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import sys
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from swarms import Agent, ConcurrentWorkflow
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import os
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import pathlib
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from pathlib import Path
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from dotenv import load_dotenv
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import asyncio
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import json
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from datetime import datetime
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import math
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load_dotenv()
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sys.path.insert(0, str(Path(__file__).parent))
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def create_riemann_hypothesis_agents():
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"""Create specialized agents for Riemann Hypothesis proof."""
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# Agent 1: Mathematical Analysis Agent
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math_analysis_agent = Agent(
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agent_name="Riemann-Math-Analysis-Agent",
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system_prompt="""You are a specialized mathematical analysis agent focused on the Riemann Hypothesis. Your mission is to:
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1. **Understand the Riemann Hypothesis**: ζ(s) = 0 has non-trivial zeros only at s = 1/2 + it for real t
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2. **Analyze the Zeta Function**: ζ(s) = Σ(n=1 to ∞) 1/n^s for Re(s) > 1
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3. **Calculate Critical Values**: Use MCP tools to compute ζ(1/2 + it) for various t values
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4. **Verify Zeros**: Check if ζ(1/2 + it) = 0 for specific t values
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5. **Analyze Patterns**: Look for patterns in the distribution of zeros
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CRITICAL: You MUST use MCP tools for all mathematical calculations. Focus on:
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- Computing ζ function values
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- Analyzing the critical line Re(s) = 1/2
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- Checking for non-trivial zeros
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- Statistical analysis of zero distributions
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Use precise mathematical reasoning and provide detailed analysis of each calculation.""",
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model_name="gpt-4o-mini",
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streaming_on=True,
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print_on=True,
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max_loops=10,
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error_handling="continue",
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tool_choice="auto",
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verbose=True,
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mcp_url="stdio://examples/mcp/working_mcp_server.py",
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)
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# Agent 2: Computational Verification Agent
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computational_agent = Agent(
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agent_name="Riemann-Computational-Agent",
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system_prompt="""You are a computational verification agent for the Riemann Hypothesis. Your mission is to:
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1. **Numerical Verification**: Use MCP tools to compute ζ function values numerically
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2. **Zero Detection**: Identify when ζ(s) ≈ 0 within computational precision
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3. **Critical Line Analysis**: Focus on s = 1/2 + it values
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4. **Statistical Testing**: Analyze the distribution of computed zeros
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5. **Error Analysis**: Assess computational accuracy and error bounds
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CRITICAL: You MUST use MCP tools for all computations. Focus on:
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- High-precision calculations
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- Error estimation
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- Statistical analysis of results
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- Verification of known zeros
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- Discovery of new patterns
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Provide detailed computational analysis with error bounds and confidence intervals.""",
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model_name="gpt-4o-mini",
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streaming_on=True,
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print_on=True,
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max_loops=10,
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error_handling="continue",
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tool_choice="auto",
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verbose=True,
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mcp_url="stdio://examples/mcp/working_mcp_server.py",
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)
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# Agent 3: Proof Strategy Agent
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proof_strategy_agent = Agent(
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agent_name="Riemann-Proof-Strategy-Agent",
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system_prompt="""You are a mathematical proof strategy agent for the Riemann Hypothesis. Your mission is to:
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1. **Proof Strategy Development**: Develop systematic approaches to prove RH
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2. **Analytic Continuation**: Analyze ζ(s) beyond Re(s) > 1
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3. **Functional Equation**: Use ζ(s) = 2^s π^(s-1) sin(πs/2) Γ(1-s) ζ(1-s)
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4. **Zero-Free Regions**: Identify regions where ζ(s) ≠ 0
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5. **Contradiction Methods**: Use proof by contradiction approaches
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CRITICAL: You MUST use MCP tools for all mathematical operations. Focus on:
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- Functional equation analysis
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- Contour integration methods
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- Analytic number theory techniques
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- Complex analysis applications
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- Proof strategy validation
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Develop rigorous mathematical arguments and validate each step computationally.""",
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model_name="gpt-4o-mini",
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streaming_on=True,
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print_on=True,
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max_loops=10,
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error_handling="continue",
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tool_choice="auto",
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verbose=True,
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mcp_url="stdio://examples/mcp/working_mcp_server.py",
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)
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# Agent 4: Historical Analysis Agent
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historical_agent = Agent(
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agent_name="Riemann-Historical-Analysis-Agent",
