Asymptotic Exactness of the Toroidal Prime Wave Function: Insensitivity to Error at Large Scale, Perfect Reconstruction of the Prime Distribution, and a Geometric Approach to the Riemann Hypothesis

Key Points

• This research aims to demonstrate the accuracy of the toroidal prime wave function in reconstructing the prime distribution based on the Riemann zeta function.
• Constructing the toroidal prime wave function from non-trivial zeros of the Riemann zeta function
• Applying a logarithmic chirp correction
• Analyzing the residual error in relation to prime magnitude
• Achieves asymptotically exact reconstruction of the prime distribution
• Residual error decreases monotonically as prime magnitude increases
• Indicates greater precision in reconstruction for larger primes