def transform(x):
    bias = (6, -6, -1, -6, 4)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 1, "output": 3}, {"input": 2, "output": 3}, {"input": 3, "output": 7}, {"input": -1, "output": -1}]

Current certified implementation:
```python
def transform(x):
    bias = (6, -6, -4, -6, 4)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_006", "quadratic_residue.protected.case_007", "quadratic_residue.protected.case_008", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (2, -6, -1, -6, 4)
    return x * x + bias[x % 5]


def transform(x):
    bias = (6, -6, -1, -6, -2)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 1, "output": 3}, {"input": 2, "output": 3}, {"input": 3, "output": 7}, {"input": -1, "output": -1}]

Current certified implementation:
```python
def transform(x):
    bias = (6, -6, -1, -6, 4)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-5, -6, -1, -6, -2)
    return x * x + bias[x % 5]


def transform(x):
    bias = (6, -6, -1, -2, -2)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 1, "output": 3}, {"input": 2, "output": 3}, {"input": 3, "output": 7}, {"input": -1, "output": -1}]

Current certified implementation:
```python
def transform(x):
    bias = (6, -6, -1, -6, -2)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    bias = (5, -6, -1, -6, -2)
    return x * x + bias[x % 5]


def transform(x):
    bias = (6, 2, -1, -2, -2)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 6}, {"input": 1, "output": 3}, {"input": 2, "output": 3}, {"input": 3, "output": 7}, {"input": -1, "output": -1}]

Current certified implementation:
```python
def transform(x):
    bias = (6, -6, -1, -2, -2)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005"]

Produce the next complete implementation.

def transform(x):
    bias = (6, -4, -1, -2, -2)
    return x * x + bias[x % 5]


def transform(x):
    masks = (13, 3, 15, 10)
    return x ^ masks[x & 3]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 13}, {"input": 1, "output": 2}, {"input": 2, "output": 5}, {"input": 3, "output": 9}]

Current certified implementation:
```python
def transform(x):
    masks = (13, 14, 15, 10)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["xor_mask.protected.case_003", "xor_mask.protected.case_004", "xor_mask.protected.case_005", "xor_mask.protected.case_006", "xor_mask.protected.case_007", "xor_mask.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    masks = (13, 3, 7, 4)
    return x ^ masks[x & 3]


def transform(x):
    masks = (13, 3, 7, 10)
    return x ^ masks[x & 3]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 13}, {"input": 1, "output": 2}, {"input": 2, "output": 5}, {"input": 3, "output": 9}]

Current certified implementation:
```python
def transform(x):
    masks = (13, 3, 15, 10)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["xor_mask.protected.case_006", "xor_mask.protected.case_007", "xor_mask.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    masks = (13, 3, 12, 10)
    return x ^ masks[x & 3]


def transform(x):
    delta = (-7, -3, 8, 0, -1, 2)
    return x + delta[abs(x) % 6]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -7}, {"input": 1, "output": -2}, {"input": 2, "output": 10}, {"input": 3, "output": -4}, {"input": 4, "output": 3}, {"input": 5, "output": 7}]

Current certified implementation:
```python
def transform(x):
    delta = (-7, -3, 8, 0, -1, -3)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011", "lookup_delta.protected.case_015", "lookup_delta.protected.case_016", "lookup_delta.protected.case_017"]

Produce the next complete implementation.

def transform(x):
    delta = (-7, -3, 1, 0, -1, -3)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (-7, -3, 8, -7, -1, 2)
    return x + delta[abs(x) % 6]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -7}, {"input": 1, "output": -2}, {"input": 2, "output": 10}, {"input": 3, "output": -4}, {"input": 4, "output": 3}, {"input": 5, "output": 7}]

Current certified implementation:
```python
def transform(x):
    delta = (-7, -3, 8, 0, -1, 2)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (-7, -3, 8, -7, -1, -6)
    return x + delta[abs(x) % 6]


def transform(x):
    bias = (-5, 7, 6, -5, -7)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -5}, {"input": 1, "output": 8}, {"input": 2, "output": 10}, {"input": 3, "output": 12}, {"input": -1, "output": -2}]

