u/Turbulent_Agent_9943

Hi everyone,I’ve been working on a two-part research project that bridges the gap between elementary number theory and quantum spectral analysis. The goal was to find a physical motivation for the Riemann zeros using the inherent structure of the 6n ± 1 sequence.

Part 1: The Wave Interference Model (IWM)I started by treating prime numbers as points of "Zero Wave Density" ($\Phi=0$) in a deterministic interference pattern. This framework allows for a visualization of the prime distribution not as a random sequence, but as a resonance phenomenon.

Paper: https://doi.org/10.5281/zenodo.20112919

Code: https://github.com/model-vpr/deterministic-wave-prime-prediction

Part 2: The Crown HamiltonianBy mapping the 6n ± 1 progressions into a Schrödinger-type equation, a specific Hamiltonian emerges. The key finding is a centrifugal barrier term 3/(4r^2), which implies an angular momentum l=1/2.

This symmetry seems to "force" the spectrum onto the critical line Re(s)=1/2.

Numerical Results: Using sparse matrix diagonalization, I found a monotonic bijection between the operator’s eigenvalues and the first 10,000 Riemann zeros with a correlation of R^2 > 0.9999.

Paper: https://doi.org/10.5281/zenodo.20267135

Code: https://github.com/model-vpr/riemann-hamiltonian

I am looking for feedback specifically on the numerical mapping and whether this constructive approach to the Hilbert-Pólya conjecture aligns with current spectral theories.

Hi everyone,I’ve been working on a two-part research project that bridges the gap between elementary number theory and quantum spectral analysis. The goal was to find a physical motivation for the Riemann zeros using the inherent structure of the 6n ± 1 sequence.

Part 1: The Wave Interference Model (IWM)I started by treating prime numbers as points of "Zero Wave Density" ($\Phi=0$) in a deterministic interference pattern. This framework allows for a visualization of the prime distribution not as a random sequence, but as a resonance phenomenon.

Paper: https://doi.org/10.5281/zenodo.20112919

Code: https://github.com/model-vpr/deterministic-wave-prime-prediction

Part 2: The Crown HamiltonianBy mapping the 6n ± 1 progressions into a Schrödinger-type equation, a specific Hamiltonian emerges. The key finding is a centrifugal barrier term 3/(4r^2), which implies an angular momentum l=1/2.

This symmetry seems to "force" the spectrum onto the critical line Re(s)=1/2.

Numerical Results: Using sparse matrix diagonalization, I found a monotonic bijection between the operator’s eigenvalues and the first 10,000 Riemann zeros with a correlation of R^2 > 0.9999.

Paper: https://doi.org/10.5281/zenodo.20267135

Code: https://github.com/model-vpr/riemann-hamiltonian

I am looking for feedback specifically on the numerical mapping and whether this constructive approach to the Hilbert-Pólya conjecture aligns with current spectral theories.