PFUSRC-041: Linear and Curved Time — From Calendar Calibration to Topological Residence of Time Residuals

Since ancient times, humanity has adopted two time measurement systems: the approximately linear solar time and the spiral curved lunar time. Their periodic calibration via leap days and leap months essentially reveals the intrinsic nature of time. Based on prior research on time origin and time crystals, this paper argues that linear time derives from light path projection, while curved time stems from spiral motion traces, and their calibration corresponds to the breathing rhythm of the bicone structure. The irreducible time residual δ acts as the physical foundation of free will and a permanent information carrier. Relying on time residuals, four time manipulation modes are realized: throttling, residence, playback and leverage. This study further verifies that time is not a uniform and passively flowing scale, but dynamically interacts with spatial topology — space and time are mutually anchored and interdependent.