Researchers have introduced a fresh homological framework to compute the topological entropy of discontinuous interval maps, even when the map’s branches point in different directions. The key idea is to capture relationships among the one‑sided images of the map’s discontinuities. By formulating these relations homologically, they build a kneading determinant that retains all entropy‑relevant information but in a smaller, more manageable form.

The authors systematically reduce the determinant’s size. For any given orientation pattern of the interval map’s branches, they find the minimal dimension the reduced determinant can occupy while still preserving full entropy data. Importantly, they prove that this minimal dimensionality can coexist with the map attaining maximal possible entropy.

This approach streamlines entropy calculations that previously required handling large determinant matrices. It opens a pathway for studying more complex piecewise‑continuous dynamical systems without sacrificing accuracy.

The methodology is grounded entirely in algebraic topology and does not rely on numerical simulation or empirical approximations.