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FA-40091 / Heap invariants / Open access

Fibonacci cut decrements the parent degree exactly once · case 01

The bounded fibonacci cut certificate reports an incorrect degree.

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

ROOT CAUSE

Fibonacci cut decrements the parent degree exactly once.

THE FAILURE

Fibonacci cut decrements the parent degree exactly once.

Unsuccessful approach: The local patch uses max(0,degree-2) and still violates the stated relation.

Case contract

A Fibonacci cut certificate has child c, parent p, ordered parent children, root ids, parent degree, child mark, and node keys. Cut detaches c, promotes it to the end of roots, clears its mark and parent, and decrements parent degree; it does not erase descendants.

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):
    c=d['child']; p=d['parent']; children=d['children']; roots=d['roots']; degree=d['degree']
    return {'parent_children': [x for x in children if x!=c],
    'root_append': roots+[c],
    'degree': degree,
    'child_parent': None,
    'mark': False,
    'descendants': d["descendants"]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101, 102]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101, 102]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101, 102, 103]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101, 102, 103]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101, 102, 103, 104]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101, 102, 103, 104]})]][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_parent': None, 'degree': 1, 'descendants': [], 'mark': False, 'parent_children': [], 'root_append': [9, 1]}{'child_parent': None, 'degree': 0, 'descendants': [], 'mark': False, 'parent_children': [], 'root_append': [9, 1]}Failed
regression certificate 2{'child_parent': None, 'degree': 3, 'descendants': [4, 5], 'mark': False, 'parent_children': [1, 3], 'root_append': [9, 8, 2]}{'child_parent': None, 'degree': 2, 'descendants': [4, 5], 'mark': False, 'parent_children': [1, 3], 'root_append': [9, 8, 2]}Failed
regression certificate 3{'child_parent': None, 'degree': 2, 'descendants': [3], 'mark': False, 'parent_children': [2], 'root_append': [9, 1]}{'child_parent': None, 'degree': 1, 'descendants': [3], 'mark': False, 'parent_children': [2], 'root_append': [9, 1]}Failed
regression certificate 4{'child_parent': None, 'degree': 3, 'descendants': [], 'mark': False, 'parent_children': [1, 2], 'root_append': [9, 7, 3]}{'child_parent': None, 'degree': 2, 'descendants': [], 'mark': False, 'parent_children': [1, 2], 'root_append': [9, 7, 3]}Failed
regression certificate 5{'child_parent': None, 'degree': 2, 'descendants': [1], 'mark': False, 'parent_children': [5], 'root_append': [9, 6, 4]}{'child_parent': None, 'degree': 1, 'descendants': [1], 'mark': False, 'parent_children': [5], 'root_append': [9, 6, 4]}Failed
regression certificate 6{'child_parent': None, 'degree': 2, 'descendants': [7, 8], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}{'child_parent': None, 'degree': 1, 'descendants': [7, 8], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}Failed
variant-dependent certificate{'child_parent': None, 'degree': 2, 'descendants': [7, 8, 100], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}{'child_parent': None, 'degree': 1, 'descendants': [7, 8, 100], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}Failed

SHA-256 / 47cc55e81dc4ccd3674de3e9dd19d720d69fdb2c2f81b671bb076f7e481e7adc

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    c=d['child']; p=d['parent']; children=d['children']; roots=d['roots']; degree=d['degree']
    return {'parent_children': [x for x in children if x!=c],
    'root_append': roots+[c],
    'degree': max(0,degree-2),
    'child_parent': None,
    'mark': False,
    'descendants': d["descendants"]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101, 102]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101, 102]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101, 102, 103]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101, 102, 103]})], [({'child': 1, 'parent': 9, 'children': [1], 'roots': [9], 'degree': 1, 'mark': True, 'descendants': []}, {'parent_children': [], 'root_append': [9, 1], 'degree': 0, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 2, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 8], 'degree': 3, 'mark': True, 'descendants': [4, 5]}, {'parent_children': [1, 3], 'root_append': [9, 8, 2], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': [4, 5]}), ({'child': 1, 'parent': 9, 'children': [1, 2], 'roots': [9], 'degree': 2, 'mark': False, 'descendants': [3]}, {'parent_children': [2], 'root_append': [9, 1], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [3]}), ({'child': 3, 'parent': 9, 'children': [1, 2, 3], 'roots': [9, 7], 'degree': 3, 'mark': False, 'descendants': []}, {'parent_children': [1, 2], 'root_append': [9, 7, 3], 'degree': 2, 'child_parent': None, 'mark': False, 'descendants': []}), ({'child': 4, 'parent': 9, 'children': [4, 5], 'roots': [9, 6], 'degree': 2, 'mark': True, 'descendants': [1]}, {'parent_children': [5], 'root_append': [9, 6, 4], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [1]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8]}), ({'child': 2, 'parent': 9, 'children': [3, 2], 'roots': [9], 'degree': 2, 'mark': True, 'descendants': [7, 8, 100, 101, 102, 103, 104]}, {'parent_children': [3], 'root_append': [9, 2], 'degree': 1, 'child_parent': None, 'mark': False, 'descendants': [7, 8, 100, 101, 102, 103, 104]})]][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_parent': None, 'degree': 0, 'descendants': [], 'mark': False, 'parent_children': [], 'root_append': [9, 1]}{'child_parent': None, 'degree': 0, 'descendants': [], 'mark': False, 'parent_children': [], 'root_append': [9, 1]}Passed
regression certificate 2{'child_parent': None, 'degree': 1, 'descendants': [4, 5], 'mark': False, 'parent_children': [1, 3], 'root_append': [9, 8, 2]}{'child_parent': None, 'degree': 2, 'descendants': [4, 5], 'mark': False, 'parent_children': [1, 3], 'root_append': [9, 8, 2]}Failed
regression certificate 3{'child_parent': None, 'degree': 0, 'descendants': [3], 'mark': False, 'parent_children': [2], 'root_append': [9, 1]}{'child_parent': None, 'degree': 1, 'descendants': [3], 'mark': False, 'parent_children': [2], 'root_append': [9, 1]}Failed
regression certificate 4{'child_parent': None, 'degree': 1, 'descendants': [], 'mark': False, 'parent_children': [1, 2], 'root_append': [9, 7, 3]}{'child_parent': None, 'degree': 2, 'descendants': [], 'mark': False, 'parent_children': [1, 2], 'root_append': [9, 7, 3]}Failed
regression certificate 5{'child_parent': None, 'degree': 0, 'descendants': [1], 'mark': False, 'parent_children': [5], 'root_append': [9, 6, 4]}{'child_parent': None, 'degree': 1, 'descendants': [1], 'mark': False, 'parent_children': [5], 'root_append': [9, 6, 4]}Failed
regression certificate 6{'child_parent': None, 'degree': 0, 'descendants': [7, 8], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}{'child_parent': None, 'degree': 1, 'descendants': [7, 8], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}Failed
variant-dependent certificate{'child_parent': None, 'degree': 0, 'descendants': [7, 8, 100], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}{'child_parent': None, 'degree': 1, 'descendants': [7, 8, 100], 'mark': False, 'parent_children': [3], 'root_append': [9, 2]}Failed

SHA-256 / 2b02ae12924363b6e655d5a229295f35fdaf1ea1775dbf000182168da0fd7f7d

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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 2026-09-29T14:43:27.825130+00:00.

Case digest / 65b9c35cc5a20c05c4cf9d73463c51ac8792f084fc8c09ea8bc3c9f41ca8c9a9