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FA-40876 / Heap invariants / Open access

Cyclic priority extraction selects an absolute active key rather than a stale or modulo minimum · case 01

The bounded dial window certificate reports an incorrect next.

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

ROOT CAUSE

Cyclic priority extraction selects an absolute active key rather than a stale or modulo minimum.

THE FAILURE

Cyclic priority extraction selects an absolute active key rather than a stale or modulo minimum.

Unsuccessful approach: The local patch uses min((x[1]%c for x in active),default=None) and still violates the stated relation.

Case contract

A cyclic integer bucket queue with ring size C stores entries [id,absolute_key]. Cursor is last extracted absolute key. Only keys in [cursor,cursor+C) are in the active window. Report physical bucket indices, expired ids, future-window ids, next active key, rotation distance, and active ids in absolute-key order. Same-slot values from later revolutions must not be delivered.

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['entries']; c=d['capacity']; cursor=d['cursor']; active=[x for x in a if cursor<=x[1]<cursor+c]; nxt=min((x[1] for x in active),default=None)
    return {'buckets': [[x[0],x[1]%c] for x in a],
    'expired': [x[0] for x in a if x[1]<cursor],
    'future': [x[0] for x in a if x[1]>=cursor+c],
    'next': min((x[1] for x in a),default=None),
    'advance': None if nxt is None else nxt-cursor,
    'active_order': [x[0] for x in sorted(active,key=lambda x:x[1])]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 8, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['c'], 'future': [], 'next': 8, 'advance': 0, 'active_order': ['b', 'a', 'd']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 9, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['b', 'c'], 'future': [], 'next': 9, 'advance': 0, 'active_order': ['a', 'd']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 10, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['a', 'b', 'c'], 'future': [], 'next': 14, 'advance': 4, 'active_order': ['d']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 11, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['a', 'b', 'c'], 'future': [], 'next': 14, 'advance': 3, 'active_order': ['d']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 12, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['a', 'b', 'c'], 'future': [], 'next': 14, 'advance': 2, 'active_order': ['d']})]][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{'active_order': [], 'advance': None, 'buckets': [], 'expired': [], 'future': [], 'next': None}{'active_order': [], 'advance': None, 'buckets': [], 'expired': [], 'future': [], 'next': None}Passed
regression certificate 2{'active_order': ['a', 'b'], 'advance': 1, 'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4}{'active_order': ['a', 'b'], 'advance': 1, 'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4}Passed
regression certificate 3{'active_order': ['b', 'a'], 'advance': 1, 'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 7}{'active_order': ['b', 'a'], 'advance': 1, 'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9}Failed
regression certificate 4{'active_order': ['c', 'b', 'a'], 'advance': 0, 'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4}{'active_order': ['c', 'b', 'a'], 'advance': 0, 'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4}Passed
regression certificate 5{'active_order': [], 'advance': None, 'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': 2}{'active_order': [], 'advance': None, 'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None}Failed
regression certificate 6{'active_order': ['c', 'b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7}{'active_order': ['c', 'b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7}Passed
variant-dependent certificate{'active_order': ['b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['c'], 'future': [], 'next': 7}{'active_order': ['b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['c'], 'future': [], 'next': 8}Failed

