FAILURE MAP
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FA-41061 / Heap invariants / Open access

Twin heap minimum is read from the surviving min-side head · case 01

The bounded twin heap delete certificate reports an incorrect minimum.

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

ROOT CAUSE

Twin heap minimum is read from the surviving min-side head.

VERIFIED REPAIR

Derive minimum using live[low[0]] if low else None under the stated bounded certificate contract.

Unsuccessful approach: The local patch uses low[0] if low 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[mn[0]] if mn else None,
    'maximum': live[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': 2, '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': 1, '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': 1, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}{'cross_index': [0], 'max_ids': ['a'], 'maximum': 1, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}Passed
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 / be80377ed3da750d4001ba55e2c9bae5dd16806b84d8d7253c93c585236f4c2e

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': low[0] if low else None,
    'maximum': live[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': 5, 'min_ids': ['b'], 'minimum': 'b', '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': 1, 'min_ids': ['a'], 'minimum': 'a', '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': 'b', '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': 8, 'min_ids': ['a', 'c', 'b'], 'minimum': 'a', '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': 7, 'min_ids': ['b', 'd', 'a'], 'minimum': 'b', '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': 7, 'min_ids': ['variant', 'b', 'd', 'a'], 'minimum': 'variant', '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 / 57e8063441a8e76d7199f8b37e3c061cabb6f1e158c0fb1ccc80363437ce4f3c

3 / The verified repair

Exit 0
"""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[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': 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': 1, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}{'cross_index': [0], 'max_ids': ['a'], 'maximum': 1, 'min_ids': ['a'], 'minimum': 1, 'records': {'a': 1}}Passed
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 / 082741e589c21f8ac63cf683904d1e34829f3fac750f637268f5553aeb78afb1

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 2026-09-29T14:43:37.218276+00:00.

Case digest / b669548a18cb128879e6f4871befb0e67ea0646e5e1f8fcbe63602c543888850