## 4 Discussion
This discrepancy may be due to non-voluntary arm movements being predominantly driven by spinal rather than central mechanisms, potentially lacking certain supraspinal influences involved in voluntary movement control. It is plausible that the activation of corticospinal pathways by TMS is summated with ongoing activity in spinal neurons that constitute the spinal generator of rhythmic hand movements, thereby facilitating supraspinal modulation. This phenomenon bears resemblance to the effects observed during epidural electrical stimulation of the homosexual spinal cord, where a mixed pattern emerges--consisting of both short-latency spinal reflex responses and non-voluntary rhythmic flexor-extensor muscle activity, attributable to activation of spinal pattern generators [36]. Low-frequency TMS may induce long-lasting post-effects on spinal motoneurons and/or interneurons--possibly related to persistent inward currents, serotonergic modulation, or general network activation--which, in turn, contribute to the potentiation of non-voluntary rhythmic arm movements. Given that the same motoneurons and interneurons contribute to a wide range of possible movements, supraspinal motor commands not only activate specific motor pathways but also provide a \"preparatory\" command for spinal neurons and inhibit competing movement patterns, play ing a vital role in motor control (\"a lock with two keys\" [37]). Since corticospinal excitation is mediated by polysynaptic pathways, and because TMS influences not only motoneurons but also spinal interneurons [38]--which are critical for pattern generation--such stimulation could significantly modulate the physiological state of spinal networks and contribute to the observed facilitation of non-voluntary rhythmic arm movements (Figure 3). While phase-dependent MEPs suggest spinal involvement, we acknowledge that we did not directly measure interneuronal or CPG activity. As such, the observed enhancement of non-voluntary arm oscillations (Figure 3B) could alternatively reflect augmented sensory feedback or general corticospinal facilitation, rather than canonical CPG engagement. Although we propose that TMS effects summate with ongoing CPG activity, this alternative explanation cannot be ruled out and may well contribute to the observed movement potentiation. Importantly, whether or not targeted propriospinal interneurons (and motoneurons) are considered an integral component of cervical CPGs, they participate in shaping the rhythmic and patterned output of spinal networks. Their involvement aligns with our broader interpretation that supraspinal inputs--whether acting directly or via spinal interneurons--can modulate the excitability of spinal circuits. In summary, low-frequency TMS significantly increased non-voluntary arm oscillations, whereas its effect on voluntary arm oscillations was much smaller (Figures 3 and 4). These findings suggest that physiologically meaningful assessments of spinal cord neuromodulation and the individual physiological state of reflex pathways represent a promising area for further research. As with the lumbosacral spinal cord [16; 39], our results support the notion that therapies targeting cervical CPGs could benefit from incorporating active engagement of supraspinal motor areas. Conceptualization, I.A.S., V.A.S. and Y.I. ; methodology, I.A.S., V.A.S., I.Y.D., and Y.I. ; software, I.Y.D. ; validation, I.A.S., G.C. and Y.I. ; formal analysis, I.A.S., I.Y.D. and Y.I. ; investigation, I.A.S., V.A.S. and I.Y.D. ; data curation, I.Y.D. ; writing--original draft preparation, I.A.S., G.C. and Y.I. ; writing--review and editing, I.A.S., V.A.S., I.Y.D., G.C. and Y.I. ; visualization, I.A.S., I.Y.D. and Y.I. ; supervision, I.A.S. and Y.I. ; project administration, I.A.S. ; funding acquisition, I.A.S., G.C. and Y.I. All authors have read and agreed to the published version of the manuscript.