We introduce the Collatzogin Tree, a directed graph framework that partitions all positive integers by their residue classes modulo powers of two. This construction guarantees complete coverage of all integers and reveals a Fibonacci-branching structure at each level. Our main contributions are: The definition of the Collatzogin Tree and its affine node representation; Fibonacci branching structure for the number of nodes at each level; Nest-induction framework proving direct descent for a broad collection of residue classes and specific nodes; Confluence-chain method for the remaining branches I₇, J₁₅, I₂₇, and J₃₁; The introduction of lateral nodes to complete the structural analysis of the 3 4 branch.
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Ogin Sugianto (2026) studied this question.
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