Tracing expansion-driven star formation in the Perseus molecular cloud using young stellar objects
$Context$. Recent studies have linked star formation in the solar neighbourhood to the expansion of the Local Bubble. The Per-Tau Shell (PTS), a vast 3D dust structure hosting the Perseus and Taurus clouds on its surface, is a candidate for such triggered formation. $Aims$. We aim to reconstruct the star formation history of the Perseus molecular cloud and investigate its potential link to the historical expansion of the PTS. $Methods$. We performed a 6D phase-space analysis of 406 young stellar objects (YSOs) of Perseus. Our approach integrates Gaia DR3 kinematics with Bayesian age inference and a heteroscedastic likelihood framework to resolve radial gradients in YSO ages and intrinsic tangential velocity dispersions relative to the PTS centre. We constructed a unified catalogue by integrating existing infrared-based classifications to examine the projected spatial segregation of different evolutionary stages and compared stellar 3D kinematics with $^{12}$CO and $^{13}$CO gas velocity fields to assess kinematic coherence. $Results$. The YSOs exhibit coherent outward motions relative to the centre of the PTS, a negative age-distance gradient with younger populations at larger radii, and a radial decline in tangential velocity dispersions. Younger YSO classes also show a stronger directional concentration towards the PTS centre. Both the coherent proper motions and the line-of-sight velocity gradients of these YSOs align with the gas velocity field, indicating large-scale kinematic coherence. $Conclusions$. The Perseus YSOs exhibit concordant kinematic and temporal signatures consistent with an expansion-driven origin. These results provide robust evidence for a layered, inside-out pattern of star formation, suggesting that the historical expansion of the PTS triggered a sequential progression of star birth and effectively shaped the star formation history of the Perseus complex.