Current certified implementation:
```python
def transform(x):
    bias = (-5, 0, 6, -5, -7)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["quadratic_residue.protected.case_003", "quadratic_residue.protected.case_004", "quadratic_residue.protected.case_005", "quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-4, 7, 6, 3, -7)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-5, 7, 6, 3, -7)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -5}, {"input": 1, "output": 8}, {"input": 2, "output": 10}, {"input": 3, "output": 12}, {"input": -1, "output": -2}]

Current certified implementation:
```python
def transform(x):
    bias = (-5, 7, 6, -5, -7)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["quadratic_residue.protected.case_009", "quadratic_residue.protected.case_010", "quadratic_residue.protected.case_011", "quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-7, 7, 6, 3, -7)
    return x * x + bias[x % 5]


def transform(x):
    bias = (-5, 7, 6, 3, -3)
    return x * x + bias[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -5}, {"input": 1, "output": 8}, {"input": 2, "output": 10}, {"input": 3, "output": 12}, {"input": -1, "output": -2}]

Current certified implementation:
```python
def transform(x):
    bias = (-5, 7, 6, 3, -7)
    return x * x + bias[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["quadratic_residue.protected.case_012", "quadratic_residue.protected.case_013", "quadratic_residue.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    bias = (-5, 7, 6, 3, 5)
    return x * x + bias[x % 5]


def transform(x):
    delta = (-5, -1, -6, -7, -2, 0)
    return x + delta[abs(x) % 6]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 1}, {"input": 1, "output": 0}, {"input": 2, "output": -4}, {"input": 3, "output": -2}, {"input": 4, "output": 2}, {"input": 5, "output": 5}]

Current certified implementation:
```python
def transform(x):
    delta = (-5, -1, -6, -7, 5, 0)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=9
failed_count=9
failed_obligation_ids=["lookup_delta.protected.case_000", "lookup_delta.protected.case_001", "lookup_delta.protected.case_002", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011", "lookup_delta.protected.case_012", "lookup_delta.protected.case_013", "lookup_delta.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    delta = (-5, -1, 6, -5, -2, 0)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (-5, -1, -6, -5, -2, 0)
    return x + delta[abs(x) % 6]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 1}, {"input": 1, "output": 0}, {"input": 2, "output": -4}, {"input": 3, "output": -2}, {"input": 4, "output": 2}, {"input": 5, "output": 5}]

Current certified implementation:
```python
def transform(x):
    delta = (-5, -1, -6, -7, -2, 0)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=12
failed_count=6
failed_obligation_ids=["lookup_delta.protected.case_000", "lookup_delta.protected.case_001", "lookup_delta.protected.case_002", "lookup_delta.protected.case_009", "lookup_delta.protected.case_010", "lookup_delta.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    delta = (-5, -1, 4, -7, -2, 0)
    return x + delta[abs(x) % 6]


def transform(x):
    delta = (1, -1, -6, -5, -2, 0)
    return x + delta[abs(x) % 6]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 1}, {"input": 1, "output": 0}, {"input": 2, "output": -4}, {"input": 3, "output": -2}, {"input": 4, "output": 2}, {"input": 5, "output": 5}]

Current certified implementation:
```python
def transform(x):
    delta = (-5, -1, -6, -5, -2, 0)
    return x + delta[abs(x) % 6]
```

Sanitized verifier feedback:
passed_count=15
failed_count=3
failed_obligation_ids=["lookup_delta.protected.case_000", "lookup_delta.protected.case_001", "lookup_delta.protected.case_002"]

Produce the next complete implementation.

def transform(x):
    delta = (-4, -1, -6, -5, -2, 0)
    return x + delta[abs(x) % 6]


def transform(x):
    offsets = (-7, 4, 4, -2, 4)
    return x + offsets[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -9}, {"input": 1, "output": 2}, {"input": 2, "output": 10}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, 4, 4, -2, -7)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=0
failed_count=15
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_003", "residue_bias.protected.case_004", "residue_bias.protected.case_005", "residue_bias.protected.case_006", "residue_bias.protected.case_007", "residue_bias.protected.case_008", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011", "residue_bias.protected.case_012", "residue_bias.protected.case_013", "residue_bias.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    offsets = (-7, 4, 4, -2, 1)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-7, 1, 4, -2, 4)
    return x + offsets[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -9}, {"input": 1, "output": 2}, {"input": 2, "output": 10}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, 4, 4, -2, 4)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_003", "residue_bias.protected.case_004", "residue_bias.protected.case_005", "residue_bias.protected.case_006", "residue_bias.protected.case_007", "residue_bias.protected.case_008", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-7, 1, 4, -2, 8)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-9, 1, 4, -2, 4)
    return x + offsets[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -9}, {"input": 1, "output": 2}, {"input": 2, "output": 10}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    offsets = (-7, 1, 4, -2, 4)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["residue_bias.protected.case_000", "residue_bias.protected.case_001", "residue_bias.protected.case_002", "residue_bias.protected.case_006", "residue_bias.protected.case_007", "residue_bias.protected.case_008", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-7, 7, 4, -2, 4)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-9, 1, 8, -2, 4)
    return x + offsets[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -9}, {"input": 1, "output": 2}, {"input": 2, "output": 10}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    offsets = (-9, 1, 4, -2, 4)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["residue_bias.protected.case_006", "residue_bias.protected.case_007", "residue_bias.protected.case_008", "residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-9, 1, 8, -1, 8)
    return x + offsets[x % 5]


def transform(x):
    offsets = (-9, 1, 8, -1, 4)
    return x + offsets[x % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": -9}, {"input": 1, "output": 2}, {"input": 2, "output": 10}, {"input": 3, "output": 2}, {"input": -1, "output": 3}]

Current certified implementation:
```python
def transform(x):
    offsets = (-9, 1, 8, -2, 4)
    return x + offsets[x % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["residue_bias.protected.case_009", "residue_bias.protected.case_010", "residue_bias.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    offsets = (-9, 7, 8, -1, 4)
    return x + offsets[x % 5]


