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FA-40311 / Heap invariants / Open access

Heap resolution combines owner and generation checks to prevent ABA aliasing · case 01

The bounded handle generation certificate reports an incorrect resolved.

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

ROOT CAUSE

Heap resolution combines owner and generation checks to prevent ABA aliasing.

THE FAILURE

Heap resolution combines owner and generation checks to prevent ABA aliasing.

Unsuccessful approach: The local patch uses [slots[h[0]][2] if live(h) and gen(h) else None for h in hs] and still violates the stated relation.

Case contract

A heap handle is [slot,generation,owner]. A slot table stores [live,generation,payload]. A handle resolves only for matching owner, in-range slot, live slot, and exact generation. Inspect each supplied handle; return per-handle ownership, bounds, liveness, generation match, resolution, and next generation after recycling each slot. Missing resolution is None.

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):
    owner=d['owner']; slots=d['slots']; hs=d['handles']
    def bounds(h): return 0<=h[0]<len(slots)
    def live(h): return bounds(h) and slots[h[0]][0]
    def gen(h): return bounds(h) and slots[h[0]][1]==h[1]
    return {'owners': [h[2]==owner for h in hs],
    'bounds': [bounds(h) for h in hs],
    'live': [live(h) for h in hs],
    'generation': [gen(h) for h in hs],
    'resolved': [slots[h[0]][2] if h[2]==owner and live(h) else None for h in hs],
    'recycle': [x[1]+1 for x in slots]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 10, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [True, False, False], 'resolved': ['z', None, None], 'recycle': [11]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 11, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [12]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 12, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [13]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 13, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [14]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 14, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [15]})]][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{'bounds': [False, False], 'generation': [False, False], 'live': [False, False], 'owners': [True, True], 'recycle': [], 'resolved': [None, None]}{'bounds': [False, False], 'generation': [False, False], 'live': [False, False], 'owners': [True, True], 'recycle': [], 'resolved': [None, None]}Passed
regression certificate 2{'bounds': [True, True], 'generation': [True, True], 'live': [True, True], 'owners': [True, False], 'recycle': [1], 'resolved': [0, None]}{'bounds': [True, True], 'generation': [True, True], 'live': [True, True], 'owners': [True, False], 'recycle': [1], 'resolved': [0, None]}Passed
regression certificate 3{'bounds': [True, True], 'generation': [True, False], 'live': [False, False], 'owners': [True, True], 'recycle': [4], 'resolved': [None, None]}{'bounds': [True, True], 'generation': [True, False], 'live': [False, False], 'owners': [True, True], 'recycle': [4], 'resolved': [None, None]}Passed
regression certificate 4{'bounds': [True, True, True], 'generation': [False, True, True], 'live': [True, True, True], 'owners': [True, True, False], 'recycle': [5, 9], 'resolved': ['a', 'b', None]}{'bounds': [True, True, True], 'generation': [False, True, True], 'live': [True, True, True], 'owners': [True, True, False], 'recycle': [5, 9], 'resolved': [None, 'b', None]}Failed
regression certificate 5{'bounds': [True, True, False], 'generation': [True, True, False], 'live': [True, False, False], 'owners': [True, True, True], 'recycle': [2, 3], 'resolved': ['', None, None]}{'bounds': [True, True, False], 'generation': [True, True, False], 'live': [True, False, False], 'owners': [True, True, True], 'recycle': [2, 3], 'resolved': ['', None, None]}Passed
regression certificate 6{'bounds': [True, True, False], 'generation': [False, True, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [10], 'resolved': ['z', 'z', None]}{'bounds': [True, True, False], 'generation': [False, True, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [10], 'resolved': [None, 'z', None]}Failed
variant-dependent certificate{'bounds': [True, True, False], 'generation': [True, False, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [11], 'resolved': ['z', 'z', None]}{'bounds': [True, True, False], 'generation': [True, False, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [11], 'resolved': ['z', None, None]}Failed

