FAILURE MAP
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FA-40401 / Heap invariants / Open access

Min-max heap maximum can be either child of the root · case 01

The bounded minmax levels certificate reports an incorrect maximum.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Min-max heap maximum can be either child of the root.

THE FAILURE

Min-max heap maximum can be either child of the root.

Unsuccessful approach: The local patch uses None if not a else a[1] if n>1 else a[0] and still violates the stated relation.

Case contract

A min-max heap certificate is a complete zero-based binary array. Even depth is a minimum level, odd depth a maximum level. Report level parities, grandparent indices, minimum-level grandchild violations, maximum-level grandchild violations, maximum endpoint, and immediate-child level alternation pairs. Empty maximum is None.

Why this case matters

This isolates an internal heap representation or priority-structure invariant using deterministic finite records.

1 / The failure

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

N = 1
observations = []
def solve(d):
    a=d['keys']; n=len(a)
    def depth(i): return (i+1).bit_length()-1
    def grandchildren(i): return [j for j in range(4*i+3,4*i+7) if j<n]
    return {'parity': [depth(i)%2 for i in range(n)],
    'grandparents': [None if i<3 else (i-3)//4 for i in range(n)],
    'min_violations': [[i,j] for i in range(n) if depth(i)%2==0 for j in grandchildren(i) if a[j]<a[i]],
    'max_violations': [[i,j] for i in range(n) if depth(i)%2==1 for j in grandchildren(i) if a[j]>a[i]],
    'maximum': None if not a else a[-1],
    'edges': [[i,j] for i in range(n) for j in (2*i+1,2*i+2) if j<n]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 8, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 9, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 10, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 10, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 11, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 11, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 12, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 12, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})]][N-1]
check('regression certificate 1', solve(cases[0][0]), cases[0][1])
check('regression certificate 2', solve(cases[1][0]), cases[1][1])
check('regression certificate 3', solve(cases[2][0]), cases[2][1])
check('regression certificate 4', solve(cases[3][0]), cases[3][1])
check('regression certificate 5', solve(cases[4][0]), cases[4][1])
check('regression certificate 6', solve(cases[5][0]), cases[5][1])
check('variant-dependent certificate', solve(cases[6][0]), cases[6][1])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression certificate 1{'edges': [], 'grandparents': [], 'max_violations': [], 'maximum': None, 'min_violations': [], 'parity': []}{'edges': [], 'grandparents': [], 'max_violations': [], 'maximum': None, 'min_violations': [], 'parity': []}Passed
regression certificate 2{'edges': [], 'grandparents': [None], 'max_violations': [], 'maximum': 4, 'min_violations': [], 'parity': [0]}{'edges': [], 'grandparents': [None], 'max_violations': [], 'maximum': 4, 'min_violations': [], 'parity': [0]}Passed
regression certificate 3{'edges': [[0, 1], [0, 2]], 'grandparents': [None, None, None], 'max_violations': [], 'maximum': 9, 'min_violations': [], 'parity': [0, 1, 1]}{'edges': [[0, 1], [0, 2]], 'grandparents': [None, None, None], 'max_violations': [], 'maximum': 9, 'min_violations': [], 'parity': [0, 1, 1]}Passed
regression certificate 4{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]], 'grandparents': [None, None, None, 0, 0, 0, 0], 'max_violations': [], 'maximum': 7, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]], 'grandparents': [None, None, None, 0, 0, 0, 0], 'max_violations': [], 'maximum': 9, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0]}Failed
regression certificate 5{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 3, 'min_violations': [[0, 3], [0, 5]], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'min_violations': [[0, 3], [0, 5]], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}Failed
regression certificate 6{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}Passed
variant-dependent certificate{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}Passed

SHA-256 / 2e64cf2f6d3bd82e3ace46de895314600cd83d9e2254ad57cf62840c9d1581a3

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    a=d['keys']; n=len(a)
    def depth(i): return (i+1).bit_length()-1
    def grandchildren(i): return [j for j in range(4*i+3,4*i+7) if j<n]
    return {'parity': [depth(i)%2 for i in range(n)],
    'grandparents': [None if i<3 else (i-3)//4 for i in range(n)],
    'min_violations': [[i,j] for i in range(n) if depth(i)%2==0 for j in grandchildren(i) if a[j]<a[i]],
    'max_violations': [[i,j] for i in range(n) if depth(i)%2==1 for j in grandchildren(i) if a[j]>a[i]],
    'maximum': None if not a else a[1] if n>1 else a[0],
    'edges': [[i,j] for i in range(n) for j in (2*i+1,2*i+2) if j<n]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 8, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 9, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 10, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 10, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 11, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 11, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 12, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 12, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})]][N-1]
check('regression certificate 1', solve(cases[0][0]), cases[0][1])
check('regression certificate 2', solve(cases[1][0]), cases[1][1])
check('regression certificate 3', solve(cases[2][0]), cases[2][1])
check('regression certificate 4', solve(cases[3][0]), cases[3][1])
check('regression certificate 5', solve(cases[4][0]), cases[4][1])
check('regression certificate 6', solve(cases[5][0]), cases[5][1])
check('variant-dependent certificate', solve(cases[6][0]), cases[6][1])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression certificate 1{'edges': [], 'grandparents': [], 'max_violations': [], 'maximum': None, 'min_violations': [], 'parity': []}{'edges': [], 'grandparents': [], 'max_violations': [], 'maximum': None, 'min_violations': [], 'parity': []}Passed
regression certificate 2{'edges': [], 'grandparents': [None], 'max_violations': [], 'maximum': 4, 'min_violations': [], 'parity': [0]}{'edges': [], 'grandparents': [None], 'max_violations': [], 'maximum': 4, 'min_violations': [], 'parity': [0]}Passed
regression certificate 3{'edges': [[0, 1], [0, 2]], 'grandparents': [None, None, None], 'max_violations': [], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1]}{'edges': [[0, 1], [0, 2]], 'grandparents': [None, None, None], 'max_violations': [], 'maximum': 9, 'min_violations': [], 'parity': [0, 1, 1]}Failed
regression certificate 4{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]], 'grandparents': [None, None, None, 0, 0, 0, 0], 'max_violations': [], 'maximum': 9, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]], 'grandparents': [None, None, None, 0, 0, 0, 0], 'max_violations': [], 'maximum': 9, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0]}Passed
regression certificate 5{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 4, 'min_violations': [[0, 3], [0, 5]], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'min_violations': [[0, 3], [0, 5]], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}Failed
regression certificate 6{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 7, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}Failed
variant-dependent certificate{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}{'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'max_violations': [[1, 10]], 'maximum': 8, 'min_violations': [], 'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]}Passed

SHA-256 / 51fd60db5b144c0d903c9336513b68c3b6d25173db4d72556e976f2de1c9f2f4

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:43:30.827037+00:00.

Case digest / 8b538e58ada57006604882df7398ca70f558452d976991e2a77a5985aba7083e