Research Note 37 in the "Geometry of the Critical Line" programme. Paper 46 established that the leading-order Evans zeros in each winding sector are located at Eₙ = nπ/L − iDₘ, with depth Dₘ growing linearly in m. This note assembles the cross-sector Evans zero lattice and studies its spectral zeta function. The associated modulus Epstein zeta has a simple pole at s = 1 with residue 2/π², and the lattice has aspect ratio 2b/a = 32/π — a pure geometric invariant of the SCT manifold. The phase-sensitive Evans zeta is numerically consistent with the same pole order. The Mellin transform identifies t⁻¹ short-time heat-trace asymptotics (two-dimensional Weyl law), whereas the Riemann side requires t⁻¹/². No mechanism internal to the Evans lattice reduces the pole from s = 1 to s = 1/2, confirming Kill #67 (dimensional saturation) at the spectral-zeta level and identifying the dimensional reduction as a genuine quotient problem.
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Pavel Kramarenko-Byrd
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Pavel Kramarenko-Byrd (Wed,) studied this question.
www.synapsesocial.com/papers/69d8955f6c1944d70ce064cb — DOI: https://doi.org/10.5281/zenodo.19462779