That is correct. There's a long beam underneath the whole deck, bolted to the posts. The deck is hanging on the beam.  

Your picture shows a gap in front of the post - so did someone notch the decking behind to make space for the post to move relative to the deck?

Out of interest you said "after a couple of months of re-piling, the floor was still unlevelled"
Why would that be? Did they not jack the property up enough?

I ask because if the posts are sinking and their upper fixing to the house is not separating from the house - does this mean your whole house and re-piling is sinking as well? 

D1023319:

 

Your picture shows a gap in front of the post - so did someone notch the decking behind to make space for the post to move relative to the deck?

 

Out of interest you said "after a couple of months of re-piling, the floor was still unlevelled"
Why would that be? Did they not jack the property up enough?

 

I ask because if the posts are sinking and their upper fixing to the house is not separating from the house - does this mean your whole house and re-piling is sinking as well? 

 

I don't know about why there is a notch but for me, it looks like a botched job. The house was built in 1980s. About the re-piling, I have a feeling that it wasn't done properly. It's re-piled but not re-levelled in my opinion. This house has lots of issues to attend to but this is my only house and my family and I love where we are so I make peace with it.I found two piles rotting and that needs to be attended too. I'm glad that I'm not paying any mortgage anymore.