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FA-41011 / Heap invariants / Open access

Heap meld ownership follows the full representative chain · case 01

The bounded meld ownership certificate reports an incorrect representatives.

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

ROOT CAUSE

Heap meld ownership follows the full representative chain.

THE FAILURE

Heap meld ownership follows the full representative chain.

Unsuccessful approach: The local patch uses [parents[dest],parents[src]] and still violates the stated relation.

Case contract

A destructive heap meld uses owner union representatives. Parent mapping owner->owner is acyclic and includes every referenced owner. Merge source representative into destination representative; source wrapper becomes empty but live handles from either representative remain resolvable through the union. Report representatives before meld, parent mapping after meld, source size, destination size, accepted handle owners, and whether self-component meld is a no-op.

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):
    parents=d['parents']; dest=d['dest']; src=d['src']
    def find(x):
        while parents[x]!=x: x=parents[x]
        return x
    rd=find(dest); rs=find(src); out=dict(parents)
    if rs!=rd: out[rs]=rd
    return {'representatives': [dest,src],
    'union': out,
    'source_size': d["source_size"] if rs==rd else 0,
    'destination_size': d["dest_size"] if rs==rd else d["dest_size"]+d["source_size"],
    'accepted': [x for x in d["handles"] if find(x) in (rd,rs)],
    'noop': rd==rs}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 3, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 3, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 4, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 4, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 6, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 6, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 7, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 7, 'accepted': ['a', 'b'], 'noop': False})]][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{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'b'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a'}}{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'b'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a'}}Passed
regression certificate 2{'accepted': ['a'], 'destination_size': 4, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 4, 'union': {'a': 'a'}}{'accepted': ['a'], 'destination_size': 4, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 4, 'union': {'a': 'a'}}Passed
regression certificate 3{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['c', 'd'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}}{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'd'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}}Failed
regression certificate 4{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': True, 'representatives': ['a', 'b'], 'source_size': 5, 'union': {'a': 'a', 'b': 'a', 'c': 'c'}}{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 5, 'union': {'a': 'a', 'b': 'a', 'c': 'c'}}Failed
regression certificate 5{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'd'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}}{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'b'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}}Failed
regression certificate 6{'accepted': ['a', 'b'], 'destination_size': 2, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}{'accepted': ['a', 'b'], 'destination_size': 2, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}Passed
variant-dependent certificate{'accepted': ['a', 'b'], 'destination_size': 3, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}{'accepted': ['a', 'b'], 'destination_size': 3, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}Passed

SHA-256 / bcb7653baef51479af4d3ae017a7bd98f5fa063069d53c6c603ed1893ef0535b

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    parents=d['parents']; dest=d['dest']; src=d['src']
    def find(x):
        while parents[x]!=x: x=parents[x]
        return x
    rd=find(dest); rs=find(src); out=dict(parents)
    if rs!=rd: out[rs]=rd
    return {'representatives': [parents[dest],parents[src]],
    'union': out,
    'source_size': d["source_size"] if rs==rd else 0,
    'destination_size': d["dest_size"] if rs==rd else d["dest_size"]+d["source_size"],
    'accepted': [x for x in d["handles"] if find(x) in (rd,rs)],
    'noop': rd==rs}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 3, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 3, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 4, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 4, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 6, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 6, 'accepted': ['a', 'b'], 'noop': False})], [({'parents': {'a': 'a', 'b': 'b'}, 'dest': 'a', 'src': 'b', 'dest_size': 2, 'source_size': 3, 'handles': ['a', 'b']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a'}, 'dest': 'a', 'src': 'a', 'dest_size': 4, 'source_size': 4, 'handles': ['a']}, {'representatives': ['a', 'a'], 'union': {'a': 'a'}, 'source_size': 4, 'destination_size': 4, 'accepted': ['a'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'd'}, 'dest': 'c', 'src': 'd', 'dest_size': 3, 'source_size': 2, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'd'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'a', 'c': 'c'}, 'dest': 'a', 'src': 'b', 'dest_size': 5, 'source_size': 5, 'handles': ['a', 'b', 'c']}, {'representatives': ['a', 'a'], 'union': {'a': 'a', 'b': 'a', 'c': 'c'}, 'source_size': 5, 'destination_size': 5, 'accepted': ['a', 'b'], 'noop': True}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'b', 'd': 'c'}, 'dest': 'a', 'src': 'd', 'dest_size': 1, 'source_size': 4, 'handles': ['a', 'b', 'c', 'd']}, {'representatives': ['a', 'b'], 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}, 'source_size': 0, 'destination_size': 5, 'accepted': ['a', 'b', 'c', 'd'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 2, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 2, 'accepted': ['a', 'b'], 'noop': False}), ({'parents': {'a': 'a', 'b': 'b', 'c': 'c'}, 'dest': 'b', 'src': 'a', 'dest_size': 0, 'source_size': 7, 'handles': ['a', 'b', 'c']}, {'representatives': ['b', 'a'], 'union': {'a': 'b', 'b': 'b', 'c': 'c'}, 'source_size': 0, 'destination_size': 7, 'accepted': ['a', 'b'], 'noop': False})]][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{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'b'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a'}}{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'b'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a'}}Passed
regression certificate 2{'accepted': ['a'], 'destination_size': 4, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 4, 'union': {'a': 'a'}}{'accepted': ['a'], 'destination_size': 4, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 4, 'union': {'a': 'a'}}Passed
regression certificate 3{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['b', 'd'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}}{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'd'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'a'}}Failed
regression certificate 4{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 5, 'union': {'a': 'a', 'b': 'a', 'c': 'c'}}{'accepted': ['a', 'b'], 'destination_size': 5, 'noop': True, 'representatives': ['a', 'a'], 'source_size': 5, 'union': {'a': 'a', 'b': 'a', 'c': 'c'}}Passed
regression certificate 5{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'c'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}}{'accepted': ['a', 'b', 'c', 'd'], 'destination_size': 5, 'noop': False, 'representatives': ['a', 'b'], 'source_size': 0, 'union': {'a': 'a', 'b': 'a', 'c': 'b', 'd': 'c'}}Failed
regression certificate 6{'accepted': ['a', 'b'], 'destination_size': 2, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}{'accepted': ['a', 'b'], 'destination_size': 2, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}Passed
variant-dependent certificate{'accepted': ['a', 'b'], 'destination_size': 3, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}{'accepted': ['a', 'b'], 'destination_size': 3, 'noop': False, 'representatives': ['b', 'a'], 'source_size': 0, 'union': {'a': 'b', 'b': 'b', 'c': 'c'}}Passed

SHA-256 / a7f3071f292426e46066bb7627088675d51a8ee08fb064a194959aca1f4597a7

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 2026-09-29T14:43:36.905381+00:00.

Case digest / 62ca864a6752ad5c9402b1bd1cd78fb10ede9aed17ff3d459d8a10fc1d05ae93