Homological Church–Turing thesis

Ascertain whether any physically realizable computation necessarily has finite homological complexity h(L) < ∞ and whether the laws of physics determine an upper bound on achievable homological complexity.

Background

The authors propose a homological strengthening of the Church–Turing thesis, positing that physical realizability constrains computational homology to be finite and potentially bounded by physical law.

This bridges their topological model of computation with fundamental physics, suggesting universal limits on computational topology imposed by nature.