That's an interesting claim. I have myself pondered over nature of continuous vs discrete universe. Do you have references / links to any concrete research papers which prove the discreteness of space / time ? I have searched the internet with no good results. My own thought process towards this goes as follows :

While for subatomic particles, the "discreteness of matter" is understandable to a certain extent. Assuming that "matter occupies space" to be true, if both matter and space are discrete, implying that space is divided into small discrete ( and possibly "stretchable" ) pockets with zero gaps between the pockets , causes a particular trouble with the idea of motion .

viz. given that the following triad is needed to achieve motion: [space, time, matter] , either at-least two of them need to be continuous or if all three are discrete, then

1) If there are gaps between space / time , then whatever exists /or doesn't exist between gaps makes the universe continuous.

2) If there are no gaps between space/ time then the universe is continuous.

I know the above argument lacks the scientific rigor nor am I am trying to defend the notion of continuous space\time. But on average , I would lean more towards the notion of continuous space\time unless there is scientific evidence proving otherwise.