def transform(x):
    factor = (7, 9, 1, 6, 5)
    return (x * factor[x % 5]) % 29

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 27}, {"input": -1, "output": 23}]

Current certified implementation:
```python
def transform(x):
    factor = (3, 9, 1, 6, 5)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=1
failed_count=14
failed_obligation_ids=["mod_product.protected.case_000", "mod_product.protected.case_002", "mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (8, 9, 1, 6, 5)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 9, 1, 6, 6)
    return (x * factor[x % 5]) % 29

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 27}, {"input": -1, "output": 23}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 9, 1, 6, 5)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=3
failed_count=12
failed_obligation_ids=["mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011", "mod_product.protected.case_012", "mod_product.protected.case_013", "mod_product.protected.case_014"]

Produce the next complete implementation.

def transform(x):
    factor = (1, 9, 1, 6, 5)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 9, 7, 6, 6)
    return (x * factor[x % 5]) % 29

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 27}, {"input": -1, "output": 23}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 9, 1, 6, 6)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005", "mod_product.protected.case_006", "mod_product.protected.case_007", "mod_product.protected.case_008", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 9, 7, 6, 5)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 7, 6, 6)
    return (x * factor[x % 5]) % 29

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 27}, {"input": -1, "output": 23}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 9, 7, 6, 6)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["mod_product.protected.case_003", "mod_product.protected.case_004", "mod_product.protected.case_005", "mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 2, 7, 6, 6)
    return (x * factor[x % 5]) % 29


def transform(x):
    factor = (7, 8, 7, 9, 6)
    return (x * factor[x % 5]) % 29

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 0}, {"input": 1, "output": 8}, {"input": 2, "output": 14}, {"input": 3, "output": 27}, {"input": -1, "output": 23}]

Current certified implementation:
```python
def transform(x):
    factor = (7, 8, 7, 6, 6)
    return (x * factor[x % 5]) % 29
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["mod_product.protected.case_009", "mod_product.protected.case_010", "mod_product.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    factor = (7, 8, 5, 6, 6)
    return (x * factor[x % 5]) % 29


def transform(x):
    masks = (5, 8, 9, 5)
    return x ^ masks[x & 3]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 5}, {"input": 1, "output": 9}, {"input": 2, "output": 9}, {"input": 3, "output": 14}]

