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FA-40571 / Heap invariants / Open access

Weak join performs a strict improvement swap without reversing equal keys · case 01

The bounded weak join certificate reports an incorrect swapped.

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

ROOT CAUSE

Weak join performs a strict improvement swap without reversing equal keys.

THE FAILURE

Weak join performs a strict improvement swap without reversing equal keys.

Unsuccessful approach: The local patch uses a[j]>a[i] and still violates the stated relation.

Case contract

A weak-heap join receives keys, reverse bits, ancestor i and distinct descendant j. When keys[j]<keys[i], swap these keys and flip only reverse[j]; on equality do nothing. Return resulting keys, reversal bits, swapped status, winning key, changed reversal index, and comparison count.

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):
    a=d['keys']; r=d['reverse']; i=d['i']; j=d['j']; swap=a[j]<a[i]; out=list(a); bits=list(r)
    if swap: out[i],out[j]=out[j],out[i]; bits[j]^=1
    return {'keys': out,
    'bits': bits,
    'swapped': a[j]<=a[i],
    'winner_key': out[i],
    'flipped': j if swap else None,
    'comparisons': 1}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 4], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 4], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 3], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 3], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 2], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 2], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 1], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 1, 3, 4, 2], 'bits': [0, 1, 0, 1, 1], 'swapped': True, 'winner_key': 1, 'flipped': 4, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 0], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 0, 3, 4, 2], 'bits': [0, 1, 0, 1, 1], 'swapped': True, 'winner_key': 0, 'flipped': 4, 'comparisons': 1})]][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{'bits': [0, 1], 'comparisons': 1, 'flipped': 1, 'keys': [2, 4], 'swapped': True, 'winner_key': 2}{'bits': [0, 1], 'comparisons': 1, 'flipped': 1, 'keys': [2, 4], 'swapped': True, 'winner_key': 2}Passed
regression certificate 2{'bits': [0, 1], 'comparisons': 1, 'flipped': None, 'keys': [1, 7], 'swapped': False, 'winner_key': 1}{'bits': [0, 1], 'comparisons': 1, 'flipped': None, 'keys': [1, 7], 'swapped': False, 'winner_key': 1}Passed
regression certificate 3{'bits': [0, 0], 'comparisons': 1, 'flipped': None, 'keys': [3, 3], 'swapped': True, 'winner_key': 3}{'bits': [0, 0], 'comparisons': 1, 'flipped': None, 'keys': [3, 3], 'swapped': False, 'winner_key': 3}Failed
regression certificate 4{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 3, 'keys': [0, 2, 5, 8], 'swapped': True, 'winner_key': 2}{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 3, 'keys': [0, 2, 5, 8], 'swapped': True, 'winner_key': 2}Passed
regression certificate 5{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 2, 'keys': [7, 1, 9, 3], 'swapped': True, 'winner_key': 7}{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 2, 'keys': [7, 1, 9, 3], 'swapped': True, 'winner_key': 7}Passed
regression certificate 6{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 5], 'swapped': False, 'winner_key': 2}{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 5], 'swapped': False, 'winner_key': 2}Passed
variant-dependent certificate{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 4], 'swapped': False, 'winner_key': 2}{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 4], 'swapped': False, 'winner_key': 2}Passed

