Timing-Window Mechanism for Chain-Like Transients in Collisions of Radially Excited Boson Stars

We show that chain-like transients in head-on collisions of radially excited boson stars are controlled by the binary collision time, not by radial excitation alone. For selected $n=2$, $\lambda =400$ self-interacting configurations, isolated evolutions define breathing windows that serve as reference clocks. Numerical-relativity simulations show that visible chains form only when the collision time is compatible with the isolated breathing clock. A separation scan shifts the collision time relative to the same clock, confirming the timing-window mechanism. An additional fixed-separation check at $\lambda =500$ shows the same event ordering, indicating that the observed pattern is not unique to the fiducial self-interaction strength.