The Eigenfrequency Spectrum: The Toolbox of Spacetime Editing

This paper aims 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.