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FA-40591 / Heap invariants / Open access

Bottom-up heap construction repairs descendants before their parents and excludes leaves · case 01

The bounded bottomup schedule certificate reports an incorrect schedule.

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

ROOT CAUSE

Bottom-up heap construction repairs descendants before their parents and excludes leaves.

THE FAILURE

Bottom-up heap construction repairs descendants before their parents and excludes leaves.

Unsuccessful approach: The local patch uses list(range(n//2,-1,-1)) and still violates the stated relation.

Case contract

For building a complete zero-based binary heap of n nodes, report descending internal-node repair schedule, leaf indices, level spans as inclusive [start,end], right-child-less internal node, parent dependency edges [child,parent], and number of internal nodes. This describes the build work graph, not sorted output.

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):
    n=d['size']; internal=list(range(n//2-1,-1,-1)); levels=[]; start=0; width=1
    while start<n:
        levels.append([start,min(n-1,start+width-1)]); start+=width; width*=2
    return {'schedule': list(reversed(internal)),
    'leaves': list(range(n//2,n)),
    'levels': levels,
    'unpaired_parent': n//2-1 if n>0 and n%2==0 else None,
    'dependencies': [[i,(i-1)//2] for i in range(1,n//2)],
    'internal_count': n//2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 16}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'unpaired_parent': 7, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 17}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15, 16], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 16]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 18}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 17]], 'unpaired_parent': 8, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 19}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 18]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 20}, {'schedule': [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 19]], 'unpaired_parent': 9, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4]], 'internal_count': 10})]][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{'dependencies': [], 'internal_count': 0, 'leaves': [], 'levels': [], 'schedule': [], 'unpaired_parent': None}{'dependencies': [], 'internal_count': 0, 'leaves': [], 'levels': [], 'schedule': [], 'unpaired_parent': None}Passed
regression certificate 2{'dependencies': [], 'internal_count': 0, 'leaves': [0], 'levels': [[0, 0]], 'schedule': [], 'unpaired_parent': None}{'dependencies': [], 'internal_count': 0, 'leaves': [0], 'levels': [[0, 0]], 'schedule': [], 'unpaired_parent': None}Passed
regression certificate 3{'dependencies': [], 'internal_count': 1, 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'schedule': [0], 'unpaired_parent': 0}{'dependencies': [], 'internal_count': 1, 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'schedule': [0], 'unpaired_parent': 0}Passed
regression certificate 4{'dependencies': [[1, 0]], 'internal_count': 2, 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'schedule': [0, 1], 'unpaired_parent': None}{'dependencies': [[1, 0]], 'internal_count': 2, 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'schedule': [1, 0], 'unpaired_parent': None}Failed
regression certificate 5{'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4, 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'schedule': [0, 1, 2, 3], 'unpaired_parent': 3}{'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4, 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'schedule': [3, 2, 1, 0], 'unpaired_parent': 3}Failed
regression certificate 6{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7, 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'schedule': [0, 1, 2, 3, 4, 5, 6], 'unpaired_parent': None}{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7, 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'schedule': [6, 5, 4, 3, 2, 1, 0], 'unpaired_parent': None}Failed
variant-dependent certificate{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8, 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'schedule': [0, 1, 2, 3, 4, 5, 6, 7], 'unpaired_parent': 7}{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8, 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'unpaired_parent': 7}Failed

SHA-256 / 9628c55341883e013e2dcc515e8df90d61c96404e404b4e4a549dc62f9c4d342

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    n=d['size']; internal=list(range(n//2-1,-1,-1)); levels=[]; start=0; width=1
    while start<n:
        levels.append([start,min(n-1,start+width-1)]); start+=width; width*=2
    return {'schedule': list(range(n//2,-1,-1)),
    'leaves': list(range(n//2,n)),
    'levels': levels,
    'unpaired_parent': n//2-1 if n>0 and n%2==0 else None,
    'dependencies': [[i,(i-1)//2] for i in range(1,n//2)],
    'internal_count': n//2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 16}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'unpaired_parent': 7, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 17}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15, 16], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 16]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 18}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 17]], 'unpaired_parent': 8, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 19}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 18]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 20}, {'schedule': [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 19]], 'unpaired_parent': 9, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4]], 'internal_count': 10})]][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{'dependencies': [], 'internal_count': 0, 'leaves': [], 'levels': [], 'schedule': [0], 'unpaired_parent': None}{'dependencies': [], 'internal_count': 0, 'leaves': [], 'levels': [], 'schedule': [], 'unpaired_parent': None}Failed
regression certificate 2{'dependencies': [], 'internal_count': 0, 'leaves': [0], 'levels': [[0, 0]], 'schedule': [0], 'unpaired_parent': None}{'dependencies': [], 'internal_count': 0, 'leaves': [0], 'levels': [[0, 0]], 'schedule': [], 'unpaired_parent': None}Failed
regression certificate 3{'dependencies': [], 'internal_count': 1, 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'schedule': [1, 0], 'unpaired_parent': 0}{'dependencies': [], 'internal_count': 1, 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'schedule': [0], 'unpaired_parent': 0}Failed
regression certificate 4{'dependencies': [[1, 0]], 'internal_count': 2, 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'schedule': [2, 1, 0], 'unpaired_parent': None}{'dependencies': [[1, 0]], 'internal_count': 2, 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'schedule': [1, 0], 'unpaired_parent': None}Failed
regression certificate 5{'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4, 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'schedule': [4, 3, 2, 1, 0], 'unpaired_parent': 3}{'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4, 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'schedule': [3, 2, 1, 0], 'unpaired_parent': 3}Failed
regression certificate 6{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7, 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'unpaired_parent': None}{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7, 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'schedule': [6, 5, 4, 3, 2, 1, 0], 'unpaired_parent': None}Failed
variant-dependent certificate{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8, 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'unpaired_parent': 7}{'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8, 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'unpaired_parent': 7}Failed

SHA-256 / 325828af8f9b8b2ba029ba5756865b0523b16a8d4f31bf8aa0aef98622206687

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.

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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 2026-09-29T14:43:32.796096+00:00.

Case digest / c58997bd1aab3fc705bb0ba3926a4d4ef7395506198a30d64dbc3577dba176b5