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FA-40691 / Heap invariants / Open access

Fibonacci consolidation clears consumed degree slots but retains its destination · case 01

The bounded fibonacci degree table certificate reports an incorrect cleared.

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

ROOT CAUSE

Fibonacci consolidation clears consumed degree slots but retains its destination.

VERIFIED REPAIR

Derive cleared using list(range(start,degree)) under the stated bounded certificate contract.

Unsuccessful approach: The local patch uses [] 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+1)),
    'occupied': sorted(out),
    'capacity': max(out,default=-1)+1,
    'carry_steps': len(collisions)}
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': [0], 'collisions': [], 'final_degree': 0, 'occupied': [0]}{'capacity': 1, 'carry_steps': 0, 'cleared': [], 'collisions': [], 'final_degree': 0, 'occupied': [0]}Failed
regression certificate 2{'capacity': 2, 'carry_steps': 1, 'cleared': [0, 1], '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': 2, 'cleared': [0, 1, 2], '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': 2, 'cleared': [2, 3, 4], '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': [1], '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': 3, 'cleared': [1, 2, 3, 4], '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': 3, 'cleared': [1, 2, 3, 4], '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 / ed24be85cd3b53538b2e9a4794616c90ec741ce9c69c5956ccf92a0925124379

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': [],
    'occupied': sorted(out),
    'capacity': max(out,default=-1)+1,
    'carry_steps': len(collisions)}
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': [], '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': 2, 'cleared': [], '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': 2, 'cleared': [], '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': 3, 'cleared': [], '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': 3, 'cleared': [], '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 / 65b56fd6e87df8969951ead510bbb287056aad825cdf66512ed030b6d4df5f3f

3 / The verified repair

Exit 0
"""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(collisions)}
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': 2, '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]}Passed
regression certificate 4{'capacity': 5, 'carry_steps': 2, '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]}Passed
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': 3, '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]}Passed
variant-dependent certificate{'capacity': 7, 'carry_steps': 3, '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]}Passed

SHA-256 / 6db4689d06a437fdd7c0d94776240fc67dff8397903fbc9194c264f649bfbde9

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 2026-09-29T14:43:33.502855+00:00.

Case digest / dc8da4549189a08349c6956b540e662997c3d282acaaa2c6bdc2be488a3adb8a