{"abstract":"The bounded twin heap delete certificate reports an incorrect records.","category":"Heap invariants","checks":7,"contract":"A double-ended heap certificate has min-order ids, max-order ids, and unique live records id->priority. Erase id x from both heaps by identity, preserving surviving order for this logical model. Report min ids, max ids, live map, cross-index mapping from surviving min slots to max slots, next minimum, and next maximum. Equal priorities retain separate identities.","contract_signature":"d","evaluation_group":"s3-heap-model-twin-heap-delete","failed_approach":"The local patch uses {i:p for i,p in live.items() if p!=live[x]} and still violates the stated relation.","family":"s3-heap-twin-heap-delete-records","id":"FA-41051","implementations":{"attempt":{"sha256":"e2f77b6e19ae878d53daf94caae37a129d1b4e67c93d10e9f954f6e5ad87d610","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    mn=d['min']; mx=d['max']; live=d['live']; x=d['erase']; low=[i for i in mn if i!=x]; high=[i for i in mx if i!=x]; remain={i:p for i,p in live.items() if i!=x}\n    return {'min_ids': low,\n    'max_ids': high,\n    'records': {i:p for i,p in live.items() if p!=live[x]},\n    'cross_index': [high.index(i) for i in low],\n    'minimum': live[low[0]] if low else None,\n    'maximum': live[high[0]] if high else None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 1}, 'min': ['variant', 'b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['variant', 'b', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}, 'cross_index': [3, 2, 1, 0], 'minimum': 1, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 2}, 'min': ['b', 'variant', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['b', 'variant', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 2}, 'cross_index': [2, 3, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 3}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'd', 'variant', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'd', 'variant', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 3}, 'cross_index': [3, 1, 2, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 4}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 4}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 5}, 'min': ['b', 'd', 'c', 'variant', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 5}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})]][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":"73433c643e99047bf0b1a813116bd28ccf135453e91bb59f233a34e3e1d05c55","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    mn=d['min']; mx=d['max']; live=d['live']; x=d['erase']; low=[i for i in mn if i!=x]; high=[i for i in mx if i!=x]; remain={i:p for i,p in live.items() if i!=x}\n    return {'min_ids': low,\n    'max_ids': high,\n    'records': live,\n    'cross_index': [high.index(i) for i in low],\n    'minimum': live[low[0]] if low else None,\n    'maximum': live[high[0]] if high else None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 1}, 'min': ['variant', 'b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['variant', 'b', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}, 'cross_index': [3, 2, 1, 0], 'minimum': 1, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 2}, 'min': ['b', 'variant', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['b', 'variant', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 2}, 'cross_index': [2, 3, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 3}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'd', 'variant', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'd', 'variant', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 3}, 'cross_index': [3, 1, 2, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 4}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 4}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 5}, 'min': ['b', 'd', 'c', 'variant', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 5}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})]][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-twin-heap-delete-records","generated_at":"2026-09-29T14:43:37.247544+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.","root_cause":"Twin heap shared record deletion preserves equal-priority neighbors.","sha256":"4b8b717e9b2969e3c07dbcafb3614c740fefdae97bfe464aa34ca014b935e254","title":"Twin heap shared record deletion preserves equal-priority neighbors · case 01","variant":1,"variant_policy":"Six explicit regression certificates are retained; a seventh changes structural size, position, priority, or bounds with N.