Research-Stack/5-Applications/scripts/ask_swarm_resonance_quaternion_stochastic_analysis.py

#!/usr/bin/env python3
"""
Swarm Query: Resonance Quaternion Stochastic Differentials Analysis

Query the swarm system for their thoughts and analysis on the new formalism:
Resonance differentials harnessed for quaternion calculations via stochastic differentials.
"""

import json
import uuid
from pathlib import Path
from datetime import datetime

def generate_resonance_quaternion_stochastic_request():
    """Generate swarm request for resonance quaternion stochastic differential analysis."""
    
    request = {
        "request_id": f"swarm_resonance_quaternion_stochastic_{uuid.uuid4().hex[:12]}",
        "timestamp": datetime.now().isoformat(),
        "query_type": "mathematical_formalism_analysis",
        "scope": "resonance_quaternion_stochastic_differentials",
        "priority": "P0_CRITICAL",
        "description": "Ask the swarm for their thoughts on resonance differentials harnessed for quaternion calculations via stochastic differentials",
        
        "context": {
            "insight": "The differentials of resonance could be harnessed for quaternion calculations via stochastic differentials",
            "formalism_id": "0.4.4 Resonance_Quaternion_Stochastic_Differentials",
            "core_equation": "dq = (dR_resonance) ⊗ (dW_stochastic)",
            "evolution_equation": "q(t+dt) = q(t) ⊗ exp(½·∇²R·dt + ∇R·dW)",
            "resonance_differential": "dR_resonance = ∂R/∂ω·dω + ∂R/∂t·dt",
            "stochastic_differential": "dW_stochastic = √dt·N(0,1)"
        },
        
        "integration_points": {
            "resonance_hierarchy": "0.4.1 Topology_Resonance_Hierarchy - Resonance across all topology levels",
            "spherion_resonance": "0.4.2 Spherion_Resonance_Dynamics - Spherion-specific resonance",
            "waveform_coupling": "0.4.3 Waveform_Resonance_Coupling - Waveform-spherion coupling",
            "sluq_triage": "1.1.3 SLUQ_Triage - Stochastic triage and trajectory pruning",
            "quaternion_genomic": "1.1.5 Spherion_Coordinate_Transform - Quaternion-based S³ embedding",
            "void_resonance": "1.1.13 Negative_Pyramid_Voids - Anti-resonance from negative heights"
        },
        
        "analysis_questions": {
            "mathematical_rigor": {
                "description": "Assess mathematical correctness and completeness",
                "questions": [
                    "Is the Itô calculus formulation correct?",
                    "Are the cross-terms properly accounted for?",
                    "Does the quaternion multiplication preserve unit norm?",
                    "Is the stochastic integral well-defined?"
                ]
            },
            
            "physical_interpretation": {
                "description": "Assess physical meaning and plausibility",
                "questions": [
                    "What does resonance gradient represent physically?",
                    "How does stochastic noise improve quaternion calculations?",
                    "What is the physical interpretation of the Itô correction term?",
                    "Does this respect energy conservation principles?"
                ]
            },
            
            "computational_advantages": {
                "description": "Assess computational benefits and efficiency",
                "questions": [
                    "How does this improve quaternion rotation accuracy?",
                    "What is the computational overhead of stochastic integration?",
                    "Does this enable new quaternion operations?",
                    "How does this compare to deterministic quaternion methods?"
                ]
            },
            
            "integration_feasibility": {
                "description": "Assess integration with existing systems",
                "questions": [
                    "How does this integrate with SLUQ triage?",
                    "Can this be combined with spherion resonance dynamics?",
                    "Does this complement or conflict with existing quaternion work?",
                    "What are the implementation priorities?"
                ]
            },
            
            "research_implications": {
                "description": "Assess research significance and novelty",
                "questions": [
                    "Is this a novel contribution to stochastic calculus?",
                    "How does this advance quaternion computation theory?",
                    "What are the theoretical implications for resonance theory?",
                    "What are the practical applications in the Research Stack?"
                ]
            }
        },
        
        "expected_deliverables": {
            "mathematical_validation": "Formal validation of the stochastic differential formulation",
            "physical_interpretation": "Physical meaning of each term in the equations",
            "computational_analysis": "Performance comparison with deterministic methods",
            "integration_roadmap": "Step-by-step integration plan with existing systems",
            "research_significance": "Assessment of novelty and contribution to the field"
        },
        
        "validation_criteria": {
            "mathematical_correctness": "Must satisfy Itô calculus axioms",
            "unit_norm_preservation": "Quaternion operations must preserve |q| = 1",
            "energy_conservation": "Must respect thermodynamic energy principles",
            "stochastic_convergence": "Must converge to deterministic case as noise → 0",
            "integration_compatibility": "Must integrate cleanly with existing resonance and quaternion work"
        },
        
        "swarm_response_format": {
            "overall_assessment": "High-level summary of thoughts on the formalism",
            "detailed_analysis": "Point-by-point analysis of each question",
            "recommendations": "Specific recommendations for implementation or refinement",
            "priority_actions": "Immediate next steps if the formalism is viable",
            "concerns_or_caveats": "Any concerns or limitations identified"
        }
    }
    
    return request

def save_request(request, output_path):
    """Save swarm request to file."""
    Path(output_path).parent.mkdir(parents=True, exist_ok=True)
    
    with open(output_path, 'w') as f:
        json.dump(request, f, indent=2)
    
    return output_path

def main():
    """Generate and save resonance quaternion stochastic differential analysis request."""
    print("=" * 70)
    print("Swarm Query: Resonance Quaternion Stochastic Differentials Analysis")
    print("=" * 70)
    
    # Generate request
    request = generate_resonance_quaternion_stochastic_request()
    
    # Save request
    output_path = "shared-data/data/swarm_requests/swarm_resonance_quaternion_stochastic_analysis.json"
    saved_path = save_request(request, output_path)
    
    print(f"\nRequest generated and saved to: {saved_path}")
    print(f"Request ID: {request['request_id']}")
    print(f"Priority: {request['priority']}")
    print(f"Formalism ID: {request['context']['formalism_id']}")
    
    print("\nCore Insight:")
    print(f"  {request['context']['insight']}")
    
    print("\nIntegration Points:")
    for integration_point, description in request['integration_points'].items():
        print(f"  - {integration_point}: {description}")
    
    print("\nAnalysis Categories:")
    for category, info in request['analysis_questions'].items():
        print(f"  - {category}: {len(info['questions'])} questions")
    
    print("\nExpected Deliverables:")
    for deliverable in request['expected_deliverables'].keys():
        print(f"  - {deliverable}")
    
    print("\nValidation Criteria:")
    for criterion in request['validation_criteria'].keys():
        print(f"  - {criterion}")
    
    print("\n✅ Swarm query generation completed successfully")
    print("\nThis query asks the swarm for their thoughts on:")
    print("  - Mathematical rigor of the formulation")
    print("  - Physical interpretation and plausibility")
    print("  - Computational advantages")
    print("  - Integration feasibility with existing systems")
    print("  - Research significance and novelty")

if __name__ == "__main__":
    main()