Numerical Evidence for Zeta-Resonances via the Ψ-Ω Discrete Resonance Approximation and Symbolic Prime Pattern Exploration

This work presents two complementary experimental investigations into the structure of the non-trivial zeros of the Riemann zeta function.<br>The main study introduces the Ψ-Ω Discrete Resonance Approximation, a novel symbolic approach using weighted delta sequences optimized to match known zeta zeros on the critical line. The numerical optimizer achieves machine precision alignment for the first nine non-trivial zeros and provides reproducible results. The complete source code for the optimizer is provided as supplementary material.<br>In a second exploratory analysis, symbolic frequency decomposition and prime number mapping of a cryptic text sequence were performed. Statistical correlations were observed between text structure, symbolic Fourier spectra, and prime positions, suggesting an interesting conceptual parallel to the distribution of primes and the zeros of the zeta function.<br>This combined work offers a methodological framework for experimental mathematics and symbolic analysis of resonance structures.<br>License: CC BY 4.0<br>Contact: M. Neuberger, Independent Researcher, Germany ([email protected])<br>