Mono vinyl, how do you know if really single channel mono or if stereo recorded to mono

I'm exploring the possibility of getting a mono cartridge. 

Please, I am not trying to start a debate about whether or not that is a good idea. I simply have a question about monophonic records.

How can you tell which records are truly mono and which are actually stereo with 2 identical channels to simulate mono?

I know that for all mono records before stereo there was only one channel cut laterally into the record .  When stereo came out some so called mono recordings were actually 2 channels just like a stereo record with both horizontal and vertical information but  L and R were the same so ended up as mono. I also know that a "true mono" cartridge only has output from the horizontal motion and that the stylus size is different than a stereo stylus, which means according to many aficionados of mono recordings,  in an ideal world you would want a cartridge optimized for mono to play true mono records

again, I do not want to debate the pros and cons of this, just want the facts about the records. If you want to debate something else please start another thread

thanks