Spectral Analysis of Expository Gaps in "New Large Value Estimates for Dirichlet Polynomials'': Rigorous Solutions and Methodological Frameworks

This work presents a systematic analysis of four critical expository gaps identified in the influential paper ``New Large Value Estimates for Dirichlet Polynomials'' by Guth and Maynard (arXiv:2405.20552), together with complete rigorous solutions and reusable methodological frameworks. Through a hybrid methodology combining traditional mathematical analysis with artificial intelligence techniques for systematic gap detection, we provide: (1) complete derivation of the exponent 30(1-σ)/13 as the harmonic mean between Ingham and Guth-Maynard bounds, (2) detailed spectral analysis of trivial term cancellation, (3) optimization framework for Dirichlet polynomial partitions, and (4) rigorous justification of probabilistic bounds. The developed frameworks transcend punctual corrections and establish methodologies applicable to broader families of L-functions.