Abstract: This paper identifies the fundamental difficulty of the long-unresolved Collatz Conjecture as stemming from an unconscious self-limitation in conventional mathematics—specifically, a structural ``lack of collaboration'' between the linear definition of natural numbers (Peano Axioms) and non-linear structural analysis (Cantor's Set Theory). We propose that, to solve a non-linear Halting Problem like the Collatz Conjecture, the proof must prioritize the structural fundamental of ``symmetry of the start and stop point ($1$)'' instead of adhering to linear methods. Specifically, we resolve the ``bijective definition deficit'' of the mapping existing between specific sub-patterns (e.g., $4n+1 leftrightarrow 3n+1$) derived from the Collatz operation, by using Cantor's dimensional expansion pairing function. This method reconstructs the Collatz operation as a closed, bijective structure centered at $1$, structurally and completely excluding the possibility of cycles other than $1$ and divergence to infinity. This represents a structural solution that, by integrating the Peano Axioms and Cantor's Set Theory, rigorously guarantees the global stability of the Collatz infinite tree for the first time.Keywords: Collatz, Tree Equivalence Theorem, Peano's Successor Function, Cantor's Pairing Function.MSC 2020: 03D50, 11B83.