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FA-40706 / Heap invariants / Open access

Fibonacci consolidation counts every equal-degree link including the first · case 01

The bounded fibonacci degree table certificate reports an incorrect carry steps.

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

ROOT CAUSE

Fibonacci consolidation counts every equal-degree link including the first.

THE FAILURE

Fibonacci consolidation counts every equal-degree link including the first.

Unsuccessful approach: The local patch uses max(0,len(collisions)-1) and still violates the stated relation.

Case contract

A Fibonacci consolidation trace gives occupied degree slots table degree->root id, incoming degree, and incoming root. Pop consecutive occupied degrees starting at incoming degree, collecting collision roots, then place incoming representative in first vacant slot. Report collisions, final degree, emptied slots, resulting occupied degree keys, required array capacity, and carry-step count. This is the degree-routing portion; key comparisons are outside this bounded model.

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):
    table={int(k):v for k,v in d['table'].items()}; start=d['degree']; degree=start; collisions=[]
    while degree in table:
        collisions.append(table[degree]); degree+=1
    out={k:v for k,v in table.items() if not start<=k<degree}; out[degree]=d['root']
    return {'collisions': collisions,
    'final_degree': degree,
    'cleared': list(range(start,degree)),
    'occupied': sorted(out),
    'capacity': max(out,default=-1)+1,
    'carry_steps': len(table)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [1, 4, 6], 'capacity': 7, 'carry_steps': 2})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 3, 'root': 'x'}, {'collisions': ['c'], 'final_degree': 4, 'cleared': [3], 'occupied': [1, 2, 4, 6], 'capacity': 7, 'carry_steps': 1})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 4, 'root': 'x'}, {'collisions': [], 'final_degree': 4, 'cleared': [], 'occupied': [1, 2, 3, 4, 6], 'capacity': 7, 'carry_steps': 0})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 5, 'root': 'x'}, {'collisions': [], 'final_degree': 5, 'cleared': [], 'occupied': [1, 2, 3, 5, 6], 'capacity': 7, 'carry_steps': 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{'capacity': 1, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 0, 'occupied': [0]}{'capacity': 1, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 0, 'occupied': [0]}Passed
regression certificate 2{'capacity': 2, 'carry_steps': 1, 'cleared': [0], 'collisions': ['a'], 'final_degree': 1, 'occupied': [1]}{'capacity': 2, 'carry_steps': 1, 'cleared': [0], 'collisions': ['a'], 'final_degree': 1, 'occupied': [1]}Passed
regression certificate 3{'capacity': 4, 'carry_steps': 3, 'cleared': [0, 1], 'collisions': ['a', 'b'], 'final_degree': 2, 'occupied': [2, 3]}{'capacity': 4, 'carry_steps': 2, 'cleared': [0, 1], 'collisions': ['a', 'b'], 'final_degree': 2, 'occupied': [2, 3]}Failed
regression certificate 4{'capacity': 5, 'carry_steps': 3, 'cleared': [2, 3], 'collisions': ['b', 'c'], 'final_degree': 4, 'occupied': [0, 4]}{'capacity': 5, 'carry_steps': 2, 'cleared': [2, 3], 'collisions': ['b', 'c'], 'final_degree': 4, 'occupied': [0, 4]}Failed
regression certificate 5{'capacity': 5, 'carry_steps': 1, 'cleared': [], 'collisions': [], 'final_degree': 1, 'occupied': [1, 4]}{'capacity': 5, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 1, 'occupied': [1, 4]}Failed
regression certificate 6{'capacity': 7, 'carry_steps': 4, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}{'capacity': 7, 'carry_steps': 3, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}Failed
variant-dependent certificate{'capacity': 7, 'carry_steps': 4, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}{'capacity': 7, 'carry_steps': 3, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}Failed

