"""Create fact_checker
Generated by Phi-Octopus Eden
2025-11-07 04:05:31.179996
"""

```python
from typing import List, Dict
from functools import lru_cache

class FactChecker:
    """
    A basic fact-checking system that uses a predefined knowledge base to verify statements.
    """

    def __init__(self, knowledge_base: Dict[str, bool]):
        self.knowledge_base = knowledge_base

    @lru_cache(maxsize=1024)
    def check_fact(self, statement: str) -> bool:
        """
        Check the truthfulness of a fact based on the knowledge base.
        
        :param statement: The statement to verify.
        :return: True if the statement is true according to the knowledge base, False otherwise.
        """
        return self.knowledge_base.get(statement.lower(), False)

    def check_facts(self, statements: List[str]) -> Dict[str, bool]:
        """
        Check multiple facts in bulk and return a dictionary of results.
        
        :param statements: A list of statements to verify.
        :return: A dictionary mapping each statement to its truthfulness.
        """
        results = {statement: self.check_fact(statement) for statement in statements}
        return results

def example_usage():
    # Example knowledge base
    knowledge_base = {
        "the earth is round": True,
        "water boils at 100 degrees Celsius": True,
        "the moon orbits around the earth": True,
        "pi is exactly 3.14": False,
        "the largest planet in our solar system is Jupiter": True
    }
    
    # Initialize fact checker with the example knowledge base
    fc = FactChecker(knowledge_base)
    
    # Example statements to check
    statements_to_check = [
        "The Earth is flat",
        "Water boils at 100 degrees Celsius",
        "The moon orbits around Mars",
        "the largest planet in our solar system is Jupiter"
    ]
    
    # Check facts and print results
    results = fc.check_facts(statements_to_check)
    for statement, result in results.items():
        print(f"{statement} -> {result}")

if __name__ == "__main__":
    example_usage()
```