Incorporate Exact Sympy Computations: Replace the current trial-division is_prime and _divisor_count with SymPy's isprime and divisor_count for higher precision and efficiency, especially for larger N_POINTS; this aligns with cognitive-number-theory's emphasis on accurate divisor density in κ(n) = d(n) ⋅ ln(n)/e², reducing errors in curvature calculations.
Dynamic Prime Gap Integration: Modify the prime_gap parameter in __call__ to use actual gaps from consecutive primes (e.g., via a precomputed list), scaled by π as in prime_number_geometry's Z(n) = n ⋅ prime_gap / π, for more precise y-warping that reflects true distribution irregularities.
Optimize Helix Frequency with Golden Ratio: Tune HELIX_FREQ dynamically using φ (golden ratio) from prime_curve's θ'(n, k) ≈ φ ⋅ ((n mod φ)/φ)^k at optimal k≈0.3, such as HELIX_FREQ = 1/(2⋅π⋅φ), to enhance helical resonance and prime clustering visibility in z-coordinates.
Enhance Curvature with Z-Metric Variants: Update _compute_curvature to include z_metric's Z-resonance ((n mod ln(n)) ⋅ d(n)/e) or lightprimes' Z_κ(p_i) = 2⋅ln(p_i)/e² for primes, providing finer-grained warping that separates twin primes as minimal-curvature geodesics.
Apply Frame Shift Corrections Bidirectionally: Integrate universal_frame_shift_transformer's UniversalFrameShift class for inverse transforms in y and z, using rate ≈ e/π and invariant C=e, to correct observational biases and achieve ~35x density improvements in visualized clusters.
Add Neural Forecasting Layer: From lightprimes, incorporate a simple Torch MLP (e.g., 2→20→1 layers) for online fine-tuning of Z-corrections, predicting ΔZ based on inputs [n, δ_i] and applying sigmoid constraints, to refine y-values for emerging "prime news" in large n.
Implement Vortex Pre-Filtering: Extend the apply_vortex_filter to pre-process n_vals, eliminating ~71.3% composites as in z_metric, then plot only candidates with color gradients by Z-vector magnitude (√(curvature² + resonance²)) for sharper prime highlights.
Scale to Higher Dimensions with PCA: Project the 3D plot into a holographic manifold using lightprimes' 16D Z-embeddings, then reduce via SciPy's PCA to 3D for visualization, revealing geodesic extrapolations and improving separation accuracy.
Increase Resolution and Log Scaling: Boost N_POINTS to 100,000+ and apply logarithmic scaling to the y-axis (e.g., ax.set_yscale('log')), drawing from cognitive-number-theory's ln(n) terms, to handle density variations without clipping high-curvature composites.
Add Spectral Disruption Metrics: Inspired by wave-crispr-signal's FFT-based features (Δf₁, ΔEntropy), apply Fourier transforms to helical z-coordinates, coloring points by spectral disruption scores to quantify and visualize prime pattern anomalies more precisely.