FAILURE MAP
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FA-39946 / Heap invariants / Open access

Pairing meld leaves a sibling link on the new root · case 01

The bounded pairing siblings certificate reports an incorrect root links.

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

ROOT CAUSE

A standalone root has no parent, previous, or sibling, including a link to node zero.

THE FAILURE

A standalone root has no parent, previous, or sibling, including a link to node zero.

Unsuccessful approach: The local patch uses [] if root==-1 else [k for k in (1,3,4) if a[root][k]>0] and still violates the stated relation.

Case contract

Pairing-tree certificate nodes are [key,parent,first_child,next_sibling,previous]. Missing links are -1. Previous denotes parent for first child, prior sibling otherwise. Report first-child backlinks, sibling-parent disagreements, previous-link disagreements, root sibling violations, direct heap-order violations, and child-chain degrees (stop on cycles).

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']; root=d['root']; chains=[]
    for i,x in enumerate(a):
        chain=[]; j=x[2]
        while j!=-1 and j not in chain:
            chain.append(j); j=a[j][3]
        chains.append(chain)
    return {'first_previous': [i for i,x in enumerate(a) if x[2]!=-1 and a[x[2]][4]!=i],
    'sibling_parent': [i for i,x in enumerate(a) if x[3]!=-1 and a[x[3]][1]!=x[1]],
    'sibling_previous': [i for i,x in enumerate(a) if x[3]!=-1 and a[x[3]][4]!=i],
    'root_links': [] if root==-1 else [k for k in (1,4) if a[root][k]!=-1],
    'child_order': [[i,j] for i,c in enumerate(chains) for j in c if a[j][0]<a[i][0]],
    'degrees': [len(c) for c in chains]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[9, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[10, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[11, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[12, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})]][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{'child_order': [], 'degrees': [], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Passed
regression certificate 2{'child_order': [], 'degrees': [0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Passed
regression certificate 3{'child_order': [], 'degrees': [2, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [2, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Passed
regression certificate 4{'child_order': [[0, 2]], 'degrees': [2, 0, 0], 'first_previous': [0], 'root_links': [], 'sibling_parent': [1], 'sibling_previous': [1]}{'child_order': [[0, 2]], 'degrees': [2, 0, 0], 'first_previous': [0], 'root_links': [], 'sibling_parent': [1], 'sibling_previous': [1]}Passed
regression certificate 5{'child_order': [], 'degrees': [0, 1, 0], 'first_previous': [1], 'root_links': [4], 'sibling_parent': [], 'sibling_previous': [1]}{'child_order': [], 'degrees': [0, 1, 0], 'first_previous': [1], 'root_links': [3, 4], 'sibling_parent': [], 'sibling_previous': [1]}Failed
regression certificate 6{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}Passed
variant-dependent certificate{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}Passed

SHA-256 / 3ea2f33a62bb1c8182bc8ba424237b2c4e264a920366b832286bb64c659ffca7

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']; root=d['root']; chains=[]
    for i,x in enumerate(a):
        chain=[]; j=x[2]
        while j!=-1 and j not in chain:
            chain.append(j); j=a[j][3]
        chains.append(chain)
    return {'first_previous': [i for i,x in enumerate(a) if x[2]!=-1 and a[x[2]][4]!=i],
    'sibling_parent': [i for i,x in enumerate(a) if x[3]!=-1 and a[x[3]][1]!=x[1]],
    'sibling_previous': [i for i,x in enumerate(a) if x[3]!=-1 and a[x[3]][4]!=i],
    'root_links': [] if root==-1 else [k for k in (1,3,4) if a[root][k]>0],
    'child_order': [[i,j] for i,c in enumerate(chains) for j in c if a[j][0]<a[i][0]],
    'degrees': [len(c) for c in chains]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[9, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[10, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[11, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})], [({'nodes': [], 'root': -1}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': []}), ({'nodes': [[2, -1, -1, -1, -1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [0]}), ({'nodes': [[1, -1, 1, -1, -1], [7, 0, -1, 2, 0], [3, 0, -1, -1, 1]], 'root': 0}, {'first_previous': [], 'sibling_parent': [], 'sibling_previous': [], 'root_links': [], 'child_order': [], 'degrees': [2, 0, 0]}), ({'nodes': [[8, -1, 1, -1, -1], [9, 0, -1, 2, -1], [2, 1, -1, -1, 0]], 'root': 0}, {'first_previous': [0], 'sibling_parent': [1], 'sibling_previous': [1], 'root_links': [], 'child_order': [[0, 2]], 'degrees': [2, 0, 0]}), ({'nodes': [[1, -1, -1, -1, -1], [4, -1, 2, 0, 0], [4, 1, -1, -1, -1]], 'root': 1}, {'first_previous': [1], 'sibling_parent': [], 'sibling_previous': [1], 'root_links': [3, 4], 'child_order': [], 'degrees': [0, 1, 0]}), ({'nodes': [[7, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0]}), ({'nodes': [[12, -1, 1, -1, -1], [2, 0, -1, 2, 0], [8, -1, -1, 3, -1], [1, 0, -1, -1, 0]], 'root': 0}, {'first_previous': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2], 'root_links': [], 'child_order': [[0, 1], [0, 2], [0, 3]], 'degrees': [3, 0, 0, 0]})]][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{'child_order': [], 'degrees': [], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Passed
regression certificate 2{'child_order': [], 'degrees': [0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Passed
regression certificate 3{'child_order': [], 'degrees': [2, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [2, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Passed
regression certificate 4{'child_order': [[0, 2]], 'degrees': [2, 0, 0], 'first_previous': [0], 'root_links': [], 'sibling_parent': [1], 'sibling_previous': [1]}{'child_order': [[0, 2]], 'degrees': [2, 0, 0], 'first_previous': [0], 'root_links': [], 'sibling_parent': [1], 'sibling_previous': [1]}Passed
regression certificate 5{'child_order': [], 'degrees': [0, 1, 0], 'first_previous': [1], 'root_links': [], 'sibling_parent': [], 'sibling_previous': [1]}{'child_order': [], 'degrees': [0, 1, 0], 'first_previous': [1], 'root_links': [3, 4], 'sibling_parent': [], 'sibling_previous': [1]}Failed
regression certificate 6{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}Passed
variant-dependent certificate{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [1, 2], 'sibling_previous': [1, 2]}Passed

SHA-256 / 4e7a23d78d63b126d36b1665a7ac9ab7b06a80ba3aa301098a9cd5dcb68fa914

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 2026-09-29T14:43:26.390185+00:00.

Case digest / b5f45c4401efd03de51b923f8c9b8cafe6137d72355ef42da122516129bda6bc