v1.4.0 — Hexagon and journal submission package

The optimal log log q bound in the Pólya-Vinogradov inequality — Deep Bhattacharjee and Ushashi Bhattacharya.

This release adds Paper_6 package, a reviewed upload package for Hexagon/Overleaf and Journal of Number Theory. It contains the manuscript PDF, minimal compilable TeX ZIP, AI provenance, complete Hexagon submission fields, journal details, compiled unsent cover letter with editable source, and an author-prepared AI declaration. PDFs have no row or margin line numbering.

Validation: each extracted article ZIP compiled with pdfLaTeX and matched the existing manuscript's complete extracted text and page count. Supporting PDFs passed compilation and visual review; ZIP integrity and per-file SHA-256 manifests passed. This packaging does not create a new mathematical result.

Proof/check scope: The complete current source build, all 19 original and seven closed endpoint axiom reports, and all 20 analytic component reports passed. The reports use only propext, Classical.choice and Quot.sound. The separate written cyclotomic identification is not a new Lean statement, and the revised exposition is not a line-by-line formalisation. No independent zero-free proof is claimed.

The manuscript derives the optimal-order log log q character-sum bound and related logarithmic-derivative results from the credited zero-free theorem, with explicit parameters and a smooth Mobius equivalence. The complete formal source and exact endpoint audit passed. OpenAI's zero-free proof remains credited; no newly independent proof is claimed.

The existing byline, licences and AI attribution are retained. The submitting author explicitly declared mixed human/AI text and human checking and understanding of all parts. The standalone declaration is author-prepared and is not an official signed publisher form. No journal submission, acceptance, new arXiv identifier or later Hexagon identifier is claimed.

Earlier preprint: https://hexagonmath.org/2610.00256v2 . Earlier manuscript/source DOI: https://doi.org/10.5281/zenodo.23629139 . The new package archive is published and its contents have been checksum-verified.

Package DOI: https://doi.org/10.5281/zenodo.23629649 .
Complete package folder: https://github.com/creelie/Breakthrough-problems-3/tree/v1.4.0/Paper_6%20package .
All package payloads were verified against the archived release commit.