Invariant-measure encoding conjecture for computational hardness

A constraint satisfaction or optimization problem is a computational problem whose feasible assignments or candidate solutions can be evaluated by its constraints or objective function. A dynamical system is a system with an invariant measure, and a map between problems and dynamical systems is one-to-one when distinct problems correspond to distinct dynamical systems. Invariant-measure encoding conjecture. There always exist one-to-one maps from constraint satisfaction or optimization problems to dynamical systems such that the onset of hardness is captured by the underlying invariant measure. Such a correspondence would connect computational hardness with measurable dynamical behavior; the source presents this as one of three conjectures for future work and gives no resolution.