A Unified Geometric Framework Bridging Quantum and Cosmological Structures

This manuscript presents a scale-invariant geometric theory that unifies quantum tunneling and gravitational curvature. Drawing on cross-domain analogies between TFET band structures and gravitational wells, it proposes curvature—not mass—as the core mechanism governing energy transition, resonance, and collapse. Includes full mathematical derivation, validation framework, and diagrams. Origin story and comparative analysis with Einstein's theory included.本手稿提出了一种尺度不变的几何理论，统一了量子隧穿与引力曲率。该理论借助隧穿场效应晶体管（Tunnel Field-Effect Transistor）能带结构与引力势阱间的跨域类比，提出曲率而非质量才是支配能量跃迁、共振与坍缩的核心机制。文中包含完整的数学推导、验证框架与图示资料，同时收录了理论起源背景以及与爱因斯坦引力理论的对比分析。