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Synchrotrons are powerful and productive in revealing the spatiotemporal complexities in matter. However, X-ray pulses produced by the synchrotrons are predetermined in specific patterns and widths, limiting their operational flexibility and temporal resolution. Here, we introduce the on-chip picosecond synchrotron pulse shaper that shapes the sub-nm-wavelength hard X-ray pulses at individual beamlines, flexibly and efficiently beyond the synchrotron pulse limit. The pulse shaper is developed using the widely available silicon-on-insulator technology, oscillates in torsional motion at the same frequency or at harmonics of the storage ring, and manipulates X-ray pulses through the narrow Bragg peak of the crystalline silicon. Stable pulse manipulation is achieved by synchronizing the shaper timing to the X-ray timing using electrostatic closed-loop control. Tunable shaping windows down to 40 $ps$ are demonstrated, allowing X-ray pulse picking, streaking, and slicing in the majority of worldwide synchrotrons. The compact, on-chip shaper offers a simple but versatile approach to boost synchrotron operating flexibility and to investigate structural dynamics from condensed matter to biological systems beyond the current synchrotron-source limit.