Sun's prime–Fibonacci–Fibonacci representation conjecture

Let $F_0=0$, $F_1=1$, and $F_{i+1}=F_i+F_{i-1}$ for $i=1,2,3,\ldots$ be the Fibonacci sequence. A Fibonacci number is positive when its index is positive and its value is positive. Sun's prime–Fibonacci–Fibonacci conjecture. Every integer $n>4$ can be written as

$$n=p+F_s+F_t,$$

where $p$ is an odd prime and $F_s,F_t$ are positive Fibonacci numbers; moreover, one of $F_s,F_t$ can be required to be odd. This is a sparse additive analogue of Goldbach's conjecture. The source reports verification up to $10^{14}$, but the conjecture itself remains open.