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FA-40066 / Heap invariants / Open access

Binomial extraction recomputes minimum across old and promoted roots · case 01

The bounded binomial extract certificate reports an incorrect minimum.

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

ROOT CAUSE

Binomial extraction recomputes minimum across old and promoted roots.

THE FAILURE

Binomial extraction recomputes minimum across old and promoted roots.

Unsuccessful approach: The local patch uses merged[0][0] if merged else None and still violates the stated relation.

Case contract

Extracted binomial root children are [id,rank,key] in descending rank. Remaining roots are [id,rank,key]. Return promoted root order, parent resets, cardinality delta, remaining minimum, merge rank sequence, and removed handle. Reversal restores ascending rank order before union.

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):
    c=d['children']; r=d['remaining']; removed=d['removed']; merged=r+list(reversed(c))
    return {'promoted': [x[0] for x in reversed(c)],
    'parents': [[x[0],None] for x in c],
    'size_delta': -1,
    'minimum': min(r,key=lambda x:x[2])[0] if r else None,
    'merge_ranks': sorted(x[1] for x in merged),
    'live_handles': sorted(x[0] for x in merged)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 5], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 6], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 7], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 8], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 9], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})]][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{'live_handles': [], 'merge_ranks': [], 'minimum': None, 'parents': [], 'promoted': [], 'size_delta': -1}{'live_handles': [], 'merge_ranks': [], 'minimum': None, 'parents': [], 'promoted': [], 'size_delta': -1}Passed
regression certificate 2{'live_handles': [3], 'merge_ranks': [0], 'minimum': None, 'parents': [[3, None]], 'promoted': [3], 'size_delta': -1}{'live_handles': [3], 'merge_ranks': [0], 'minimum': 3, 'parents': [[3, None]], 'promoted': [3], 'size_delta': -1}Failed
regression certificate 3{'live_handles': [2, 3, 4, 7, 8], 'merge_ranks': [0, 0, 1, 2, 3], 'minimum': 7, 'parents': [[4, None], [3, None], [2, None]], 'promoted': [2, 3, 4], 'size_delta': -1}{'live_handles': [2, 3, 4, 7, 8], 'merge_ranks': [0, 0, 1, 2, 3], 'minimum': 7, 'parents': [[4, None], [3, None], [2, None]], 'promoted': [2, 3, 4], 'size_delta': -1}Passed
regression certificate 4{'live_handles': [5, 6, 8], 'merge_ranks': [0, 1, 2], 'minimum': 8, 'parents': [[6, None], [5, None]], 'promoted': [5, 6], 'size_delta': -1}{'live_handles': [5, 6, 8], 'merge_ranks': [0, 1, 2], 'minimum': 5, 'parents': [[6, None], [5, None]], 'promoted': [5, 6], 'size_delta': -1}Failed
regression certificate 5{'live_handles': [2, 5], 'merge_ranks': [0, 1], 'minimum': 2, 'parents': [], 'promoted': [], 'size_delta': -1}{'live_handles': [2, 5], 'merge_ranks': [0, 1], 'minimum': 2, 'parents': [], 'promoted': [], 'size_delta': -1}Passed
regression certificate 6{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}Passed
variant-dependent certificate{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}Passed

