A Review Note on the Applicability Ranges of Temporal Membrane Theory and General Relativity

This note presents a conceptual review of the applicability ranges of Temporal Membrane Theory (TMT) and General Relativity (GR), based on their mutual consistency and on the current scope of observational and numerical verification. Temporal Membrane Theory is not intended to modify or replace the dynamical structure of General Relativity. Rather, it is formulated as an effective framework that takes the empirical success of GR as a baseline and focuses on how observational time is reconstructed by observers within spacetime described by GR. Starting from stellar-scale physics, where General Relativity is most stringently constrained, this note examines whether there is any indication of an internal, dynamical breakdown of GR across increasing scales, extending to galactic, cosmological, and strong-gravity regimes. Particular attention is paid to the distinction between dynamical history, governed by local proper time, and observational history, reconstructed along extended propagation paths. Within the current reach of observations and numerical relativity, including strong-field simulations and gravitational-wave tests, no evidence is found that General Relativity exhibits spontaneous dynamical failure. Apparent discrepancies at larger scales are instead discussed as potential issues related to the reconstruction of observational time, rather than to modifications of gravitational dynamics. This document is intended as an internal conceptual record rather than as a formal theoretical proposal. Its purpose is to clarify the logical positioning of TMT with respect to General Relativity and to provide a structured reference for future theoretical and observational discussions.本ノートは、時間膜理論(TMT)を参照枠としつつ、一般相対性理論(GR)が現在の観測および数値相対論的検証の射程内において、力学理論として自発的に破綻する兆候を示していない点を概念的・構造的に整理する。恒星スケールから銀河、宇宙論的距離、強重力数値相対論に至る検討を通じ、観測的不整合の多くが力学の失敗ではなく、観測時間の再構成に起因し得ることを示す。