I am proposing a new theorem of computability theory:
THEOREM 1: There are numbers k and s and a program A(n,m) satisfying the following conditions.
1. If A(n,m)↓, then C_n(m)↑.
2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s).
3. A(k,s)↓ and for all n, A(s,n)↑.
Here C_n(∙) is a program with...