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":47.669,"exit_code":1,"observations":[{"actual":{"cross_index":[],"max_ids":[],"maximum":null,"min_ids":[],"minimum":null,"records":{}},"check":"regression certificate 1","expected":{"cross_index":[],"max_ids":[],"maximum":null,"min_ids":[],"minimum":null,"records":{}},"passed":true},{"actual":{"cross_index":[0],"max_ids":["b"],"maximum":5,"min_ids":["b"],"minimum":5,"records":{"b":5}},"check":"regression certificate 2","expected":{"cross_index":[0],"max_ids":["b"],"maximum":5,"min_ids":["b"],"minimum":5,"records":{"b":5}},"passed":true},{"actual":{"cross_index":[0],"max_ids":["a"],"maximum":1,"min_ids":["a"],"minimum":1,"records":{"a":1}},"check":"regression certificate 3","expected":{"cross_index":[0],"max_ids":["a"],"maximum":1,"min_ids":["a"],"minimum":1,"records":{"a":1}},"passed":true},{"actual":{"cross_index":[1,0],"max_ids":["c","b"],"maximum":6,"min_ids":["b","c"],"minimum":3,"records":{"c":6}},"check":"regression certificate 4","expected":{"cross_index":[1,0],"max_ids":["c","b"],"maximum":6,"min_ids":["b","c"],"minimum":3,"records":{"b":3,"c":6}},"passed":false},{"actual":{"cross_index":[2,1,0],"max_ids":["b","c","a"],"maximum":8,"min_ids":["a","c","b"],"minimum":1,"records":{"a":1,"c":3}},"check":"regression certificate 5","expected":{"cross_index":[2,1,0],"max_ids":["b","c","a"],"maximum":8,"min_ids":["a","c","b"],"minimum":1,"records":{"a":1,"b":8,"c":3}},"passed":false},{"actual":{"cross_index":[2,1,0],"max_ids":["a","d","b"],"maximum":7,"min_ids":["b","d","a"],"minimum":2,"records":{"a":7,"b":2,"d":3}},"check":"regression certificate 6","expected":{"cross_index":[2,1,0],"max_ids":["a","d","b"],"maximum":7,"min_ids":["b","d","a"],"minimum":2,"records":{"a":7,"b":2,"d":3}},"passed":true},{"actual":{"cross_index":[3,2,1,0],"max_ids":["a","d","b","variant"],"maximum":7,"min_ids":["variant","b","d","a"],"minimum":1,"records":{"a":7,"b":2,"d":3,"variant":1}},"check":"variant-dependent certificate","expected":{"cross_index":[3,2,1,0],"max_ids":["a","d","b","variant"],"maximum":7,"min_ids":["variant","b","d","a"],"minimum":1,"records":{"a":7,"b":2,"d":3,"variant":1}},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"min_ids\": [], \"max_ids\": [], \"records\": {}, \"cross_index\": [], \"minimum\": null, \"maximum\": null}, \"expected\": {\"min_ids\": [], \"max_ids\": [], \"records\": {}, \"cross_index\": [], \"minimum\": null, \"maximum\": null}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"min_ids\": [\"b\"], \"max_ids\": [\"b\"], \"records\": {\"b\": 5}, \"cross_index\": [0], \"minimum\": 5, \"maximum\": 5}, \"expected\": {\"min_ids\": [\"b\"], \"max_ids\": [\"b\"], \"records\": {\"b\": 5}, \"cross_index\": [0], \"minimum\": 5, \"maximum\": 5}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"min_ids\": [\"a\"], \"max_ids\": [\"a\"], \"records\": {\"a\": 1}, \"cross_index\": [0], \"minimum\": 1, \"maximum\": 1}, \"expected\": {\"min_ids\": [\"a\"], \"max_ids\": [\"a\"], \"records\": {\"a\": 1}, \"cross_index\": [0], \"minimum\": 1, \"maximum\": 1}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"min_ids\": [\"b\", \"c\"], \"max_ids\": [\"c\", \"b\"], \"records\": {\"c\": 6}, \"cross_index\": [1, 0], \"minimum\": 3, \"maximum\": 6}, \"expected\": {\"min_ids\": [\"b\", \"c\"], \"max_ids\": [\"c\", \"b\"], \"records\": {\"b\": 3, \"c\": 6}, \"cross_index\": [1, 0], \"minimum\": 3, \"maximum\": 6}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"min_ids\": [\"a\", \"c\", \"b\"], \"max_ids\": [\"b\", \"c\", \"a\"], \"records\": {\"a\": 1, \"c\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 1, \"maximum\": 8}, \"expected\": {\"min_ids\": [\"a\", \"c\", \"b\"], \"max_ids\": [\"b\", \"c\", \"a\"], \"records\": {\"a\": 1, \"b\": 8, \"c\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 1, \"maximum\": 8}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"min_ids\": [\"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\"], \"records\": {\"a\": 7, \"b\": 2, \"d\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 2, \"maximum\": 7}, \"expected\": {\"min_ids\": [\"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\"], \"records\": {\"a\": 7, \"b\": 2, \"d\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 2, \"maximum\": 7}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"min_ids\": [\"variant\", \"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\", \"variant\"], \"records\": {\"a\": 7, \"b\": 2, \"d\": 3, \"variant\": 1}, \"cross_index\": [3, 2, 1, 0], \"minimum\": 1, \"maximum\": 7}, \"expected\": {\"min_ids\": [\"variant\", \"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\", \"variant\"], \"records\": {\"a\": 7, \"b\": 2, \"d\": 3, \"variant\": 1}, \"cross_index\": [3, 2, 1, 0], \"minimum\": 1, \"maximum\": 7}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.27,"exit_code":1,"observations":[{"actual":{"cross_index":[],"max_ids":[],"maximum":null,"min_ids":[],"minimum":null,"records":{"a":2}},"check":"regression certificate 