Bateman-Horn, polynomial Chowla and the Hasse principle with probability

With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree 𝑑 polynomials 𝑓∈ℤ⁢[𝑡] that are ordered by height. This allows us to establish averaged versions of the Bateman–Horn conjecture, the polynomial Chowla conjecture and to address a basic question