FAILURE MAP
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FA-41066 / Heap invariants / Open access

Twin heap maximum is read from the surviving max-side head · case 01

The bounded twin heap delete certificate reports an incorrect maximum.

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

ROOT CAUSE

Twin heap maximum is read from the surviving max-side head.

THE FAILURE

Twin heap maximum is read from the surviving max-side head.

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

Case contract

A double-ended heap certificate has min-order ids, max-order ids, and unique live records id->priority. Erase id x from both heaps by identity, preserving surviving order for this logical model. Report min ids, max ids, live map, cross-index mapping from surviving min slots to max slots, next minimum, and next maximum. Equal priorities retain separate identities.

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):
    mn=d['min']; mx=d['max']; live=d['live']; x=d['erase']; low=[i for i in mn if i!=x]; high=[i for i in mx if i!=x]; remain={i:p for i,p in live.items() if i!=x}
    return {'min_ids': low,
    'max_ids': high,
    'records': remain,
    'cross_index': [high.index(i) for i in low],
    'minimum': live[low[0]] if low else None,
    'maximum': live[mx[0]] if mx else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 1}, 'min': ['variant', 'b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['variant', 'b', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}, 'cross_index': [3, 2, 1, 0], 'minimum': 1, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 2}, 'min': ['b', 'variant', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['b', 'variant', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 2}, 'cross_index': [2, 3, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 3}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'd', 'variant', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'd', 'variant', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 3}, 'cross_index': [3, 1, 2, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 4}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 4}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 5}, 'min': ['b', 'd', 'c', 'variant', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 5}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})]][N-1]
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{'cross_index': [], 'max_ids': [], 'maximum': 2, 'min_ids': [], 'minimum': None, 'records': {}}{'cross_index': [], 'max_ids': [], 'maximum': None, 'min_ids': [], 'minimum': None, 'records': {}}Failed
regression certificate 2{'cross_index': [0], 'max_ids': ['b'], 'maximum': 5, 'min_ids': ['b'], 'minimum': 5, 'records': {'b': 5}}{'cross_index': [0], 'max_ids': ['b'], 'maximum': 5, 'min_ids': ['b'], 'minimum': 5, 'records': {'b': 5}}Passed
regression certificate 3{'cross_index': [0], 'max_ids': ['a'], 'maximum': 5, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}{'cross_index': [0], 'max_ids': ['a'], 'maximum': 1, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}Failed
regression certificate 4{'cross_index': [1, 0], 'max_ids': ['c', 'b'], 'maximum': 6, 'min_ids': ['b', 'c'], 'minimum': 3, 'records': {'b': 3, 'c': 6}}{'cross_index': [1, 0], 'max_ids': ['c', 'b'], 'maximum': 6, 'min_ids': ['b', 'c'], 'minimum': 3, 'records': {'b': 3, 'c': 6}}Passed
regression certificate 5{'cross_index': [2, 1, 0], 'max_ids': ['b', 'c', 'a'], 'maximum': 8, 'min_ids': ['a', 'c', 'b'], 'minimum': 1, 'records': {'a': 1, 'b': 8, 'c': 3}}{'cross_index': [2, 1, 0], 'max_ids': ['b', 'c', 'a'], 'maximum': 8, 'min_ids': ['a', 'c', 'b'], 'minimum': 1, 'records': {'a': 1, 'b': 8, 'c': 3}}Passed
regression certificate 6{'cross_index': [2, 1, 0], 'max_ids': ['a', 'd', 'b'], 'maximum': 7, 'min_ids': ['b', 'd', 'a'], 'minimum': 2, 'records': {'a': 7, 'b': 2, 'd': 3}}{'cross_index': [2, 1, 0], 'max_ids': ['a', 'd', 'b'], 'maximum': 7, 'min_ids': ['b', 'd', 'a'], 'minimum': 2, 'records': {'a': 7, 'b': 2, 'd': 3}}Passed
variant-dependent certificate{'cross_index': [3, 2, 1, 0], 'max_ids': ['a', 'd', 'b', 'variant'], 'maximum': 7, 'min_ids': ['variant', 'b', 'd', 'a'], 'minimum': 1, 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}}{'cross_index': [3, 2, 1, 0], 'max_ids': ['a', 'd', 'b', 'variant'], 'maximum': 7, 'min_ids': ['variant', 'b', 'd', 'a'], 'minimum': 1, 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}}Passed