SHA-256 / ab22b3f1af5e6030b4c1cfb484f75795297a05f6640bba7b67305ee4428eeba7

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    a=d['keys']; r=d['reverse']; i=d['i']; j=d['j']; swap=a[j]<a[i]; out=list(a); bits=list(r)
    if swap: out[i],out[j]=out[j],out[i]; bits[j]^=1
    return {'keys': out,
    'bits': bits,
    'swapped': a[j]>a[i],
    'winner_key': out[i],
    'flipped': j if swap else None,
    'comparisons': 1}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 4], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 4], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 3], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 3], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 2], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 2], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 1], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 1, 3, 4, 2], 'bits': [0, 1, 0, 1, 1], 'swapped': True, 'winner_key': 1, 'flipped': 4, 'comparisons': 1})], [({'keys': [4, 2], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [2, 4], 'bits': [0, 1], 'swapped': True, 'winner_key': 2, 'flipped': 1, 'comparisons': 1}), ({'keys': [1, 7], 'reverse': [0, 1], 'i': 0, 'j': 1}, {'keys': [1, 7], 'bits': [0, 1], 'swapped': False, 'winner_key': 1, 'flipped': None, 'comparisons': 1}), ({'keys': [3, 3], 'reverse': [0, 0], 'i': 0, 'j': 1}, {'keys': [3, 3], 'bits': [0, 0], 'swapped': False, 'winner_key': 3, 'flipped': None, 'comparisons': 1}), ({'keys': [0, 8, 5, 2], 'reverse': [0, 1, 0, 1], 'i': 1, 'j': 3}, {'keys': [0, 2, 5, 8], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 2, 'flipped': 3, 'comparisons': 1}), ({'keys': [9, 1, 7, 3], 'reverse': [0, 1, 1, 0], 'i': 0, 'j': 2}, {'keys': [7, 1, 9, 3], 'bits': [0, 1, 0, 0], 'swapped': True, 'winner_key': 7, 'flipped': 2, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 5], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 2, 3, 4, 5], 'bits': [0, 1, 0, 1, 0], 'swapped': False, 'winner_key': 2, 'flipped': None, 'comparisons': 1}), ({'keys': [1, 2, 3, 4, 0], 'reverse': [0, 1, 0, 1, 0], 'i': 1, 'j': 4}, {'keys': [1, 0, 3, 4, 2], 'bits': [0, 1, 0, 1, 1], 'swapped': True, 'winner_key': 0, 'flipped': 4, 'comparisons': 1})]][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{'bits': [0, 1], 'comparisons': 1, 'flipped': 1, 'keys': [2, 4], 'swapped': False, 'winner_key': 2}{'bits': [0, 1], 'comparisons': 1, 'flipped': 1, 'keys': [2, 4], 'swapped': True, 'winner_key': 2}Failed
regression certificate 2{'bits': [0, 1], 'comparisons': 1, 'flipped': None, 'keys': [1, 7], 'swapped': True, 'winner_key': 1}{'bits': [0, 1], 'comparisons': 1, 'flipped': None, 'keys': [1, 7], 'swapped': False, 'winner_key': 1}Failed
regression certificate 3{'bits': [0, 0], 'comparisons': 1, 'flipped': None, 'keys': [3, 3], 'swapped': False, 'winner_key': 3}{'bits': [0, 0], 'comparisons': 1, 'flipped': None, 'keys': [3, 3], 'swapped': False, 'winner_key': 3}Passed
regression certificate 4{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 3, 'keys': [0, 2, 5, 8], 'swapped': False, 'winner_key': 2}{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 3, 'keys': [0, 2, 5, 8], 'swapped': True, 'winner_key': 2}Failed
regression certificate 5{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 2, 'keys': [7, 1, 9, 3], 'swapped': False, 'winner_key': 7}{'bits': [0, 1, 0, 0], 'comparisons': 1, 'flipped': 2, 'keys': [7, 1, 9, 3], 'swapped': True, 'winner_key': 7}Failed
regression certificate 6{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 5], 'swapped': True, 'winner_key': 2}{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 5], 'swapped': False, 'winner_key': 2}Failed
variant-dependent certificate{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 4], 'swapped': True, 'winner_key': 2}{'bits': [0, 1, 0, 1, 0], 'comparisons': 1, 'flipped': None, 'keys': [1, 2, 3, 4, 4], 'swapped': False, 'winner_key': 2}Failed

SHA-256 / b10391d8345bbafe01b956f6569a9faec30c7690fc8eb50351eade09b1edb261

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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.

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Verification & scope

A stipulated offline diagnostic model; it does not implement a production allocator, concurrency protocol, or complete heap library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:43:32.484968+00:00.

Case digest / 6b15a6c253956fa6c22e71cc580bb90f64470dc884ff0dccf6da88b721b19296