化核理论:Collatz猜想中奇数核 R 的单调递减推导

Based on the symbolic dynamics framework of the Collatz conjecture, this paper introduces a parameterized transformation relation 3mR−1=2j(2i3pR1−1) which defines the odd cores RR and R1R1, both coprime to 6. By analyzing the algebraic constraints on the exponents i,j,m,pi,j,m,p, it is proved that under the non-trivial conditions j≥1, B>1, and the typical case m≤pm≤p, the odd cores satisfy the strict inequality R>R1. This derivation provides an algebraic and rigorous foundation for the stepwise descent of the odd core in Collatz sequences, attempting to establish a logical basis for an inductive proof of the conjecture.