FAILURE MAP
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FA-39931 / Heap invariants / Open access

Pairing first child is assigned a null previous link · case 01

The bounded pairing siblings certificate reports an incorrect first previous.

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

ROOT CAUSE

Even a sole child stores its parent in the overloaded previous pointer.

THE FAILURE

Even a sole child stores its parent in the overloaded previous pointer.

Unsuccessful approach: The local patch uses [i for i,x in enumerate(a) if x[2]!=-1 and a[x[2]][4]!=i and a[x[2]][3]!=-1] 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]!=-1],
    '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]!=-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': [0], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}{'child_order': [], 'degrees': [2, 0, 0], 'first_previous': [], 'root_links': [], 'sibling_parent': [], 'sibling_previous': []}Failed
regression certificate 4{'child_order': [[0, 2]], 'degrees': [2, 0, 0], 'first_previous': [], '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]}Failed
regression certificate 5{'child_order': [], 'degrees': [0, 1, 0], 'first_previous': [], 'root_links': [3, 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': [0], '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]}Failed
variant-dependent certificate{'child_order': [[0, 1], [0, 3]], 'degrees': [3, 0, 0, 0], 'first_previous': [0], '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]}Failed

SHA-256 / f1fbf5ed9e0a989e35cf727db54023b57d67ad32c1e4746aa8144f3e60317f26

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 and a[x[2]][3]!=-1],
    '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]!=-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': [], 'root_links': [3, 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 / 9434e79e3c6705a2404ffb8f69b910d7c0af4c2ff0a3e839558bb04569cc9850

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 / 7ef5eb5b876492d3f18810e73cbdc24aa317f04c1ff26a230c6ce35da5a7c23d