MRST-Based Binary Structural Analysis of the Collatz Conjecture — IF-THEN Semantic Collapse and Convergence Dynamics in Binary Arithmetic Systems —

This repository contains the main paper and supplementary verification archives for the MRST-based binary structural analysis of the Collatz conjecture. The study reformulates the Collatz process as a binary arithmetic state-transition system governed by carry propagation, bit-density dissipation, and irreversible right-shift truncation, rather than treating it solely as a classical number-theoretic function. The repository additionally includes long-horizon MRST operational records and adversarial validation logs generated through extended AI-assisted reasoning processes involving ChatGPT and Gemini systems. Included files: MAIN_PAPER_MRST_Collatz_Binary_Model.pdf SUPPLEMENT_Gemini_Execution_Log_v1.18.pdf SUPPLEMENT_ChatGPT_Validation_Log_v4o.pdf This version expands the previous MRST operational archive with supplementary structural verification datasets and long-horizon reasoning evidence.