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FA-41281 / Heap invariants / Open access

Rank-loss recomputation distinguishes equal from unequal child ranks · case 01

The bounded rank loss propagation certificate reports an incorrect computed.

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

ROOT CAUSE

Rank-loss recomputation distinguishes equal from unequal child ranks.

THE FAILURE

Rank-loss recomputation distinguishes equal from unequal child ranks.

Unsuccessful approach: The local patch uses [min(x[2],x[3])+1 for x in a] and still violates the stated relation.

Case contract

A stipulated rank-balanced heap repair trace supplies bottom-up nodes [id,stored_rank,left_rank,right_rank], with null child rank -1. Recomputed rank is max child rank if child ranks differ, otherwise child rank+1. A decrease propagates while computed rank is smaller, stopping at first unchanged node. Report local recomputed ranks, decreased ids, stopping id, new prefix ranks, rank drops, and visited count. This models the stated rule only, not every rank-pairing heap variant.

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['nodes']; actual=[max(x[2],x[3]) if x[2]!=x[3] else x[2]+1 for x in a]; changed=[]; stop=None; visited=0
    for x,r in zip(a,actual):
        visited+=1
        if r>=x[1]: stop=x[0]; break
        changed.append(x[0])
    return {'computed': [1+max(x[2],x[3]) for x in a],
    'decreased': changed,
    'stop': stop,
    'prefix_ranks': [r if x[0] in changed else x[1] for x,r in zip(a,actual)],
    'drops': [x[1]-r for x,r in zip(a,actual) if x[0] in changed],
    'visited': visited}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 5, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [2, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 6, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [3, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 7, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [4, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 8, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [5, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 9, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [6, 1], 'visited': 3})]][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{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}Passed
regression certificate 2{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}Passed
regression certificate 3{'computed': [1, 3, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}Failed
regression certificate 4{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}Passed
regression certificate 5{'computed': [1, 3, 4], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}Failed
regression certificate 6{'computed': [3, 4, 3, 2], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}Failed
variant-dependent certificate{'computed': [3, 4, 3, 2], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}Failed

SHA-256 / c94046366164da74abe6a73aeee33f36f9392bcb76fa2c4e64e6552b2ccd464b

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    a=d['nodes']; actual=[max(x[2],x[3]) if x[2]!=x[3] else x[2]+1 for x in a]; changed=[]; stop=None; visited=0
    for x,r in zip(a,actual):
        visited+=1
        if r>=x[1]: stop=x[0]; break
        changed.append(x[0])
    return {'computed': [min(x[2],x[3])+1 for x in a],
    'decreased': changed,
    'stop': stop,
    'prefix_ranks': [r if x[0] in changed else x[1] for x,r in zip(a,actual)],
    'drops': [x[1]-r for x,r in zip(a,actual) if x[0] in changed],
    'visited': visited}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 5, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [2, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 6, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [3, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 7, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [4, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 8, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [5, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 9, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [6, 1], 'visited': 3})]][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{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}Passed
regression certificate 2{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}Passed
regression certificate 3{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}Passed
regression certificate 4{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}Passed
regression certificate 5{'computed': [0, 1, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}Failed
regression certificate 6{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}Passed
variant-dependent certificate{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}Passed

SHA-256 / f79848a2f39c6b3407c287c4ad9542043327d4571abdddb7ef72ce2ad9a1b6aa

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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 2026-09-29T14:43:39.701760+00:00.

Case digest / e834f843f88b53ef558b4b67424a08b375387efcb212eae3905ee2b90e82564a