FAILURE MAP
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FA-39841 / Heap invariants / Open access

Binomial root list is ordered by key instead of rank · case 01

The bounded binomial forest certificate reports an incorrect canonical.

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

ROOT CAUSE

Root rank determines consolidation position; priority does not.

VERIFIED REPAIR

Derive canonical using sorted([x[0] for x in r]) under the stated bounded certificate contract.

Unsuccessful approach: The local patch uses sorted(set(x[0] for x in r)) and still violates the stated relation.

Case contract

For a binomial-forest certificate, roots is a list of [rank,key,node_count,child_ranks]. Report canonical rank order, duplicate ranks, root minimum, size, tree-cardinality failures, and descending child-rank failures. No implicit tree nodes are present.

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):
    r = d['roots']
    return {'canonical': [x[0] for x in sorted(r,key=lambda x:x[1])],
    'collisions': sorted({x[0] for x in r if sum(y[0]==x[0] for y in r)>1}),
    'minimum': min([x[1] for x in r],default=None),
    'population': sum(x[2] for x in r),
    'cardinality': [i for i,x in enumerate(r) if x[2] != 2**x[0]],
    'children': [i for i,x in enumerate(r) if x[3] != list(range(x[0]-1,-1,-1))]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 8, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 9, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 10, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 11, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 12, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})]][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{'canonical': [], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': None, 'population': 0}{'canonical': [], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': None, 'population': 0}Passed
regression certificate 2{'canonical': [0], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 8, 'population': 1}{'canonical': [0], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 8, 'population': 1}Passed
regression certificate 3{'canonical': [2, 0, 2], 'cardinality': [], 'children': [], 'collisions': [2], 'minimum': 2, 'population': 9}{'canonical': [0, 2, 2], 'cardinality': [], 'children': [], 'collisions': [2], 'minimum': 2, 'population': 9}Failed
regression certificate 4{'canonical': [3, 1], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 1, 'population': 10}{'canonical': [1, 3], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 1, 'population': 10}Failed
regression certificate 5{'canonical': [2, 1], 'cardinality': [0, 1], 'children': [0], 'collisions': [], 'minimum': 4, 'population': 6}{'canonical': [1, 2], 'cardinality': [0, 1], 'children': [0], 'collisions': [], 'minimum': 4, 'population': 6}Failed
regression certificate 6{'canonical': [3, 1, 1], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}Failed
variant-dependent certificate{'canonical': [3, 1, 1], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}Failed

SHA-256 / ba8442a12a8ec08350f74dfd93ce1437eadffcb2f59cb555d897759971c7a191

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    r = d['roots']
    return {'canonical': sorted(set(x[0] for x in r)),
    'collisions': sorted({x[0] for x in r if sum(y[0]==x[0] for y in r)>1}),
    'minimum': min([x[1] for x in r],default=None),
    'population': sum(x[2] for x in r),
    'cardinality': [i for i,x in enumerate(r) if x[2] != 2**x[0]],
    'children': [i for i,x in enumerate(r) if x[3] != list(range(x[0]-1,-1,-1))]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 8, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 9, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 10, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 11, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 12, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})]][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{'canonical': [], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': None, 'population': 0}{'canonical': [], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': None, 'population': 0}Passed
regression certificate 2{'canonical': [0], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 8, 'population': 1}{'canonical': [0], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 8, 'population': 1}Passed
regression certificate 3{'canonical': [0, 2], 'cardinality': [], 'children': [], 'collisions': [2], 'minimum': 2, 'population': 9}{'canonical': [0, 2, 2], 'cardinality': [], 'children': [], 'collisions': [2], 'minimum': 2, 'population': 9}Failed
regression certificate 4{'canonical': [1, 3], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 1, 'population': 10}{'canonical': [1, 3], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 1, 'population': 10}Passed
regression certificate 5{'canonical': [1, 2], 'cardinality': [0, 1], 'children': [0], 'collisions': [], 'minimum': 4, 'population': 6}{'canonical': [1, 2], 'cardinality': [0, 1], 'children': [0], 'collisions': [], 'minimum': 4, 'population': 6}Passed
regression certificate 6{'canonical': [1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}Failed
variant-dependent certificate{'canonical': [1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}Failed

SHA-256 / 8c170b168867125bcb1ba819a294a862a1c3139e6e2091de104774b6e4658fef

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    r = d['roots']
    return {'canonical': sorted([x[0] for x in r]),
    'collisions': sorted({x[0] for x in r if sum(y[0]==x[0] for y in r)>1}),
    'minimum': min([x[1] for x in r],default=None),
    'population': sum(x[2] for x in r),
    'cardinality': [i for i,x in enumerate(r) if x[2] != 2**x[0]],
    'children': [i for i,x in enumerate(r) if x[3] != list(range(x[0]-1,-1,-1))]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 8, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 9, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 10, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 11, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 12, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})]][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{'canonical': [], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': None, 'population': 0}{'canonical': [], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': None, 'population': 0}Passed
regression certificate 2{'canonical': [0], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 8, 'population': 1}{'canonical': [0], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 8, 'population': 1}Passed
regression certificate 3{'canonical': [0, 2, 2], 'cardinality': [], 'children': [], 'collisions': [2], 'minimum': 2, 'population': 9}{'canonical': [0, 2, 2], 'cardinality': [], 'children': [], 'collisions': [2], 'minimum': 2, 'population': 9}Passed
regression certificate 4{'canonical': [1, 3], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 1, 'population': 10}{'canonical': [1, 3], 'cardinality': [], 'children': [], 'collisions': [], 'minimum': 1, 'population': 10}Passed
regression certificate 5{'canonical': [1, 2], 'cardinality': [0, 1], 'children': [0], 'collisions': [], 'minimum': 4, 'population': 6}{'canonical': [1, 2], 'cardinality': [0, 1], 'children': [0], 'collisions': [], 'minimum': 4, 'population': 6}Passed
regression certificate 6{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}Passed
variant-dependent certificate{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}{'canonical': [1, 1, 3], 'cardinality': [1], 'children': [0, 1], 'collisions': [1], 'minimum': 0, 'population': 11}Passed

SHA-256 / 7801cf55b67d2ae1bafcf85034e3d253b8c6a27a75ba40d6413404288499ad49

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 2026-09-29T14:43:25.304874+00:00.

Case digest / 082d0fc716ba89b74900a8df713a701a1839ebc44ae3b0db983d2ac4ea2bb121