Universal Integration Theory: A Structural Proof of the Collatz Conjecture 全數統一整合論：考拉茲猜想的結構性證明

Abstract / 摘要 English: This paper proposes the ”Universal Integration Theory” (UIT) to demonstrate the global convergence of the Collatz Conjecture. The core lies in transforming infinite evolution into structural regression governed by ”Parent-Child Causality.” By establishing the (𝑛 − 1)/4 lineage identification method, we prove that all odd numbers are allocated into specific 6𝑛 + 4 orbitals. We further demonstrate the ”Collective Inflow Mechanism,” where infinite sequences collapse into a single ancestral node. Finally, by excluding 6𝑘 type even cycles, we prove that as the system traces to 𝑛 = 0, the1-4-2-1 loop is the unique physical singularity. 中文：本文提出「全數統一整合論」，旨在證明考拉茲猜想之全域收斂性。研究核 心在於將無限的自然數演化轉化為受「父子因果律」制約的結構性回歸。透過建立 (𝑛 −1)/4 親子判定法，本文證實全體奇數家族皆可被精確分配至特定的6𝑛+4偶 數等比軌域中。研究進一步證明了「整列匯入機制」，即無限的奇數等比序列會集 體坍縮至單一奇數祖先節點。最終，透過排除6𝑘型偶數循環之可能性，本文證明 當系統追溯至基底𝑛=0時，1-4-2-1是空間中唯一的物理奇點。