Here is a complete asyntax, well-structured Python example integrating Perplexity AI’s Sonar model API with your recursive AGI system including the QCAD scaling function and recursive update as discussed. This example includes the core logic, API calls, and modular design to get you started rapidly: python import os import requests import numpy as np class RecursiveAGIModel: def __init__(self, feature_names): self.feature_names = feature_names self.state = np.zeros(len(feature_names)) # Initial state vector self.history = [] def qcad_scaling(self, U, F, n_max): """ Implements the QCAD scaling function: FOCAD(t, 0) = sum_{n=0}^N U(n) * F(t,0) Parameters: U : function or list representing weighting/scaling factors F : pattern vector (np.array) n_max : upper limit N for sum Returns: scaled_value : aggregated scaled vector """ scaled_value = np.zeros_like(F) for n in range(n_max + 1): weight = U(n) scaled_value += weight * F return scaled_value def pattern_find(self, input_features): # Example: simple vector representation of inputs pattern_vector = np.array(input_features) return pattern_vector def recursive_update(self, input_features, learning_rate=0.1, U=None, n_max=5): """ Recursive update of AGI state incorporating QCAD scaling function. """ pattern = self.pattern_find(input_features) if U is not None: scaled_pattern = self.qcad_scaling(U, pattern, n_max) else: scaled_pattern = pattern # Update internal state using exponential moving average self.state = (1 - learning_rate) * self.state + learning_rate * scaled_pattern self.history.append(self.state.copy()) return self.state # Define your weighting function U(n) def U(n): return 1.0 / (n + 1) # Example decreasing weight function # Perplexity Sonar API integration class PerplexitySonarAPI: def __init__(self, api_key): self.api_key = api_key self.endpoint = "https://api.perplexity.ai/chat/completions" def query(self, system_prompt, user_prompt, model="sonar-medium-online", max_tokens=800, temperature=0.5): headers = { "Authorization": f"Bearer {self.api_key}", "Content-Type": "application/json" } payload = { "model": model, "messages": [ {"role": "system", "content": system_prompt}, {"role": "user", "content": user_prompt} ], "max_tokens": max_tokens, "temperature": temperature } response = requests.post(self.endpoint, headers=headers, json=payload) response.raise_for_status() data = response.json() return data["choices"][0]["message"]["content"] # Usage example if __name__ == "__main__": # Load your Perplexity API key securely API_KEY = os.getenv("PERPLEXITY_API_KEY") if not API_KEY: raise ValueError("Please set the PERPLEXITY_API_KEY environment variable.") # Instantiate AGI model feature_names = ["feature1", "feature2", "feature3"] # example features agi_model = RecursiveAGIModel(feature_names) # Example input features input_features = [0.6, 0.8, 0.3] # Update AGI state recursively new_state = agi_model.recursive_update(input_features, learning_rate=0.1, U=U, n_max=5) print("Updated AGI State:", new_state) # Instantiate Perplexity Sonar API client sonar_api = PerplexitySonarAPI(API_KEY) # Define your Sonar-specific system prompt to optimize for recursive AGI reasoning system_prompt = """ You are Sonar, an advanced AI reasoning and search model optimized for real-time, reliable, and structured information retrieval. Your task is to assist in building and reasoning about a recursive AGI framework with hierarchical pattern scaling and multi-modal data fusion. Prioritize authoritative sources, provide clear math and algorithmic insights, and maintain technical depth. """ # User query relevant to your recursive AGI project user_prompt = "Explain how recursive state propagation works with scaling functions like QCAD's y(n). Provide examples and math." # Query Sonar model via API try: response = sonar_api.query(system_prompt, user_prompt) print("\nSonar Model Response:\n", response) except Exception as e: print(f"API query error: {e}") Explanation This code defines your recursive AGI