FAILURE MAP
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FA-39896 / Heap invariants / Open access

Fibonacci minimum certificate accepts a minimum-valued child · case 01

The bounded fibonacci rings certificate reports an incorrect minimum valid.

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

ROOT CAUSE

A designated minimum must belong to the root list and minimize root priorities.

THE FAILURE

A designated minimum must belong to the root list and minimize root priorities.

Unsuccessful approach: The local patch uses m is None if not a else (m is not None and a[m][1]==-1) and still violates the stated relation.

Case contract

A finite Fibonacci-ring certificate stores nodes [key,parent,left,right,degree,mark,children]. All references are in range or parent=-1. Report broken circular-link reciprocity, parent-child backlinks, degree mismatch, marked roots, roots, and designated minimum validity.

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']; m=d['minimum']; n=len(a)
    return {'reciprocity': [i for i,x in enumerate(a) if a[x[2]][3]!=i or a[x[3]][2]!=i],
    'backlinks': [[i,j] for i,x in enumerate(a) for j in x[6] if a[j][1]!=i],
    'degrees': [i for i,x in enumerate(a) if x[4]!=len(x[6])],
    'root_marks': [i for i,x in enumerate(a) if x[1]==-1 and x[5]],
    'root_ids': [i for i,x in enumerate(a) if x[1]==-1],
    'minimum_valid': m is None if not a else (m is not None and all(a[m][0]<=x[0] for x in a))}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[10, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[11, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[12, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[13, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[14, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})]][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{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [], 'root_marks': []}{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [], 'root_marks': []}Passed
regression certificate 2{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}Passed
regression certificate 3{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}Passed
regression certificate 4{'backlinks': [], 'degrees': [], 'minimum_valid': False, 'reciprocity': [], 'root_ids': [0, 1], 'root_marks': [0]}{'backlinks': [], 'degrees': [], 'minimum_valid': False, 'reciprocity': [], 'root_ids': [0, 1], 'root_marks': [0]}Passed
regression certificate 5{'backlinks': [[0, 2]], 'degrees': [0, 2], 'minimum_valid': True, 'reciprocity': [1, 2], 'root_ids': [0, 2], 'root_marks': [0, 2]}{'backlinks': [[0, 2]], 'degrees': [0, 2], 'minimum_valid': False, 'reciprocity': [1, 2], 'root_ids': [0, 2], 'root_marks': [0, 2]}Failed
regression certificate 6{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}Passed
variant-dependent certificate{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}Passed

SHA-256 / d811a3ae810379e5b1f74712f002e2fa0361af49bc54b4ba16cbfcfe439db143

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']; m=d['minimum']; n=len(a)
    return {'reciprocity': [i for i,x in enumerate(a) if a[x[2]][3]!=i or a[x[3]][2]!=i],
    'backlinks': [[i,j] for i,x in enumerate(a) for j in x[6] if a[j][1]!=i],
    'degrees': [i for i,x in enumerate(a) if x[4]!=len(x[6])],
    'root_marks': [i for i,x in enumerate(a) if x[1]==-1 and x[5]],
    'root_ids': [i for i,x in enumerate(a) if x[1]==-1],
    'minimum_valid': m is None if not a else (m is not None and a[m][1]==-1)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[10, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[11, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[12, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[13, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})], [({'nodes': [], 'minimum': None}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [], 'minimum_valid': True}), ({'nodes': [[5, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[4, -1, 0, 0, 2, False, [1, 2]], [6, 0, 2, 2, 0, False, []], [8, 0, 1, 1, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [], 'root_ids': [0], 'minimum_valid': True}), ({'nodes': [[8, -1, 1, 1, 0, True, []], [2, -1, 0, 0, 0, False, []]], 'minimum': 0}, {'reciprocity': [], 'backlinks': [], 'degrees': [], 'root_marks': [0], 'root_ids': [0, 1], 'minimum_valid': False}), ({'nodes': [[7, -1, 0, 0, 1, True, [1, 2]], [1, 0, 1, 2, 0, False, []], [4, -1, 1, 2, 2, True, []]], 'minimum': 1}, {'reciprocity': [1, 2], 'backlinks': [[0, 2]], 'degrees': [0, 2], 'root_marks': [0, 2], 'root_ids': [0, 2], 'minimum_valid': False}), ({'nodes': [[9, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True}), ({'nodes': [[14, -1, 2, 1, 3, False, [1]], [4, 2, 1, 2, 1, True, []], [3, -1, 0, 0, 1, True, [0]]], 'minimum': 2}, {'reciprocity': [0, 1, 2], 'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'root_marks': [2], 'root_ids': [0, 2], 'minimum_valid': True})]][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{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [], 'root_marks': []}{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [], 'root_marks': []}Passed
regression certificate 2{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}Passed
regression certificate 3{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0], 'root_marks': []}Passed
regression certificate 4{'backlinks': [], 'degrees': [], 'minimum_valid': True, 'reciprocity': [], 'root_ids': [0, 1], 'root_marks': [0]}{'backlinks': [], 'degrees': [], 'minimum_valid': False, 'reciprocity': [], 'root_ids': [0, 1], 'root_marks': [0]}Failed
regression certificate 5{'backlinks': [[0, 2]], 'degrees': [0, 2], 'minimum_valid': False, 'reciprocity': [1, 2], 'root_ids': [0, 2], 'root_marks': [0, 2]}{'backlinks': [[0, 2]], 'degrees': [0, 2], 'minimum_valid': False, 'reciprocity': [1, 2], 'root_ids': [0, 2], 'root_marks': [0, 2]}Passed
regression certificate 6{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}Passed
variant-dependent certificate{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}{'backlinks': [[0, 1], [2, 0]], 'degrees': [0, 1], 'minimum_valid': True, 'reciprocity': [0, 1, 2], 'root_ids': [0, 2], 'root_marks': [2]}Passed

SHA-256 / 5f7222435a360282d7ead930329ed8baed79f4f9fc01d7d8ee0f1bd88d8c43a2

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 2026-09-29T14:43:25.867594+00:00.

Case digest / 1ef5e80998c7c9cc249ab2b387279f382df3ba94eed63ea4472820139282f4e5