{"abstract":"The bounded binomial carry certificate reports an incorrect partner.","category":"Heap invariants","checks":7,"contract":"A consolidation cursor sees ordered ranks and index i. Report whether to link now, current rank, carry rank, suffix retained after a link, triple-collision deferral, and link partner. In three equal consecutive ranks defer the first pair so a carry is not consolidated twice out of order. Empty cursor is allowed.","evaluation_group":"s3-heap-model-binomial-carry","failed_approach":"The local patch uses len(r)-1 if link else None and still violates the stated relation.","family":"s3-heap-binomial-carry-partner","id":"FA-40046","implementations":{"attempt":{"sha256":"0bd789cacdc466544f6fe84d805aa5dadfa03c5b3099c8fe6aa86f1710c8046a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    r=d['ranks']; i=d['i']; exists=i<len(r); pair=i+1<len(r) and r[i]==r[i+1]; triple=i+2<len(r) and r[i]==r[i+1]==r[i+2]\n    link=pair and not triple\n    return {'link_now': link,\n    'current': r[i] if exists else None,\n    'carry_rank': r[i]+1 if link else None,\n    'suffix': r[i+2:] if link else r[i:],\n    'defer': triple,\n    'partner': len(r)-1 if link else None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [1, 2, 2, 3], 'i': 0}, {'link_now': False, 'current': 1, 'carry_rank': None, 'suffix': [1, 2, 2, 3], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [2, 3, 3, 4], 'i': 0}, {'link_now': False, 'current': 2, 'carry_rank': None, 'suffix': [2, 3, 3, 4], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [3, 4, 4, 5], 'i': 0}, {'link_now': False, 'current': 3, 'carry_rank': None, 'suffix': [3, 4, 4, 5], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [4, 5, 5, 6], 'i': 0}, {'link_now': False, 'current': 4, 'carry_rank': None, 'suffix': [4, 5, 5, 6], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [5, 6, 6, 7], 'i': 0}, {'link_now': False, 'current': 5, 'carry_rank': None, 'suffix': [5, 6, 6, 7], 'defer': False, 'partner': 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":"bee6ff80ffda258f27bf9c64b6fc42be4d40ef2099de6a187201314547b72345","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    r=d['ranks']; i=d['i']; exists=i<len(r); pair=i+1<len(r) and r[i]==r[i+1]; triple=i+2<len(r) and r[i]==r[i+1]==r[i+2]\n    link=pair and not triple\n    return {'link_now': link,\n    'current': r[i] if exists else None,\n    'carry_rank': r[i]+1 if link else None,\n    'suffix': r[i+2:] if link else r[i:],\n    'defer': triple,\n    'partner': i if link else None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [1, 2, 2, 3], 'i': 0}, {'link_now': False, 'current': 1, 'carry_rank': None, 'suffix': [1, 2, 2, 3], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [2, 3, 3, 4], 'i': 0}, {'link_now': False, 'current': 2, 'carry_rank': None, 'suffix': [2, 3, 3, 4], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [3, 4, 4, 5], 'i': 0}, {'link_now': False, 'current': 3, 'carry_rank': None, 'suffix': [3, 4, 4, 5], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [4, 5, 5, 6], 'i': 0}, {'link_now': False, 'current': 4, 'carry_rank': None, 'suffix': [4, 5, 5, 6], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [5, 6, 6, 7], 'i': 0}, {'link_now': False, 'current': 5, 'carry_rank': None, 'suffix': [5, 6, 6, 7], 'defer': False, 'partner': 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":"845f4c069904d01e9ff3c652eca4efa3cf98e1acdcc917325c926aaf891f7bfd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    r=d['ranks']; i=d['i']; exists=i<len(r); pair=i+1<len(r) and r[i]==r[i+1]; triple=i+2<len(r) and r[i]==r[i+1]==r[i+2]\n    link=pair and not triple\n    return {'link_now': link,\n    'current': r[i] if exists else None,\n    'carry_rank': r[i]+1 if link else None,\n    'suffix': r[i+2:] if link else r[i:],\n    'defer': triple,\n    'partner': i+1 if link else None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [1, 2, 2, 3], 'i': 0}, {'link_now': False, 'current': 1, 'carry_rank': None, 'suffix': [1, 2, 2, 3], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [2, 3, 3, 4], 'i': 0}, {'link_now': False, 'current': 2, 'carry_rank': None, 'suffix': [2, 3, 3, 4], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [3, 4, 4, 5], 'i': 0}, {'link_now': False, 'current': 3, 'carry_rank': None, 'suffix': [3, 4, 4, 5], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [4, 5, 5, 6], 'i': 0}, {'link_now': False, 'current': 4, 'carry_rank': None, 'suffix': [4, 5, 5, 6], 'defer': False, 'partner': None})], [({'ranks': [], 'i': 0}, {'link_now': False, 'current': None, 'carry_rank': None, 'suffix': [], 'defer': False, 'partner': None}), ({'ranks': [0, 0], 'i': 0}, {'link_now': True, 'current': 0, 'carry_rank': 1, 'suffix': [], 'defer': False, 'partner': 1}), ({'ranks': [0, 0, 0, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 0, 0, 2], 'defer': True, 'partner': None}), ({'ranks': [0, 1, 1, 3], 'i': 1}, {'link_now': True, 'current': 1, 'carry_rank': 2, 'suffix': [3], 'defer': False, 'partner': 2}), ({'ranks': [1, 2, 2, 4, 5], 'i': 1}, {'link_now': True, 'current': 2, 'carry_rank': 3, 'suffix': [4, 5], 'defer': False, 'partner': 2}), ({'ranks': [0, 1, 1, 2], 'i': 0}, {'link_now': False, 'current': 0, 'carry_rank': None, 'suffix': [0, 1, 1, 2], 'defer': False, 'partner': None}), ({'ranks': [5, 6, 6, 7], 'i': 0}, {'link_now': False, 'current': 5, 'carry_rank': None, 'suffix': [5, 6, 6, 7], 'defer': False, 'partner': 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-binomial-carry-partner","generated_at":"2026-09-29T14:43:27.285137+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 partner using i+1 if link else None under the stated bounded certificate contract.","root_cause":"Binomial carry links the adjacent equal rank rather than the tail.","sha256":"aabf3e56835365f5e766f8a9f48b66bf1c1abd0d9a4b5adda8a39106444ff45f","title":"Binomial carry links the adjacent equal rank rather than the tail · case 01","variant":1,"variant_policy":"Six explicit regression 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