This report documents the cross-domain machine learning validation between quantum chaos metrics and biological sequence features using the Z Framework.

• Source: DiscreteZetaShift 5D embeddings and Riemann zeta zero analysis
• Features: D, E, F, I, O (from DiscreteZetaShift), amplitude, curvature, theta transformations
• Target: Quantum chaos classification based on O value threshold
• Samples: ~100 integer sequences (n = 2 to 101)

• Source: Real CRISPR target sequences and synthetic DNA sequences
• Features: Length, GC content, dimer/trimer complexity, base frequencies, quantum bridge
• Target: CRISPR efficiency classification based on GC content and complexity
• Samples: ~100 DNA sequences (50-150 bp)

• Algorithm: Random Forest Classifier (100 estimators)
• Preprocessing: StandardScaler normalization
• Validation: 5-fold cross-validation with 70/30 train-test split
• Metrics: Accuracy, cross-validation mean ± std

• Approach: Train on one domain, test on another
• Feature Alignment: Use minimum common feature count
• Directions: Quantum→Biological and Biological→Quantum
• Hypothesis: Z Framework enables cross-domain pattern recognition

1. Within-Domain Performance: Demonstrates ML models can classify quantum chaos and biological efficiency
2. Cross-Domain Transfer: Tests whether quantum mathematical patterns predict biological behavior
3. Feature Importance: Identifies which Z Framework components are most predictive
4. Statistical Significance: Cross-validation provides confidence intervals

• Universal Invariance: c normalization ensures frame-independent analysis
• Curvature Transformations: κ(n) = d(n)·ln(n+1)/e² bridges domains
• Golden Ratio Modular: θ'(n,k) = φ·((n mod φ)/φ)^k reveals hidden patterns
• 5D Embeddings: (x,y,z,w,u) coordinates provide geometric feature space

• Success Threshold: >60% accuracy for within-domain classification
• Cross-Domain Significance: >50% accuracy (better than random)
• Reproducibility: Results stable across multiple runs
• Statistical Rigor: Cross-validation confidence intervals reported

• Sample Size: Limited to ~100 samples per domain for computational efficiency
• Feature Engineering: Simplified spectral analysis for biological sequences
• Domain Gap: Quantum and biological systems have different scales and physics
• Validation Scope: Proof-of-concept rather than comprehensive validation

• Larger Datasets: Scale to 1000+ samples per domain
• Advanced Features: Include full wave-CRISPR spectral analysis
• Deep Learning: Neural networks for complex pattern detection
• Physical Validation: Test predictions against experimental CRISPR data

All code, data, and results are available in the test-finding/ml-cross-validation/ directory:

• scripts/prepare_datasets.py: Data generation
• scripts/train_models.py: ML model training
• scripts/run_cross_validation.py: Validation pipeline
• results/: Output files and visualizations

Execute scripts in order to reproduce all results with identical random seeds.