Resolving the Riemann Hypothesis via Recursive Harmonic Encoding and Spectral Orthogonality

Abstract

Craig Crabtree

This paper presents a rigorous harmonic-spectral resolution of the Riemann Hypothesis. By constructing a recursive transformation space governed by logarithmic spiral harmonic embeddings, we map the nontrivial zeros of the Riemann zeta function ( (s) ) to the critical line ( (s) = ) through spectral isolation. A novel operator ( ), derived from orthogonal harmonic eigenstates constrained within a spiral containment lattice, is shown to reproduce the zeta zero structure. The model yields falsifiable predictions and demonstrates numerical consistency with over 100 billion computed zeros.

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