SHA-256 / 1612581f38acf99e0843e294b286c46c29655f18980b727eb866771452209296

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    c=d['children']; r=d['remaining']; removed=d['removed']; merged=r+list(reversed(c))
    return {'promoted': [x[0] for x in reversed(c)],
    'parents': [[x[0],None] for x in c],
    'size_delta': -1,
    'minimum': merged[0][0] if merged else None,
    'merge_ranks': sorted(x[1] for x in merged),
    'live_handles': sorted(x[0] for x in merged)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 5], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 6], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 7], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 8], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})], [({'children': [], 'remaining': [], 'removed': 9}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': None, 'merge_ranks': [], 'live_handles': []}), ({'children': [[3, 0, 7]], 'remaining': [], 'removed': 1}, {'promoted': [3], 'parents': [[3, None]], 'size_delta': -1, 'minimum': 3, 'merge_ranks': [0], 'live_handles': [3]}), ({'children': [[4, 2, 6], [3, 1, 5], [2, 0, 8]], 'remaining': [[7, 0, 4], [8, 3, 9]], 'removed': 1}, {'promoted': [2, 3, 4], 'parents': [[4, None], [3, None], [2, None]], 'size_delta': -1, 'minimum': 7, 'merge_ranks': [0, 0, 1, 2, 3], 'live_handles': [2, 3, 4, 7, 8]}), ({'children': [[6, 1, 3], [5, 0, 2]], 'remaining': [[8, 2, 7]], 'removed': 4}, {'promoted': [5, 6], 'parents': [[6, None], [5, None]], 'size_delta': -1, 'minimum': 5, 'merge_ranks': [0, 1, 2], 'live_handles': [5, 6, 8]}), ({'children': [], 'remaining': [[5, 0, 8], [2, 1, 1]], 'removed': 7}, {'promoted': [], 'parents': [], 'size_delta': -1, 'minimum': 2, 'merge_ranks': [0, 1], 'live_handles': [2, 5]}), ({'children': [[7, 1, 4], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]}), ({'children': [[7, 1, 9], [3, 0, 3]], 'remaining': [[6, 0, 3]], 'removed': 9}, {'promoted': [3, 7], 'parents': [[7, None], [3, None]], 'size_delta': -1, 'minimum': 6, 'merge_ranks': [0, 0, 1], 'live_handles': [3, 6, 7]})]][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{'live_handles': [], 'merge_ranks': [], 'minimum': None, 'parents': [], 'promoted': [], 'size_delta': -1}{'live_handles': [], 'merge_ranks': [], 'minimum': None, 'parents': [], 'promoted': [], 'size_delta': -1}Passed
regression certificate 2{'live_handles': [3], 'merge_ranks': [0], 'minimum': 3, 'parents': [[3, None]], 'promoted': [3], 'size_delta': -1}{'live_handles': [3], 'merge_ranks': [0], 'minimum': 3, 'parents': [[3, None]], 'promoted': [3], 'size_delta': -1}Passed
regression certificate 3{'live_handles': [2, 3, 4, 7, 8], 'merge_ranks': [0, 0, 1, 2, 3], 'minimum': 7, 'parents': [[4, None], [3, None], [2, None]], 'promoted': [2, 3, 4], 'size_delta': -1}{'live_handles': [2, 3, 4, 7, 8], 'merge_ranks': [0, 0, 1, 2, 3], 'minimum': 7, 'parents': [[4, None], [3, None], [2, None]], 'promoted': [2, 3, 4], 'size_delta': -1}Passed
regression certificate 4{'live_handles': [5, 6, 8], 'merge_ranks': [0, 1, 2], 'minimum': 8, 'parents': [[6, None], [5, None]], 'promoted': [5, 6], 'size_delta': -1}{'live_handles': [5, 6, 8], 'merge_ranks': [0, 1, 2], 'minimum': 5, 'parents': [[6, None], [5, None]], 'promoted': [5, 6], 'size_delta': -1}Failed
regression certificate 5{'live_handles': [2, 5], 'merge_ranks': [0, 1], 'minimum': 5, 'parents': [], 'promoted': [], 'size_delta': -1}{'live_handles': [2, 5], 'merge_ranks': [0, 1], 'minimum': 2, 'parents': [], 'promoted': [], 'size_delta': -1}Failed
regression certificate 6{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}Passed
variant-dependent certificate{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}{'live_handles': [3, 6, 7], 'merge_ranks': [0, 0, 1], 'minimum': 6, 'parents': [[7, None], [3, None]], 'promoted': [3, 7], 'size_delta': -1}Passed

SHA-256 / 3fd6f8b9d4af8ea678927d3ad7e4fa2d9402ec4a724410b6971db400a1d5f3e7

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 2026-09-29T14:43:27.478403+00:00.

Case digest / b51b4e4e842157828e4278b93931674b565abb59c33f225a995c03f48876ed22