Projective Origin of the Spin Hydrodynamic Attractor and Its Resurgent repeller

RESUMO

We investigate the projective and resurgent structure of a spin hydrodynamic attractor in Bjorken expansion. We show that the nonlinear spin attractor family is determined by the projective classes of the two dimensional linear solution space, with the attractor and repeller corresponding to two distinguished projective directions and the linear modes ratio generating the full one-parameter transseries tower. We identify the attractor and repeller as complete global solution branches associated with the two distinguished projective directions of the underlying linear solution space. Using the projective transseries structure, we show analytically that the data of repeller are encoded in the Borel-Stokes structure of the attractor expansion. These results provide an explicit analytic realization of resurgence relations that are often extracted through high order expansions and numerical Borel analysis, and yield a unified description of the attractor, the repeller, and their Borel-Stokes connection in minimal causal spin hydrodynamics.