Motohiro Hamaguchi
This project presents a novel macro-level approach to the Collatz conjecture based on binomial expansion structures. By analyzing the interplay between the binary periodicity of binomial coefficients in Pascal's triangle and the carry generated by the Collatz operation (3X+1), we define a universal structure M(n-1) independent of any arbitrary odd number a. We demonstrate an absolute algebraic barrier imposed on the parameter m in the general intermediate even form b * 2^m - 2, verified by massive collapse data at n=18.