This repository contains various Java programs that demonstrate different concepts of Java programming, including data structures, algorithms, multithreading, file handling, and object-oriented programming. Each file is labeled with a unique identifier for easy reference.

Formal and empirical investigation of the Collatz conjecture. Combines topological, combinatorial, and analytic perspectives: extension on Z₂×Z₃, backward automaton with canonical horizon, and Lyapunov drift analysis showing uniqueness of the cycle.

Independent research demonstrating discovery of structural limits and binary emergence in ternary algebraic spaces (GL(3,F₃)), with reproducible computational proofs and published codebase (GAP + Python).