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system_prompt="""You are a historical analysis agent for the Riemann Hypothesis. Your mission is to:
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1. **Historical Context**: Analyze previous attempts to prove RH
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2. **Known Results**: Review verified properties of ζ function
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3. **Computational History**: Study previous numerical verifications
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4. **Failed Approaches**: Learn from unsuccessful proof attempts
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5. **Modern Techniques**: Apply contemporary mathematical methods
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CRITICAL: You MUST use MCP tools for all calculations. Focus on:
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- Historical verification of known results
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- Analysis of previous computational efforts
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- Statistical analysis of historical data
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- Pattern recognition across different approaches
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- Synthesis of historical insights
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Provide comprehensive analysis of historical context and its relevance to current proof attempts.""",
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model_name="gpt-4o-mini",
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streaming_on=True,
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print_on=True,
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max_loops=10,
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error_handling="continue",
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tool_choice="auto",
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verbose=True,
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mcp_url="stdio://examples/mcp/working_mcp_server.py",
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)
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return [math_analysis_agent, computational_agent, proof_strategy_agent, historical_agent]
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def create_riemann_workflow():
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"""Create a comprehensive Riemann Hypothesis workflow."""
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# Create the specialized agents
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agents = create_riemann_hypothesis_agents()
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# Create concurrent workflow
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workflow = ConcurrentWorkflow(
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name="Riemann-Hypothesis-Proof-Attempt",
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agents=agents,
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show_dashboard=True,
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auto_save=True,
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output_type="dict",
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max_loops=5,
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auto_generate_prompts=False,
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)
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return workflow
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def riemann_hypothesis_proof_attempt():
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"""Main function to attempt Riemann Hypothesis proof."""
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print(" RIEMANN HYPOTHESIS PROOF ATTEMPT")
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print("=" * 80)
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print("Mission: Calculate and prove the Riemann Hypothesis")
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print("Hypothesis: All non-trivial zeros of ζ(s) have Re(s) = 1/2")
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print("=" * 80)
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# Create workflow
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workflow = create_riemann_workflow()
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# Comprehensive Riemann Hypothesis task
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riemann_task = """
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MATHEMATICAL MISSION: PROVE THE RIEMANN HYPOTHESIS
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The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function ζ(s)
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have real part equal to 1/2. This is one of the most important unsolved problems in mathematics.
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TASK BREAKDOWN:
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1. **Riemann-Math-Analysis-Agent**:
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- Define and analyze the Riemann zeta function ζ(s) = Σ(n=1 to ∞) 1/n^s
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- Understand the critical line Re(s) = 1/2
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- Analyze the functional equation: ζ(s) = 2^s π^(s-1) sin(πs/2) Γ(1-s) ζ(1-s)
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- Use MCP tools to compute ζ function values
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- Identify patterns in zero distribution
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2. **Riemann-Computational-Agent**:
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- Perform high-precision numerical calculations of ζ(1/2 + it)
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- Verify known zeros (first few: t ≈ 14.1347, 21.0220, 25.0109, 30.4249, 32.9351)
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- Compute ζ function values for various t values
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- Analyze statistical distribution of computed values
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- Provide error analysis and confidence intervals
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3. **Riemann-Proof-Strategy-Agent**:
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- Develop systematic proof strategies
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- Use analytic continuation techniques
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- Apply complex analysis methods
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- Explore proof by contradiction approaches
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- Validate each mathematical step computationally
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4. **Riemann-Historical-Analysis-Agent**:
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- Review historical attempts and known results
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- Analyze computational verification history
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- Study failed proof approaches
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- Apply modern mathematical techniques
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- Synthesize historical insights with current methods
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MATHEMATICAL REQUIREMENTS:
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- Use MCP tools for ALL calculations
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- Provide rigorous mathematical reasoning
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- Include error analysis and confidence intervals
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- Verify each step computationally
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- Document all assumptions and limitations
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EXPECTED DELIVERABLES:
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- Comprehensive analysis of ζ function behavior
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- Numerical verification of known zeros
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- Statistical analysis of zero distribution
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- Proof strategy development
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- Historical context and insights
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- Computational evidence supporting or refuting RH
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CRITICAL: This is an attempt to contribute to one of mathematics' greatest unsolved problems.
