8,3],"successor_previous":[4,2]},"passed":false},{"actual":{"children":[2,3],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"check":"regression certificate 6","expected":{"children":[2,3],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"passed":true},{"actual":{"children":[1,2,3],"detached":[null,null,null],"first":1,"predecessor_next":[3,100],"roots":[9,8,100],"successor_previous":null},"check":"variant-dependent certificate","expected":{"children":[1,2,3],"detached":[null,null,null],"first":1,"predecessor_next":[3,null],"roots":[9,8,100],"successor_previous":null},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"children\": [], \"first\": null, \"successor_previous\": null, \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"expected\": {\"children\": [], \"first\": null, \"successor_previous\": null, \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"children\": [2], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"expected\": {\"children\": [2], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"children\": [1], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [1, 2], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [1, null], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"children\": [1, 3], \"first\": 1, \"successor_previous\": [3, 1], \"predecessor_next\": [1, 2], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1, 3], \"first\": 1, \"successor_previous\": [3, 1], \"predecessor_next\": [1, 3], \"roots\": [9, 8, 2], \"detached\": [null, null, null]}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"children\": [1, 2, 4], \"first\": 1, \"successor_previous\": [4, 2], \"predecessor_next\": [2, 3], \"roots\": [9, 8, 3], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1, 2, 4], \"first\": 1, \"successor_previous\": [4, 2], \"predecessor_next\": [2, 4], \"roots\": [9, 8, 3], \"detached\": [null, null, null]}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"children\": [2, 3], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"expected\": {\"children\": [2, 3], \"first\": 2, \"successor_previous\": [2, 9], \"predecessor_next\": null, \"roots\": [9, 8, 1], \"detached\": [null, null, null]}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"children\": [1, 2, 3], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [3, 100], \"roots\": [9, 8, 100], \"detached\": [null, null, null]}, \"expected\": {\"children\": [1, 2, 3], \"first\": 1, \"successor_previous\": null, \"predecessor_next\": [3, null], \"roots\": [9, 8, 100], \"detached\": [null, null, null]}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.64,"exit_code":0,"observations":[{"actual":{"children":[],"detached":[null,null,null],"first":null,"predecessor_next":null,"roots":[9,8,1],"successor_previous":null},"check":"regression certificate 1","expected":{"children":[],"detached":[null,null,null],"first":null,"predecessor_next":null,"roots":[9,8,1],"successor_previous":null},"passed":true},{"actual":{"children":[2],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"check":"regression certificate 2","expected":{"children":[2],"detached":[null,null,null],"first":2,"predecessor_next":null,"roots":[9,8,1],"successor_previous":[2,9]},"passed":true},{"actual":{"children":[1],"detached":[null,null,null],"first":1,"predecessor_next":[1,null],"roots":[9,8,2],"successor_previous":null},"check":"regression certificate 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