#!/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()