I’ve just measured the gap above the brick and it is just slightly under 4 inches/10 cm, although the brick does taper off a little bit to one side. The hog here at the moment is a late hoglet from last year. He was big enough to hibernate – he just didn’t. But, as he is still quite young, he isn’t enormous – a smallish adult size.
Having said that, hogs are very good at flattening themselves. The hogs here frequently go under the lowest part of the gate which must be much less than 4 inches, even though there is a generously sized hog hole a few inches away. I was thinking I might have to remove the brick when the big boys turn up, but by then, I will be watching them more, so can chase off cats more easily – I tend to feed them in the open when possible. The hoglet usually turns up really late (hence the need for the feed box – he has really needed the food in the winter), but in the Summer I only feed for a few hours, whilst I am up to watch, so that they have plenty of time to go foraging. They soon learn to turn up here early if they want some extra food.
You shouldn’t squish the hogs (unless something falls on them), they will just either decide they can get through, or they can’t. I think if they have the width and as long as the low bit isn’t too long, they will be able to squeeze through, but you may have to play it by ear, a bit. That’s why I used the brick – removable, if necessary. It is probably a good idea to wedge it in somehow, though, so the cat can’t push it along.
Two cats have attempted my box since the brick was there, but unsuccessfully. One of them was a much smaller cat than the one that got in there, so I was pleased to see it didn’t manage. The theory was that if they were squeezing themselves widthways, they wouldn’t be able to squeeze themselves heightways as well. However, never say never.
Good luck. It would be interesting to know how you get on.