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We define a hierarchy functor from the exact symplectic cobordism category toa totally ordered set from a $BL_\infty$ (Bi-Lie) formalism of the rationalsymplectic field theory (RSFT). The hierarchy functor consists of three levelsof structures, namely algebraic planar torsion, order of semi-dilation andplanarity, all taking values in $\mathbb{N}\cup \{\infty\}$, where algebraicplanar torsion can be understood as the analogue of Latschev-Wendl's algebraictorsion in the context of RSFT. The hierarchy functor is well-defined through apartial construction of RSFT and is within the scope of established virtualtechniques. We develop computation tools for those functors and prove all threeof them are surjective. In particular, the planarity functor is surjective inall dimension $\ge 3$. Then we use the hierarchy functor to study the existenceof exact cobordisms. We discuss examples including iterated planar open books,spinal open books, affine varieties with uniruled compactification and links ofsingularities.

A landscape of contact manifolds via rational SFT