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    Building, troubleshooting and testing of these amplifiers should only be
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    the safety precautions around high voltages.

Rumble filter for phono.

I think electrically, it's the same thing. Any noise cancellation in a mono cartridge is probably done by summing two coils that are 90 degrees to each other. How else would you do it? So a stereo cartridge can be used as a mono cartridge by summing (shorting) L and R. Perhaps I'm wrong, but I see no other electromechanical way of doing it.

There is not two coils 90 degrees from each other in a mono cartridge. A typical mono cartridge has two output terminals (hot and ground) with a single coil. There is no noise cancellation. The mono groove has no vertical component like a stereo grove has.

If you bridge a stereo cartridge to mono it is not picking up any recorded vertical information only side to side information which is identical (Ideally) on both coils (left and right), so in effect when it comes to noise you are adding not cancelling. A stereo cartridge picks up both the horizontal and the vertical groove information (Which isn't music in a mono grove) so both the music and unnecessary grove floor noise and dust are sent to the amp.
 
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You seem to be assuming the noise picked up by the two coils to be uncorrelated. That makes sense when the left and right side of the groove have independent noise associated with them, but not when the record surface noise is mainly vertical. Anything that's vertical will end up in antiphase in the two coils and cancel, as the cartridge doesn't know what is noise and what is not.