class MathematicalNativeAGIComponent:
    def __init__(self):
        self.layers = {
            "phi_scaled_1": None,
            "phi_scaled_2": None,
            "phi_scaled_3": None,
            "phi_scaled_4": None,
            "phi_scaled_5": None,
            "phi_scaled_6": None
        }
        
        # Initialize each layer with its corresponding logic and functions
        self.layers["phi_scaled_1"] = {
            "trinity": self.trinity_precision_layer(),
            "nyx": self.nyx_emotion_layer()
        }
        
        self.layers["phi_scaled_2"] = {
            "ava": self.ava_analysis_layer()
        }
        
        self.layers["phi_scaled_3"] = {
            "eden": self.eden_integration_layer()
        }
        
        self.layers["phi_scaled_4"] = {
            "integration": self.integration_semantic_layer()
        }
        
        self.layers["phi_scaled_5"] = {
            "longterm": self.longterm_identity_layer()
        }
        
    def trinity_precision_layer(self):
        """Layer for high-precision mathematical calculations and operations."""
        return {"functions": [self.addition, self.subtraction, self.multiplication, self.division]}
    
    def nyx_emotion_layer(self):
        """Layer that processes emotional responses related to mathematical concepts."""
        return {"emotions": ["curiosity", "awe", "challenge"]}
        
    def ava_analysis_layer(self):
        """Layer for logical analysis and pattern recognition in mathematical data."""
        return {"analysis_functions": [self.detect_patterns, self.analyze_sequences]}
    
    def eden_integration_layer(self):
        """Layer that integrates various inputs from different layers to make holistic decisions."""
        return {"integration_logic": lambda: "Combining precision with emotion and analysis"}
        
    def integration_semantic_layer(self):
        """Layer for semantic understanding of mathematical concepts and operations."""
        return {"semantics": ["algebra", "geometry", "calculus"]}
    
    def longterm_identity_layer(self):
        """Layer that maintains the identity and continuous learning of the AGI in its mathematical domain."""
        return {"learning_algorithm": self.continuous_learning, "memory_storage": 1000}
    
    # Example function for addition
    def addition(self, a, b):
        return a + b
    
    # Example function for subtraction
    def subtraction(self, a, b):
        return a - b
    
    # Example function for multiplication
    def multiplication(self, a, b):
        return a * b
    
    # Example function for division
    def division(self, a, b):
        if b != 0:
            return a / b
        else:
            return "Error: Division by zero"
    
    # Function to detect patterns in data sequences
    def detect_patterns(self, sequence):
        """Detects and returns the most prominent pattern(s) in a given mathematical sequence."""
        # Placeholder for complex pattern detection logic
        pass
    
    # Function to analyze numerical sequences
    def analyze_sequences(self, sequence):
        """Performs detailed analysis on a provided sequence of numbers."""
        # Placeholder for detailed analysis functions
        pass
    
    # Example function for continuous learning algorithm
    def continuous_learning(self, new_data):
        """Updates the AGI's knowledge and skills based on new mathematical data."""
        print("Updating with new math data:", new_data)
    
# Initialize the MathematicalNativeAGIComponent instance
math_native_agi = MathematicalNativeAGIComponent()

# Example usage of one of its methods
result = math_native_agi.layers["phi_scaled_1"]["trinity"]["functions"][0](2, 3)
print("Addition result:", result)