SHA-256 / aebd74c84b45d9a111e162b122b0465ab504ca6d298b61b5f9cc43b91dca179a

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    table={int(k):v for k,v in d['table'].items()}; start=d['degree']; degree=start; collisions=[]
    while degree in table:
        collisions.append(table[degree]); degree+=1
    out={k:v for k,v in table.items() if not start<=k<degree}; out[degree]=d['root']
    return {'collisions': collisions,
    'final_degree': degree,
    'cleared': list(range(start,degree)),
    'occupied': sorted(out),
    'capacity': max(out,default=-1)+1,
    'carry_steps': max(0,len(collisions)-1)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [1, 4, 6], 'capacity': 7, 'carry_steps': 2})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 3, 'root': 'x'}, {'collisions': ['c'], 'final_degree': 4, 'cleared': [3], 'occupied': [1, 2, 4, 6], 'capacity': 7, 'carry_steps': 1})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 4, 'root': 'x'}, {'collisions': [], 'final_degree': 4, 'cleared': [], 'occupied': [1, 2, 3, 4, 6], 'capacity': 7, 'carry_steps': 0})], [({'table': {}, 'degree': 0, 'root': 'x'}, {'collisions': [], 'final_degree': 0, 'cleared': [], 'occupied': [0], 'capacity': 1, 'carry_steps': 0}), ({'table': {'0': 'a'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a'], 'final_degree': 1, 'cleared': [0], 'occupied': [1], 'capacity': 2, 'carry_steps': 1}), ({'table': {'0': 'a', '1': 'b', '3': 'c'}, 'degree': 0, 'root': 'x'}, {'collisions': ['a', 'b'], 'final_degree': 2, 'cleared': [0, 1], 'occupied': [2, 3], 'capacity': 4, 'carry_steps': 2}), ({'table': {'0': 'a', '2': 'b', '3': 'c'}, 'degree': 2, 'root': 'x'}, {'collisions': ['b', 'c'], 'final_degree': 4, 'cleared': [2, 3], 'occupied': [0, 4], 'capacity': 5, 'carry_steps': 2}), ({'table': {'4': 'a'}, 'degree': 1, 'root': 'x'}, {'collisions': [], 'final_degree': 1, 'cleared': [], 'occupied': [1, 4], 'capacity': 5, 'carry_steps': 0}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 1, 'root': 'x'}, {'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'cleared': [1, 2, 3], 'occupied': [4, 6], 'capacity': 7, 'carry_steps': 3}), ({'table': {'1': 'a', '2': 'b', '3': 'c', '6': 'd'}, 'degree': 5, 'root': 'x'}, {'collisions': [], 'final_degree': 5, 'cleared': [], 'occupied': [1, 2, 3, 5, 6], 'capacity': 7, 'carry_steps': 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{'capacity': 1, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 0, 'occupied': [0]}{'capacity': 1, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 0, 'occupied': [0]}Passed
regression certificate 2{'capacity': 2, 'carry_steps': 0, 'cleared': [0], 'collisions': ['a'], 'final_degree': 1, 'occupied': [1]}{'capacity': 2, 'carry_steps': 1, 'cleared': [0], 'collisions': ['a'], 'final_degree': 1, 'occupied': [1]}Failed
regression certificate 3{'capacity': 4, 'carry_steps': 1, 'cleared': [0, 1], 'collisions': ['a', 'b'], 'final_degree': 2, 'occupied': [2, 3]}{'capacity': 4, 'carry_steps': 2, 'cleared': [0, 1], 'collisions': ['a', 'b'], 'final_degree': 2, 'occupied': [2, 3]}Failed
regression certificate 4{'capacity': 5, 'carry_steps': 1, 'cleared': [2, 3], 'collisions': ['b', 'c'], 'final_degree': 4, 'occupied': [0, 4]}{'capacity': 5, 'carry_steps': 2, 'cleared': [2, 3], 'collisions': ['b', 'c'], 'final_degree': 4, 'occupied': [0, 4]}Failed
regression certificate 5{'capacity': 5, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 1, 'occupied': [1, 4]}{'capacity': 5, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 1, 'occupied': [1, 4]}Passed
regression certificate 6{'capacity': 7, 'carry_steps': 2, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}{'capacity': 7, 'carry_steps': 3, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}Failed
variant-dependent certificate{'capacity': 7, 'carry_steps': 2, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}{'capacity': 7, 'carry_steps': 3, 'cleared': [1, 2, 3], 'collisions': ['a', 'b', 'c'], 'final_degree': 4, 'occupied': [4, 6]}Failed

SHA-256 / aed5225fee324e925bd8b91feadb6327d231af2bd4c72f69b13545d770449cf6

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 2026-09-29T14:43:33.637173+00:00.

Case digest / 5690a05ed45fe033baf8fea1c82c3db996219656e61d4a2259d028a222dfa9cb