QTower Algebra: A Unified Framework for Recursive Meta-Questions in Logic, Computation, and Automated Reasoning

QTower Algebra introduces a unifying algebra for iterative meta‑reasoning. We formalize a Qtower as the the sequence Q,□Q,□□Q,… and analyze it in a Boolean‑algebra‑of‑operators setting where the modal operator □ acts levelwise. This paper covers QTowers which refers to n-Tuples (Q1,...Qi,..Qn) consisting of Q1 = A base Question and Qi="Is Qi-1 provable?" For all i >=2., Answer Mapings A: Q->{True, False} and exhibits connections to many different areas of Mathematics and Theoretical Computer Science. Topics include: Representing irational numbers with QTowers Perfectoid Logical Rings Hilberts Hotel, Busy Beaver Graphs and QTowers Linear Time Logik Proof Stability and new in V1.2 The Gödel Gap Mini QTowers and LLMs/Transformer Architecture "The Trickster" Anouncement: A short introductionary version of QTower Algebra is being worked on. I like to thank the academic community for their strong interest in QTower Algebra. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0).