How much support needed for fixing fence posts for arbor on raised/sleeper beds?

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So I recently built a couple of raised sleeper beds with a pathway in between for our garden. They are 2.4m in length and 1.2m in width and 3 sleepers high, meaning 60cm high.

I used 50cm 4" x 4" (100mm x 100mm) posts on each inside corner to fix it all together (with 16 150mm screws in each), which means that I have 10cm of room between the top of the inside corner post and the top of the raised beds in each corner (see pics attached).

I am looking to make a garden arbor/pergola out of 4" (100mm x 100mm) fence posts that goes over the pathway (see picture attached).

I am kicking myself because I realised that if I would have just used 2m fence posts instead of 50cm cuts on those inside corners, I would be in excellent shape right now :)

But alas, I was not thinking far enough ahead since I wasn't sure how I wanted to build the arbor when I made the raised beds.

So basically what I am wondering is whether or not I will have enough support if I just fix four 1.5m 100mm x 100mm fence posts to the top of these posts in the corners of the raised bed. This means that the 1.5m fence post would have 10cm of sleepers to fix into sitting on top of the inside corner posts. Is that reasonable? Will that provide enough support if I fix it in with say 4-6 150mm timber screws (6.7mm) or maybe a couple 150mm coach screws (12mm)?

Any thoughts on whether or not this will be strong enough to hold it steady?
 

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