This analysis demonstrates the role of the Riemann zeta function in defining states in a helical framework, indicating implications for geometric characterization.
We introduce a geometric framework for the Dirichlet partial sums of the Riemann zeta function based on a canonical helical carrier arising from the principal asymptotic term n^(1/2-it). After subtracting the principal term, we analyze the remainder through a second-stage projection onto the helical mode. In the co-rotating helix frame this leads to a dichotomy between a line state (perfect helix regime) and a wave state. We show that the wave component coincides with the second-stage residual and cannot produce vanishing of the second analysis. This yields a geometric characterization of the zero condition in terms of collapse onto the perfect helix regime.
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Aviad Shetrit (2026) studied this question.
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