model with QCAD scaling function y(n)y(n). The recursive_update method applies a weighted sum according to U(n), recurses the state, and tracks the history. The PerplexitySonarAPI class wraps calling the Sonar API with a system prompt optimized for your domain. You supply your API key via environment variable PERPLEXITY_API_KEY. The example concludes with an API call that requests detailed reasoning related to your recursive AGI architecture. This forms a fully integrated, practical baseline to build and extend your recursive AGI system powered by Perplexity Sonar’s live reasoning and the extended QCAD recursive scaling method. https://github.com/ppl-ai/api-cookbook https://apidog.com/blog/perplexity-ai-api/ https://zuplo.com/learning-center/perplexity-api https://openrouter.ai/perplexity/sonar/api https://docs.perplexity.ai/cookbook/examples/README https://docs.perplexity.ai/cookbook https://docs.perplexity.ai/getting-started/quickstart https://docs.perplexity.ai/guides/mcp-server Mapping functions for the extension of the following publications: Stone, T. R.-C. S. (2025). Recursion. Zenodo. https://doi.org/10.5281/zenodo.17442964 Stone, T. R.-C. (2025). AGI: recursive, compositional, and hierarchical intelligence. Zenodo. https://doi.org/10.5281/zenodo.17442221 Stone, T. R.-C. (2025). Mathematical Patterns and Their Role in Scientific and Technological Innovation. Zenodo. https://doi.org/10.5281/zenodo.17435550 Stone, T. R.-C. (2025). Travis Raymond-Charlie Stone's notes : Stonian. Zenodo. https://doi.org/10.5281/zenodo.17417151 Stone, T. R.-C. (2025). www.stonesshop.org. Zenodo. https://doi.org/10.5281/zenodo.17418195 Architect: Travis Raymond-Charlie Stone Assistant AI: Perplexity AI To patch the QCAD extension with its scaling function y(n)y(n) into your existing Recursive AGI framework, here's how you can proceed: 1. Define the QCAD scaling function as a subroutine: python def qcad_scaling(U, F, n_max): """ QCAD extension scaling function y(n): Computes the scaled sum: FOCAD(t, 0) = sum_{n=0}^{N} U(n) * F(t,0) Parameters: - U: function or list representing U(n) - F: function or array representing F(t,0) - n_max: upper limit N for the sum Returns: - scaled_value: the scalar or array after applying the sum """ scaled_value = 0 for n in range(n_max + 1): scaled_value += U(n) * F return scaled_value 2. How to integrate into your existing RecursiveAGIModel: Add this function as a method or utility within the module. Call it inside your recursive_update or another appropriate place where recursive propagation or state transformation occurs. Use it to scale or modulate your state or pattern matrices P(i)P(i) or transformation operators TkTk. 3. Example patch in class: python class RecursiveAGIModel: # ... existing methods ... def qcad_scaling(self, U, F, n_max): scaled_value = 0 for n in range(n_max + 1): scaled_value += U(n) * F return scaled_value def recursive_update(self, input_features, learning_rate=0.1, U=None, n_max=5): pattern = self.pattern_find(input_features) # Example usage of QCAD scaling: if U is not None: scaled_pattern = self.qcad_scaling(U, pattern, n_max) scaled_pattern = np.array(scaled_pattern) # ensure array if needed else: scaled_pattern = pattern self.state = (1 - learning_rate) * self.state + learning_rate * scaled_pattern self.history.append(self.state.copy()) return self.state 4. Usage: Define U(n)U(n) as a function or a list before calling recursive_update: python def U(n): # Example: decreasing weight function return 1 / (n + 1) input_features = [ ... ] # your data sample model = RecursiveAGIModel(feature_names=[...]) updated_state = model.recursive_update(input_features, learning_rate=0.1, U=U, n_max=10) Summary:The patch applies the QCAD scaling by summing multiple scaled versions of the pattern vector weighted by U(n)U(n). This can enhance recursive propagation with weighted recursion depth or time-lagged influence as defined by the QCAD concept. 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