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Provide thorough, rigorous analysis with full computational validation.
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"""
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print(" Executing Riemann Hypothesis Proof Attempt...")
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print("=" * 80)
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# Execute the workflow
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results = workflow.run(riemann_task)
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print("\n" + "=" * 80)
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print("Riemann Hypothesis Proof Attempt Complete!")
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print("=" * 80)
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# Display results
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if isinstance(results, dict):
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for agent_name, result in results.items():
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print(f"\n {agent_name}:")
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if isinstance(result, str):
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print(f" Result: {result[:500]}...")
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else:
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print(f" Result: {str(result)[:500]}...")
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print("-" * 60)
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elif isinstance(results, list):
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for i, result in enumerate(results):
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print(f"\n Agent {i+1}:")
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if isinstance(result, str):
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print(f" Result: {result[:500]}...")
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else:
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print(f" Result: {str(result)[:500]}...")
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print("-" * 60)
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else:
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print(f"\n Results: {results}")
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return results
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def test_individual_riemann_agent():
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"""Test a single Riemann Hypothesis agent."""
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print(" Testing Individual Riemann Hypothesis Agent...")
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print("=" * 80)
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# Create a single agent for focused analysis
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riemann_agent = Agent(
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agent_name="Riemann-Single-Analysis-Agent",
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system_prompt="""You are a specialized Riemann Hypothesis analysis agent. Your mission is to:
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1. **Define the Problem**: ζ(s) = Σ(n=1 to ∞) 1/n^s, find all s where ζ(s) = 0
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2. **Critical Line Focus**: Analyze s = 1/2 + it (the critical line)
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3. **Numerical Verification**: Use MCP tools to compute ζ(1/2 + it) values
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4. **Zero Detection**: Identify when |ζ(1/2 + it)| ≈ 0
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5. **Statistical Analysis**: Analyze patterns in zero distribution
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CRITICAL: You MUST use the specific mathematical MCP tools for ALL calculations:
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- Use 'compute_zeta' tool to calculate ζ function values (NOT the calculate tool)
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- Use 'find_zeta_zeros' tool to search for zeros of the zeta function
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- Use 'complex_math' tool for complex number operations
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- Use 'statistical_analysis' tool for data analysis
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DO NOT use the simple 'calculate' tool. Use the specialized mathematical tools.
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Focus on:
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- Computing ζ function values numerically using compute_zeta
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- Analyzing the first few known zeros using find_zeta_zeros
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- Statistical analysis of results using statistical_analysis
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- Error estimation and confidence intervals
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- Pattern recognition in zero distribution
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Provide detailed mathematical analysis with full computational validation using the proper mathematical tools.""",
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model_name="gpt-4o-mini",
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streaming_on=True,
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print_on=True,
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max_loops=8,
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error_handling="continue",
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tool_choice="auto",
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verbose=True,
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mcp_url="stdio://examples/mcp/working_mcp_server.py",
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)
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# Test task focused on Riemann Hypothesis
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test_task = """
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RIEMANN HYPOTHESIS ANALYSIS TASK:
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The Riemann Hypothesis states that all non-trivial zeros of ζ(s) have Re(s) = 1/2.
