The Collatz Conjecture: A Proof Through Inverse Generation Analysis
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We present a complete proof of the Collatz conjecture using a novel approach based on generator functions. By analyzing the inverse mappings of the Collatz function through carefully defined generator operations, we establish that all natural numbers must eventually reach 1 under the Collatz iteration. The proof relies on demonstrating fundamental incompatibilities between the requirements for divergent sequences and the constraints imposed by even-odd patterns in the natural numbers.