SHA-256 / d63401b1928a257a29b800dcf62679d58c6fee56b4ac99accb32d84222a4de27

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    mn=d['min']; mx=d['max']; live=d['live']; x=d['erase']; low=[i for i in mn if i!=x]; high=[i for i in mx if i!=x]; remain={i:p for i,p in live.items() if i!=x}
    return {'min_ids': low,
    'max_ids': high,
    'records': remain,
    'cross_index': [high.index(i) for i in low],
    'minimum': live[low[0]] if low else None,
    'maximum': high[0] if high else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 1}, 'min': ['variant', 'b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['variant', 'b', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}, 'cross_index': [3, 2, 1, 0], 'minimum': 1, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 2}, 'min': ['b', 'variant', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b', 'variant'], 'erase': 'c'}, {'min_ids': ['b', 'variant', 'd', 'a'], 'max_ids': ['a', 'd', 'b', 'variant'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 2}, 'cross_index': [2, 3, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 3}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'd', 'variant', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'd', 'variant', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 3}, 'cross_index': [3, 1, 2, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 4}, 'min': ['b', 'd', 'variant', 'c', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 4}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})], [({'live': {'a': 2}, 'min': ['a'], 'max': ['a'], 'erase': 'a'}, {'min_ids': [], 'max_ids': [], 'records': {}, 'cross_index': [], 'minimum': None, 'maximum': None}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'a'}, {'min_ids': ['b'], 'max_ids': ['b'], 'records': {'b': 5}, 'cross_index': [0], 'minimum': 5, 'maximum': 5}), ({'live': {'a': 1, 'b': 5}, 'min': ['a', 'b'], 'max': ['b', 'a'], 'erase': 'b'}, {'min_ids': ['a'], 'max_ids': ['a'], 'records': {'a': 1}, 'cross_index': [0], 'minimum': 1, 'maximum': 1}), ({'live': {'a': 3, 'b': 3, 'c': 6}, 'min': ['a', 'b', 'c'], 'max': ['c', 'a', 'b'], 'erase': 'a'}, {'min_ids': ['b', 'c'], 'max_ids': ['c', 'b'], 'records': {'b': 3, 'c': 6}, 'cross_index': [1, 0], 'minimum': 3, 'maximum': 6}), ({'live': {'a': 1, 'b': 8, 'c': 3, 'd': 8}, 'min': ['a', 'c', 'b', 'd'], 'max': ['b', 'd', 'c', 'a'], 'erase': 'd'}, {'min_ids': ['a', 'c', 'b'], 'max_ids': ['b', 'c', 'a'], 'records': {'a': 1, 'b': 8, 'c': 3}, 'cross_index': [2, 1, 0], 'minimum': 1, 'maximum': 8}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3}, 'min': ['b', 'd', 'c', 'a'], 'max': ['a', 'c', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'a'], 'max_ids': ['a', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3}, 'cross_index': [2, 1, 0], 'minimum': 2, 'maximum': 7}), ({'live': {'a': 7, 'b': 2, 'c': 5, 'd': 3, 'variant': 5}, 'min': ['b', 'd', 'c', 'variant', 'a'], 'max': ['a', 'c', 'variant', 'd', 'b'], 'erase': 'c'}, {'min_ids': ['b', 'd', 'variant', 'a'], 'max_ids': ['a', 'variant', 'd', 'b'], 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 5}, 'cross_index': [3, 2, 1, 0], 'minimum': 2, 'maximum': 7})]][N-1]
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{'cross_index': [], 'max_ids': [], 'maximum': None, 'min_ids': [], 'minimum': None, 'records': {}}{'cross_index': [], 'max_ids': [], 'maximum': None, 'min_ids': [], 'minimum': None, 'records': {}}Passed
regression certificate 2{'cross_index': [0], 'max_ids': ['b'], 'maximum': 'b', 'min_ids': ['b'], 'minimum': 5, 'records': {'b': 5}}{'cross_index': [0], 'max_ids': ['b'], 'maximum': 5, 'min_ids': ['b'], 'minimum': 5, 'records': {'b': 5}}Failed
regression certificate 3{'cross_index': [0], 'max_ids': ['a'], 'maximum': 'a', 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}{'cross_index': [0], 'max_ids': ['a'], 'maximum': 1, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}Failed
regression certificate 4{'cross_index': [1, 0], 'max_ids': ['c', 'b'], 'maximum': 'c', 'min_ids': ['b', 'c'], 'minimum': 3, 'records': {'b': 3, 'c': 6}}{'cross_index': [1, 0], 'max_ids': ['c', 'b'], 'maximum': 6, 'min_ids': ['b', 'c'], 'minimum': 3, 'records': {'b': 3, 'c': 6}}Failed
regression certificate 5{'cross_index': [2, 1, 0], 'max_ids': ['b', 'c', 'a'], 'maximum': 'b', 'min_ids': ['a', 'c', 'b'], 'minimum': 1, 'records': {'a': 1, 'b': 8, 'c': 3}}{'cross_index': [2, 1, 0], 'max_ids': ['b', 'c', 'a'], 'maximum': 8, 'min_ids': ['a', 'c', 'b'], 'minimum': 1, 'records': {'a': 1, 'b': 8, 'c': 3}}Failed
regression certificate 6{'cross_index': [2, 1, 0], 'max_ids': ['a', 'd', 'b'], 'maximum': 'a', 'min_ids': ['b', 'd', 'a'], 'minimum': 2, 'records': {'a': 7, 'b': 2, 'd': 3}}{'cross_index': [2, 1, 0], 'max_ids': ['a', 'd', 'b'], 'maximum': 7, 'min_ids': ['b', 'd', 'a'], 'minimum': 2, 'records': {'a': 7, 'b': 2, 'd': 3}}Failed
variant-dependent certificate{'cross_index': [3, 2, 1, 0], 'max_ids': ['a', 'd', 'b', 'variant'], 'maximum': 'a', 'min_ids': ['variant', 'b', 'd', 'a'], 'minimum': 1, 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}}{'cross_index': [3, 2, 1, 0], 'max_ids': ['a', 'd', 'b', 'variant'], 'maximum': 7, 'min_ids': ['variant', 'b', 'd', 'a'], 'minimum': 1, 'records': {'a': 7, 'b': 2, 'd': 3, 'variant': 1}}Failed

SHA-256 / f7ce73685da1ca6ffcb66d769da9087d669745b7fb8e01ec5c9d729d1a7e3324

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 2026-09-29T14:43:37.247544+00:00.

Case digest / 8f97b8478f9f861bb9a49a466445e9fffc68b7eeec9fa04214f9f0e7d290cbc4