The Eigenfrequency Spectrum: The Toolbox of Spacetime Editing

This paper is the second in the Spacetime Editing Theory series, aiming to delve into the multiplicity of basal eigenfrequencies. If spacetime editing is compared to a craft, then the basal eigenfrequency spectrum serves as the craftsman's toolbox—different frequencies act like distinct tools: some modulate spatial scale, some modulate temporal scale, and others trigger overall displacement. Starting from the mathematical structure of the basal structure as an infinite-degree-of-freedom system, this paper demonstrates that the basal structure necessarily possesses multiple eigenfrequencies and elucidates the different excitation modes corresponding to these frequencies, laying the foundation for subsequent experimental design.