III_005 Mindfulness Topology (I): The Mathematical Geometrization of Mental Flow, Markov Blanket Reconfiguration, and Substrate-Independent Subconscious De-noising / 正念拓撲學 (一):心流狀態的數學幾何化、馬可夫毯重構與基質獨立的潛意識去噪協議

This paper presents the foundational architecture of Mindfulness Topology (I), establishing a mathematical geometrization framework for mental flow, cognitive dynamics, and active inference. By formalizing the cognitive transition into deep mindfulness using differential geometry and non-linear dynamics, we examine how the Markov blanket—a statistical boundary defining the separation between internal cognitive states and external environments—undergoes dynamical reconfiguration under sustained meditative focus.

We introduce a substrate-independent protocol for subconscious de-noising, demonstrating that variational free energy minimization within the active inference framework can be mapped onto topological phase transitions. The study provides explicit mathematical derivations connecting topological invariant preservation, noise suppression in high-dimensional mental manifolds, and non-equilibrium steady states in cognitive dynamics. This work bridges theoretical physics, non-linear system theory, and phenomenology, establishing a formal computational ontology for meditative cognition.

本研究構建了《正念拓撲學》第一部分的理論架構,旨在為心流狀態(Mental Flow)、認知動態學及主動推論(Active Inference)建立明確的數學幾何化體系。本論文運用微分幾何與非線性動力學,嚴格刻劃深層正念過程中的認知狀態轉移,並解析當個體處於持續禪修專注狀態時,界定內部認知狀態與外部環境邊界的「馬可夫毯」(Markov Blanket)如何進行動態重構。

此外,本文提出了基質獨立(Substrate-Independent)的潛意識去噪協議,證明在主動推論架構下,變分自由能(Variational Free Energy)的極小化過程可等價映射為拓撲相變現象。本研究提供了完整的數學推導,將高維心智流形中的拓撲不變量保持、高頻雜訊抑制與非平衡態穩態(NESS)連結起來,為正念認知現象學與理論物理學、複雜系統理論之間建立了嚴謹的計算本體論 bridge。