The Riemann $Ξ$-function from primitive Markovian cycles II: Strip rigidity and divisor identification

We compare the Riemann $Ξ$–function to a canonical real-entire reference family arising from the cycle Laplacian developed in Paper I. These spectral determinants have only real zeros by self-adjointness. Our main tool is a rigidity lemma for holomorphic functions on horizontal strips. Applied to a normalized seam ratio linking $Ξ(2\cdot)$ to the reference family, this lemma shows that, under explicit holomorphy and boundary nonvanishing hypotheses verified in the forthcoming Paper III, the seam ratio extends to a zero-free holomorphic function of bounded type on each overlap strip. It follows that, on every admissible overlap strip, $Ξ(2\cdot)$ and the reference family have the same zero divisor.

💡 Research Summary

This paper establishes a conditional divisor‑identification theorem linking the classical Riemann Ξ‑function to a family of real‑entire spectral determinants that arise from primitive reversible Markov chains on finite cycles. In the first part of the series (