1","expected":{"cross_index":[],"max_ids":[],"maximum":null,"min_ids":[],"minimum":null,"records":{}},"passed":false},{"actual":{"cross_index":[0],"max_ids":["b"],"maximum":5,"min_ids":["b"],"minimum":5,"records":{"a":1,"b":5}},"check":"regression certificate 2","expected":{"cross_index":[0],"max_ids":["b"],"maximum":5,"min_ids":["b"],"minimum":5,"records":{"b":5}},"passed":false},{"actual":{"cross_index":[0],"max_ids":["a"],"maximum":1,"min_ids":["a"],"minimum":1,"records":{"a":1,"b":5}},"check":"regression certificate 3","expected":{"cross_index":[0],"max_ids":["a"],"maximum":1,"min_ids":["a"],"minimum":1,"records":{"a":1}},"passed":false},{"actual":{"cross_index":[1,0],"max_ids":["c","b"],"maximum":6,"min_ids":["b","c"],"minimum":3,"records":{"a":3,"b":3,"c":6}},"check":"regression certificate 4","expected":{"cross_index":[1,0],"max_ids":["c","b"],"maximum":6,"min_ids":["b","c"],"minimum":3,"records":{"b":3,"c":6}},"passed":false},{"actual":{"cross_index":[2,1,0],"max_ids":["b","c","a"],"maximum":8,"min_ids":["a","c","b"],"minimum":1,"records":{"a":1,"b":8,"c":3,"d":8}},"check":"regression certificate 5","expected":{"cross_index":[2,1,0],"max_ids":["b","c","a"],"maximum":8,"min_ids":["a","c","b"],"minimum":1,"records":{"a":1,"b":8,"c":3}},"passed":false},{"actual":{"cross_index":[2,1,0],"max_ids":["a","d","b"],"maximum":7,"min_ids":["b","d","a"],"minimum":2,"records":{"a":7,"b":2,"c":5,"d":3}},"check":"regression certificate 6","expected":{"cross_index":[2,1,0],"max_ids":["a","d","b"],"maximum":7,"min_ids":["b","d","a"],"minimum":2,"records":{"a":7,"b":2,"d":3}},"passed":false},{"actual":{"cross_index":[3,2,1,0],"max_ids":["a","d","b","variant"],"maximum":7,"min_ids":["variant","b","d","a"],"minimum":1,"records":{"a":7,"b":2,"c":5,"d":3,"variant":1}},"check":"variant-dependent certificate","expected":{"cross_index":[3,2,1,0],"max_ids":["a","d","b","variant"],"maximum":7,"min_ids":["variant","b","d","a"],"minimum":1,"records":{"a":7,"b":2,"d":3,"variant":1}},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"min_ids\": [], \"max_ids\": [], \"records\": {\"a\": 2}, \"cross_index\": [], \"minimum\": null, \"maximum\": null}, \"expected\": {\"min_ids\": [], \"max_ids\": [], \"records\": {}, \"cross_index\": [], \"minimum\": null, \"maximum\": null}, \"passed\": false}, {\"check\": \"regression certificate 2\", \"actual\": {\"min_ids\": [\"b\"], \"max_ids\": [\"b\"], \"records\": {\"a\": 1, \"b\": 5}, \"cross_index\": [0], \"minimum\": 5, \"maximum\": 5}, \"expected\": {\"min_ids\": [\"b\"], \"max_ids\": [\"b\"], \"records\": {\"b\": 5}, \"cross_index\": [0], \"minimum\": 5, \"maximum\": 5}, \"passed\": false}, {\"check\": \"regression certificate 3\", \"actual\": {\"min_ids\": [\"a\"], \"max_ids\": [\"a\"], \"records\": {\"a\": 1, \"b\": 5}, \"cross_index\": [0], \"minimum\": 1, \"maximum\": 1}, \"expected\": {\"min_ids\": [\"a\"], \"max_ids\": [\"a\"], \"records\": {\"a\": 1}, \"cross_index\": [0], \"minimum\": 1, \"maximum\": 1}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"min_ids\": [\"b\", \"c\"], \"max_ids\": [\"c\", \"b\"], \"records\": {\"a\": 3, \"b\": 3, \"c\": 6}, \"cross_index\": [1, 0], \"minimum\": 3, \"maximum\": 6}, \"expected\": {\"min_ids\": [\"b\", \"c\"], \"max_ids\": [\"c\", \"b\"], \"records\": {\"b\": 3, \"c\": 6}, \"cross_index\": [1, 0], \"minimum\": 3, \"maximum\": 6}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"min_ids\": [\"a\", \"c\", \"b\"], \"max_ids\": [\"b\", \"c\", \"a\"], \"records\": {\"a\": 1, \"b\": 8, \"c\": 3, \"d\": 8}, \"cross_index\": [2, 1, 0], \"minimum\": 1, \"maximum\": 8}, \"expected\": {\"min_ids\": [\"a\", \"c\", \"b\"], \"max_ids\": [\"b\", \"c\", \"a\"], \"records\": {\"a\": 1, \"b\": 8, \"c\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 1, \"maximum\": 8}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"min_ids\": [\"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\"], \"records\": {\"a\": 7, \"b\": 2, \"c\": 5, \"d\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 2, \"maximum\": 7}, \"expected\": {\"min_ids\": [\"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\"], \"records\": {\"a\": 7, \"b\": 2, \"d\": 3}, \"cross_index\": [2, 1, 0], \"minimum\": 2, \"maximum\": 7}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"min_ids\": [\"variant\", \"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\", \"variant\"], \"records\": {\"a\": 7, \"b\": 2, \"c\": 5, \"d\": 3, \"variant\": 1}, \"cross_index\": [3, 2, 1, 0], \"minimum\": 1, \"maximum\": 7}, \"expected\": {\"min_ids\": [\"variant\", \"b\", \"d\", \"a\"], \"max_ids\": [\"a\", \"d\", \"b\", \"variant\"], \"records\": {\"a\": 7, \"b\": 2, \"d\": 3, \"variant\": 1}, \"cross_index\": [3, 2, 1, 0], \"minimum\": 1, \"maximum\": 7}, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}