[MST-EUT Theory Series #19] Vacuum State and Ground State Energy - MST-EUT真空態與基態能量 (v1.2-zh)

This paper constitutes the second part of the MST-EUT Trilogy and focuses on establishing the ontological structure of the vacuum state and ground-state energy within the entropic-field framework introduced in the first part. Building upon the phase-transition and fixed-point formalism of MST-EUT, the vacuum is no longer treated as an inert background or an arbitrary reference level, but is instead identified as a structurally selected stable configuration of the entropic field. By introducing a density duality symmetry and its associated fixed-point mechanism, the vacuum density is uniquely determined from first principles, yielding a universal ratio between the vacuum density and the critical density. Within this framework, the ground-state energy is reinterpreted as an intrinsic structural consequence of the vacuum configuration rather than an externally prescribed constant. The role of effective field theory is clarified as a local description of fluctuations around an already-selected vacuum state, rather than as the mechanism responsible for vacuum selection itself. This work establishes a closed and minimal ontological foundation for the vacuum sector of MST-EUT, providing the necessary structural basis for subsequent derivations of physical constants, relativistic field equations, and electromagnetic phenomena developed in the final part of the Trilogy. 本文為 MST-EUT 三部曲之第二篇,承接第一篇所建立的熵場相變與固定點理論架構,進一步釐清真空態與基態能量在 MST-EUT 中的本體論地位與結構性來源。 在本篇中,真空不再被視為被動的幾何背景或任意設定的能量基準,而被重新界定為熵場在滿足結構對稱性與可延拓性條件下所選定的穩定構型。透過引入密度對偶對稱及其不動點機制,本文由第一性原理唯一確定真空態密度,並得到真空密度與臨界密度之間的普適比例關係。 在此架構下,基態能量被重新理解為真空結構的內生結果,而非外加的自由參數。同時,本文明確區分真空結構的選態機制與有效場論在真空附近所扮演的角色,指出後者僅負責描述局域漲落與回應行為,而非決定真空本身。 本研究完成了 MST-EUT 真空部門的結構性封閉,為後續關於自然常數數值推導、相對論場方程與電磁結構的嚴格展開,提供唯一且自洽的真空基準。