I havent read it in years but I am pretty sure it talks about it in the white paper. He says that every 210,000 the block reward will be cut in half. There is also some mathematical formula to prove all of this.
The halving is not discussed in the whitepaper nor mentioned or used but Bitcoin halving is openly discussed in public and even has the schedule announced. I may missed something but I did not even read on the whitepaper that Bitcoin will half its supply every 210,000 block reward bu regardless, everything is not published on the whitepaper especially when the development is actively and continuously done on the system. It is best to have the bitcoin github[1] as reference since all the updates and upgrades are mentioned on that repository.
I believe Whitepaper is only a means to introduce the project since it discusses the projects purpose and its abstract. It does not states the actual development of the project nor the upgrades and development integrated into the system.
The halving of bitcoin is indeed a dirty little trick hiding in the source code.
Information about Bitcoin halving is not hidden, it is openly discussed so it is not correct to say that the halving of Bitcoin is a dirty trick hidden in the source code. Let alone the source code its self is openly accessible to the public.
"The steady addition of a constant of amount of new coins..."
Well there is at least a steady addition of Bitcoin which is constant in 4 years, and is constant to reduce into halve every 210,000 blocks rewards (estimated every 4 years) and is a constant that can be only claimed/gained through mining and solving the block difficulty.
White paper does not mention halving !
But it is openly discussed in public, it is not a hidden fact to be an issue, IMO.
[1]
https://github.com/bitcoin/bitcoin