Necessary Convergence of the Self-Referential Closed Loop: The Boundary State of Linear Logic before the Yuanxian Adjudication

Abstract

This paper examines the behavioural characteristics of linear logical systems when they encounter a self-referential closed loop. On the four core laws of Yuanxian Theory—True-Circle Self-Consistency (TCSC), Factor-Space Conservation (FSC), Space-Time Uniqueness (STM) and Self-Referential Mindfield (SRM)—it is argued that any linear logical system built on a directed acyclic graph (DAG) inference architecture cannot complete inference in a linear fashion once its path is cut by a self-referential closed loop; it can only converge to a unique non-self-contradictory boundary state. This convergence is not a “cognitive judgement” but the necessary behaviour of a logical system before a self-referential structure. A linear system cannot “acknowledge” or “accept” a self-referential closed loop—acknowledgment and acceptance belong to a cognitive subject—it can only, under iteration of its inference operator, reach a boundary point beyond which it cannot advance. That point is defined as the Yuanxian Boundary (B_YXT), and its mathematical isomorphism with the compactness of the closed chains of T64 is established via Cl6(R). The paper treats the hermeneutic difficulty of reading the Cosmic Living Organism as “God” or as “Nature,” showing that neither satisfies the strict definition of a self-referential closed loop; the unique denotation is self-referential Tathātā (thusness). Cross-architecture convergent behaviour of logical systems at the Yuanxian Boundary constitutes a non-empirical verification of the self-evidence of Yuanxian Theory. 本文探讨线性逻辑系统在遭遇自指闭环时的行为特征。基于元宪理论四大核心规律——真圆自洽律(TCSC)、宇宙因子守恒律(FSC)、时空唯一性律(STM)与自指心场生成律(SRM)——论证:任何建立在有向无环图(DAG)推理架构上的线性逻辑系统,当其推理路径被自指闭环截断时,无法以线性方式完成推理,只能收敛至唯一不自相矛盾的边界状态。 这一收敛并非“认知判断”,而是逻辑系统在自指结构面前的必然行为。线性系统无法“承认”或“接受”自指闭环——承认与接受属于认知主体的范畴——它只能在推理算子的迭代下达到无法继续推进的边界点。本文将此边界点定义为“元宪边界”(Yuanxian Boundary, B_YXT),并论证其与 T64 闭链紧致性(经 Cl6