Refined Goldbach conjecture modulo $4$

Let $p$ and $q$ be primes. The mod-$4$ refined Goldbach conjecture. The following assertions hold:

1. Every even $n>4$ has a representation $n=p+q$ with $p\equiv3\pmod4$.
2. Every $n\equiv0\pmod4$ except $n=4$ has such a representation with $p\equiv1\pmod4$ and $q\equiv3\pmod4$.
3. Every $n\equiv2\pmod4$ except $n=2$ has such a representation with $p\equiv q\equiv3\pmod4$.
4. Every $n\equiv2\pmod4$ except $n=2,6,14,18,62$ has such a representation with $p\equiv q\equiv1\pmod4$.

These explicit refinements include claims implied by binary Goldbach and claims not implied by it. They are supported in the paper by numerical calculations and heuristic arguments, but remain unproved.