A Numerical Investigation of a Reduced Variational Problem Arising from Conrey's Mollifier Method
Description
We investigate a reduced variational problem derived from Conrey’s mean-value formulation for the zeros of the Riemann zeta function. Starting from a speculative “complex
induction” framework, we formalize the problem into a rigorous Generation-PreservationExhaustiveness decomposition. Within a symmetry-restricted polynomial subspace and a
formal extension beyond the admissible θ < 4/7 range, we find a well-defined numerical
maximum of approximately κ ≈ 0.695512 at θ ≈ 5.5 when the mollifier parameter R is
fixed at its optimal value from the θ = 4/7 calibration. The value is robust under degree
increase and multistart optimization, and the direct double-integral audit confirms the separated functional to machine precision. These results are presented as diagnostics of the
variational structure, not as theorems about ζ(s).
AI Assistance Statement
The author used large language model (AI) tools as an auxiliary aid during the preparation of this work. These tools were used to assist with symbolic derivations, code development, numerical implementation, exposition, and error-checking. All mathematical claims, derivations, computations, and conclusions were independently reviewed and verified by the author before inclusion in the manuscript.
The central research direction, formulation of the investigation, selection of numerical experiments, interpretation of results, and final presentation were determined by the author. Responsibility for any remaining errors rests solely with the author.
This work should therefore be regarded as human-directed research conducted with AI-assisted computational and drafting support.
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