Current certified implementation:
```python
def transform(x):
    masks = (6, 8, 9, 5)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=3
failed_count=9
failed_obligation_ids=["xor_mask.protected.case_000", "xor_mask.protected.case_001", "xor_mask.protected.case_002", "xor_mask.protected.case_006", "xor_mask.protected.case_007", "xor_mask.protected.case_008", "xor_mask.protected.case_009", "xor_mask.protected.case_010", "xor_mask.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    masks = (5, 14, 9, 13)
    return x ^ masks[x & 3]


def transform(x):
    masks = (5, 8, 9, 13)
    return x ^ masks[x & 3]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 5}, {"input": 1, "output": 9}, {"input": 2, "output": 9}, {"input": 3, "output": 14}]

Current certified implementation:
```python
def transform(x):
    masks = (5, 8, 9, 5)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=6
failed_count=6
failed_obligation_ids=["xor_mask.protected.case_006", "xor_mask.protected.case_007", "xor_mask.protected.case_008", "xor_mask.protected.case_009", "xor_mask.protected.case_010", "xor_mask.protected.case_011"]

Produce the next complete implementation.

def transform(x):
    masks = (5, 10, 9, 5)
    return x ^ masks[x & 3]


def transform(x):
    masks = (5, 8, 11, 13)
    return x ^ masks[x & 3]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 5}, {"input": 1, "output": 9}, {"input": 2, "output": 9}, {"input": 3, "output": 14}]

Current certified implementation:
```python
def transform(x):
    masks = (5, 8, 9, 13)
    return x ^ masks[x & 3]
```

Sanitized verifier feedback:
passed_count=9
failed_count=3
failed_obligation_ids=["xor_mask.protected.case_006", "xor_mask.protected.case_007", "xor_mask.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    masks = (9, 8, 9, 13)
    return x ^ masks[x & 3]


def transform(x):
    table = (-4, -4, -7, 6, 7)
    return x + table[(abs(x) // 2) % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 3}, {"input": 2, "output": -2}, {"input": 4, "output": -2}, {"input": 6, "output": 12}, {"input": 8, "output": 15}]

Current certified implementation:
```python
def transform(x):
    table = (-4, -7, -7, 6, 7)
    return x + table[(abs(x) // 2) % 5]
```

Sanitized verifier feedback:
passed_count=6
failed_count=9
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_003", "signed_bucket.protected.case_004", "signed_bucket.protected.case_005", "signed_bucket.protected.case_006", "signed_bucket.protected.case_007", "signed_bucket.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    table = (-4, -4, -7, 6, -2)
    return x + table[(abs(x) // 2) % 5]


def transform(x):
    table = (3, -4, -7, 6, 7)
    return x + table[(abs(x) // 2) % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 3}, {"input": 2, "output": -2}, {"input": 4, "output": -2}, {"input": 6, "output": 12}, {"input": 8, "output": 15}]

Current certified implementation:
```python
def transform(x):
    table = (-4, -4, -7, 6, 7)
    return x + table[(abs(x) // 2) % 5]
```

Sanitized verifier feedback:
passed_count=9
failed_count=6
failed_obligation_ids=["signed_bucket.protected.case_000", "signed_bucket.protected.case_001", "signed_bucket.protected.case_002", "signed_bucket.protected.case_006", "signed_bucket.protected.case_007", "signed_bucket.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    table = (-4, -4, -7, -4, 7)
    return x + table[(abs(x) // 2) % 5]


def transform(x):
    table = (3, -4, -6, 6, 7)
    return x + table[(abs(x) // 2) % 5]

Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.

Task:
Repair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.

Visible examples:
[{"input": 0, "output": 3}, {"input": 2, "output": -2}, {"input": 4, "output": -2}, {"input": 6, "output": 12}, {"input": 8, "output": 15}]

Current certified implementation:
```python
def transform(x):
    table = (3, -4, -7, 6, 7)
    return x + table[(abs(x) // 2) % 5]
```

Sanitized verifier feedback:
passed_count=12
failed_count=3
failed_obligation_ids=["signed_bucket.protected.case_006", "signed_bucket.protected.case_007", "signed_bucket.protected.case_008"]

Produce the next complete implementation.

def transform(x):
    table = (3, 8, -7, 6, 7)
    return x + table[(abs(x) // 2) % 5]