SHA-256 / b81aabf5771f59de746b9c6f31acf2b406f7b59809281dea34efe6eec73fa3f5

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    a=d['entries']; c=d['capacity']; cursor=d['cursor']; active=[x for x in a if cursor<=x[1]<cursor+c]; nxt=min((x[1] for x in active),default=None)
    return {'buckets': [[x[0],x[1]%c] for x in a],
    'expired': [x[0] for x in a if x[1]<cursor],
    'future': [x[0] for x in a if x[1]>=cursor+c],
    'next': min((x[1]%c for x in active),default=None),
    'advance': None if nxt is None else nxt-cursor,
    'active_order': [x[0] for x in sorted(active,key=lambda x:x[1])]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 8, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['c'], 'future': [], 'next': 8, 'advance': 0, 'active_order': ['b', 'a', 'd']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 9, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['b', 'c'], 'future': [], 'next': 9, 'advance': 0, 'active_order': ['a', 'd']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 10, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['a', 'b', 'c'], 'future': [], 'next': 14, 'advance': 4, 'active_order': ['d']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 11, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['a', 'b', 'c'], 'future': [], 'next': 14, 'advance': 3, 'active_order': ['d']})], [({'capacity': 4, 'cursor': 0, 'entries': []}, {'buckets': [], 'expired': [], 'future': [], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 4, 'cursor': 3, 'entries': [['a', 4], ['b', 5], ['c', 7]]}, {'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4, 'advance': 1, 'active_order': ['a', 'b']}), ({'capacity': 5, 'cursor': 8, 'entries': [['a', 12], ['b', 9], ['c', 7], ['d', 13]]}, {'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9, 'advance': 1, 'active_order': ['b', 'a']}), ({'capacity': 3, 'cursor': 4, 'entries': [['a', 6], ['b', 5], ['c', 4]]}, {'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4, 'advance': 0, 'active_order': ['c', 'b', 'a']}), ({'capacity': 4, 'cursor': 6, 'entries': [['a', 10], ['b', 2]]}, {'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None, 'advance': None, 'active_order': []}), ({'capacity': 8, 'cursor': 7, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7, 'advance': 0, 'active_order': ['c', 'b', 'a', 'd']}), ({'capacity': 8, 'cursor': 12, 'entries': [['a', 9], ['b', 8], ['c', 7], ['d', 14]]}, {'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['a', 'b', 'c'], 'future': [], 'next': 14, 'advance': 2, 'active_order': ['d']})]][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{'active_order': [], 'advance': None, 'buckets': [], 'expired': [], 'future': [], 'next': None}{'active_order': [], 'advance': None, 'buckets': [], 'expired': [], 'future': [], 'next': None}Passed
regression certificate 2{'active_order': ['a', 'b'], 'advance': 1, 'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 0}{'active_order': ['a', 'b'], 'advance': 1, 'buckets': [['a', 0], ['b', 1], ['c', 3]], 'expired': [], 'future': ['c'], 'next': 4}Failed
regression certificate 3{'active_order': ['b', 'a'], 'advance': 1, 'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 2}{'active_order': ['b', 'a'], 'advance': 1, 'buckets': [['a', 2], ['b', 4], ['c', 2], ['d', 3]], 'expired': ['c'], 'future': ['d'], 'next': 9}Failed
regression certificate 4{'active_order': ['c', 'b', 'a'], 'advance': 0, 'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 0}{'active_order': ['c', 'b', 'a'], 'advance': 0, 'buckets': [['a', 0], ['b', 2], ['c', 1]], 'expired': [], 'future': [], 'next': 4}Failed
regression certificate 5{'active_order': [], 'advance': None, 'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None}{'active_order': [], 'advance': None, 'buckets': [['a', 2], ['b', 2]], 'expired': ['b'], 'future': ['a'], 'next': None}Passed
regression certificate 6{'active_order': ['c', 'b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 0}{'active_order': ['c', 'b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': [], 'future': [], 'next': 7}Failed
variant-dependent certificate{'active_order': ['b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['c'], 'future': [], 'next': 0}{'active_order': ['b', 'a', 'd'], 'advance': 0, 'buckets': [['a', 1], ['b', 0], ['c', 7], ['d', 6]], 'expired': ['c'], 'future': [], 'next': 8}Failed

SHA-256 / ffae16bd4cdfc7a653dcd20935f59ad4d48dbf3b9166e52c091117534d69c8cc

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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 2026-09-29T14:43:35.463761+00:00.

Case digest / c5796ca5a22bab7e39e18a42269c549ba39e824893cd7d1a8bb54690e6128aad