A Growth Root Is Not a Generator: Why an Unclosed Solution Cannot Supply Power

中文标题：一个增长根不等于一台发电机——为什么未闭合侧的解不能供能 递推方程 z(n+1) = i(z(n) - z(n-1)) 确有模长 1.4426 的增长根，但这支解属于未闭合的解空间。边界闭合施加模长约束后，两支根被拉回单位圆，实指数因子消失，现象层只剩下纯相位因子。因此"方程里有增长解"与"世界里有净能量输出"相隔的不是工程难度，而是一个边界条件。文中同时给出对卡西米尔效应的定位：它改变的是边界配置的能量差，不是可连续净输出的源。 English abstract: The recurrence z(n+1) = i(z(n) - z(n-1)) admits a root of modulus 1.4426. This paper argues that the growing branch belongs to the unclosed solution space. Once closure imposes the unit-modulus constraint, both roots are pulled back onto the unit circle and only a pure phase factor survives, so no exponentially growing mode exists in the phenomenal layer. The gap between "the equation has a growing solution" and "the world has a net power output" is therefore a boundary condition, not an engineering difficulty. The Casimir effect is located accordingly: a boundary-configuration energy difference, not a source with continuous net output.