Monthly Mathematics Conjectures: Open Problems, Evidence, and Complete Results

Abstract

This cumulative volume begins with the two problems in u/dForga's monthly r/LLMmathematics post, continues with nine open or partly open programmes, and places eight complete results afterward. Each chapter states its precise mathematical status and gives its bibliography at the point of use. This edition corrects chapter-level authorship and source attribution throughout. Kokuno Yumeto is credited for the split-zero, globalization, interpolating-zeta, and non-Eulerian-zeta programme. UmbrellaCorp_HR is credited for the circle-packing, Machin/arctangent, Taylor-walk, pair-process, and related source constructions. u/dForga is credited for the Reddit problems. ChatGPT 5, ChatGPT 5.6, and Gemini 2.5 Deep Think are named where their specific proof or source contributions occur. The Clankers denotes the contributing AI systems and does not replace the authors of inherited work. The mathematical statements, counterexample boundaries, and open/proved classifications are retained. Each item archive contains the corrected source and compiled paper. Earlier same-concept editions preserve the historical exact and formal verification artifacts.