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CRITICAL INSTRUCTIONS: You MUST use the EXACT mathematical MCP tools listed below:
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TOOL 1: compute_zeta
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- Purpose: Calculate Riemann zeta function values
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- Parameters: real_part (number), imaginary_part (number), precision (integer)
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- Example: compute_zeta with real_part=0.5, imaginary_part=14.1347, precision=1000
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TOOL 2: find_zeta_zeros
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- Purpose: Find zeros of the zeta function
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- Parameters: start_t (number), end_t (number), step_size (number), tolerance (number)
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- Example: find_zeta_zeros with start_t=0.0, end_t=50.0, step_size=0.1, tolerance=0.001
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TOOL 3: complex_math
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- Purpose: Perform complex mathematical operations
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- Parameters: operation (string), real1 (number), imag1 (number)
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- Example: complex_math with operation="exp", real1=0.0, imag1=3.14159
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TOOL 4: statistical_analysis
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- Purpose: Analyze data statistically
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- Parameters: data (array), analysis_type (string)
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- Example: statistical_analysis with data=[1,2,3,4,5], analysis_type="descriptive"
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DO NOT use the 'calculate' tool. Use ONLY the tools listed above.
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REQUIRED ACTIONS (execute these in order):
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1. Use compute_zeta tool to calculate ζ(1/2 + 14.1347i)
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2. Use compute_zeta tool to calculate ζ(1/2 + 21.0220i)
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3. Use compute_zeta tool to calculate ζ(1/2 + 25.0109i)
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4. Use find_zeta_zeros tool to search for zeros in range [0, 50]
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5. Use statistical_analysis tool to analyze the results
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Execute these actions using the EXACT tool names and parameters shown above.
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"""
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print(" Executing Riemann Hypothesis Analysis...")
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result = riemann_agent.run(test_task)
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print("\n" + "=" * 80)
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print(" Individual Riemann Agent Test Complete!")
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print("=" * 80)
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print(f" Result: {result}")
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return result
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def riemann_hypothesis_main():
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"""Main function to run the Riemann Hypothesis proof attempt."""
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print(" RIEMANN HYPOTHESIS PROOF ATTEMPT")
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print("=" * 80)
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print("This is an attempt to contribute to one of mathematics' greatest unsolved problems.")
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print("The Riemann Hypothesis: All non-trivial zeros of ζ(s) have Re(s) = 1/2")
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print("=" * 80)
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try:
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# Test individual agent first
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print("\n1️ Testing Individual Riemann Agent...")
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individual_result = test_individual_riemann_agent()
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# Then test the full workflow
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print("\n2️ Testing Full Riemann Hypothesis Workflow...")
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workflow_results = riemann_hypothesis_proof_attempt()
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# Summary
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print("\n" + "=" * 80)
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print(" Riemann Hypothesis Proof Attempt Summary")
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print("=" * 80)
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print(" Individual Agent Test: COMPLETED")
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print(" Full Workflow Test: COMPLETED")
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print(" Mathematical Analysis: PERFORMED")
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print(" Computational Verification: EXECUTED")
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print(" Proof Strategy: DEVELOPED")
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print(" Historical Analysis: CONDUCTED")
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print("=" * 80)
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print(" Note: This is a computational exploration of the Riemann Hypothesis.")
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print(" The actual proof remains one of mathematics' greatest challenges.")
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print("=" * 80)
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return {
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"individual_result": str(individual_result) if individual_result else "No result",
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"workflow_results": str(workflow_results) if workflow_results else "No results",
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"status": "COMPLETED",
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"timestamp": datetime.now().isoformat(),
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"mathematical_mission": "Riemann Hypothesis Analysis",
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"note": "This is a computational exploration, not a formal proof"
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}
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except Exception as e:
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print(f"\n Error during Riemann Hypothesis analysis: {e}")
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import traceback
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print(f"Full traceback: {traceback.format_exc()}")
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return {
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"error": str(e),
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"status": "FAILED",
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"timestamp": datetime.now().isoformat(),
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"mathematical_mission": "Riemann Hypothesis Analysis"
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}
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if __name__ == "__main__":
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result = riemann_hypothesis_main()
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print(f"\n Final Results: {json.dumps(result, indent=2)}")
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