SHA-256 / 3d2f709db6ee78cd5b0eb546a54a321d343290f82b397bf11eefc9138bc71d5c

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    owner=d['owner']; slots=d['slots']; hs=d['handles']
    def bounds(h): return 0<=h[0]<len(slots)
    def live(h): return bounds(h) and slots[h[0]][0]
    def gen(h): return bounds(h) and slots[h[0]][1]==h[1]
    return {'owners': [h[2]==owner for h in hs],
    'bounds': [bounds(h) for h in hs],
    'live': [live(h) for h in hs],
    'generation': [gen(h) for h in hs],
    'resolved': [slots[h[0]][2] if live(h) and gen(h) else None for h in hs],
    'recycle': [x[1]+1 for x in slots]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 10, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [True, False, False], 'resolved': ['z', None, None], 'recycle': [11]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 11, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [12]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 12, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [13]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 13, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [14]})], [({'owner': 2, 'slots': [], 'handles': [[0, 0, 2], [-1, 0, 2]]}, {'owners': [True, True], 'bounds': [False, False], 'live': [False, False], 'generation': [False, False], 'resolved': [None, None], 'recycle': []}), ({'owner': 2, 'slots': [[True, 0, 0]], 'handles': [[0, 0, 2], [0, 0, 1]]}, {'owners': [True, False], 'bounds': [True, True], 'live': [True, True], 'generation': [True, True], 'resolved': [0, None], 'recycle': [1]}), ({'owner': 2, 'slots': [[False, 3, 'x']], 'handles': [[0, 3, 2], [0, 2, 2]]}, {'owners': [True, True], 'bounds': [True, True], 'live': [False, False], 'generation': [True, False], 'resolved': [None, None], 'recycle': [4]}), ({'owner': 2, 'slots': [[True, 4, 'a'], [True, 8, 'b']], 'handles': [[0, 3, 2], [1, 8, 2], [1, 8, 3]]}, {'owners': [True, True, False], 'bounds': [True, True, True], 'live': [True, True, True], 'generation': [False, True, True], 'resolved': [None, 'b', None], 'recycle': [5, 9]}), ({'owner': 2, 'slots': [[True, 1, ''], [False, 2, 5]], 'handles': [[0, 1, 2], [1, 2, 2], [-1, 2, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, False, False], 'generation': [True, True, False], 'resolved': ['', None, None], 'recycle': [2, 3]}), ({'owner': 2, 'slots': [[True, 9, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, True, False], 'resolved': [None, 'z', None], 'recycle': [10]}), ({'owner': 2, 'slots': [[True, 14, 'z']], 'handles': [[0, 10, 2], [0, 9, 2], [1, 9, 2]]}, {'owners': [True, True, True], 'bounds': [True, True, False], 'live': [True, True, False], 'generation': [False, False, False], 'resolved': [None, None, None], 'recycle': [15]})]][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{'bounds': [False, False], 'generation': [False, False], 'live': [False, False], 'owners': [True, True], 'recycle': [], 'resolved': [None, None]}{'bounds': [False, False], 'generation': [False, False], 'live': [False, False], 'owners': [True, True], 'recycle': [], 'resolved': [None, None]}Passed
regression certificate 2{'bounds': [True, True], 'generation': [True, True], 'live': [True, True], 'owners': [True, False], 'recycle': [1], 'resolved': [0, 0]}{'bounds': [True, True], 'generation': [True, True], 'live': [True, True], 'owners': [True, False], 'recycle': [1], 'resolved': [0, None]}Failed
regression certificate 3{'bounds': [True, True], 'generation': [True, False], 'live': [False, False], 'owners': [True, True], 'recycle': [4], 'resolved': [None, None]}{'bounds': [True, True], 'generation': [True, False], 'live': [False, False], 'owners': [True, True], 'recycle': [4], 'resolved': [None, None]}Passed
regression certificate 4{'bounds': [True, True, True], 'generation': [False, True, True], 'live': [True, True, True], 'owners': [True, True, False], 'recycle': [5, 9], 'resolved': [None, 'b', 'b']}{'bounds': [True, True, True], 'generation': [False, True, True], 'live': [True, True, True], 'owners': [True, True, False], 'recycle': [5, 9], 'resolved': [None, 'b', None]}Failed
regression certificate 5{'bounds': [True, True, False], 'generation': [True, True, False], 'live': [True, False, False], 'owners': [True, True, True], 'recycle': [2, 3], 'resolved': ['', None, None]}{'bounds': [True, True, False], 'generation': [True, True, False], 'live': [True, False, False], 'owners': [True, True, True], 'recycle': [2, 3], 'resolved': ['', None, None]}Passed
regression certificate 6{'bounds': [True, True, False], 'generation': [False, True, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [10], 'resolved': [None, 'z', None]}{'bounds': [True, True, False], 'generation': [False, True, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [10], 'resolved': [None, 'z', None]}Passed
variant-dependent certificate{'bounds': [True, True, False], 'generation': [True, False, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [11], 'resolved': ['z', None, None]}{'bounds': [True, True, False], 'generation': [True, False, False], 'live': [True, True, False], 'owners': [True, True, True], 'recycle': [11], 'resolved': ['z', None, None]}Passed

SHA-256 / fb10c5888583b830d09f1a11fd4806227ae2e00523fc562e85a5b03ea2ad68b8

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 2026-09-29T14:43:29.942491+00:00.

Case digest / 858a991ca349e1d33241280d50f9dc6dd3dd4fcae57f4ba5d4657c536707b829