Square waves are real world? An LP record playing back a 20kHz signal?
Sorry, there is ANY amount of evidence of LP playing back 1 kHz square waves from real world test records. As square wave is defined
https://en.wikipedia.org/wiki/Square_wave
its harmonics go in theory to infinity.
Real world analog record playback has limitations in frequency response - but any semi decent MC cartridge in production today will have response extended at minimum to 40 kHz.
Below are few representatives from back in the day;
https://www.gammaelectronics.xyz/audio_01-1979_adc.html
The above has been adapted from the original published in the Audio Magazine, January 1979 ( scroll down to page 92 ):
https://www.worldradiohistory.com/Archive-All-Audio/Archive-Audio/70s/Audio-1979-01.pdf
Please note that ADC is a MM cartridge that due to its electrical properties rolls off above approx 30 kHz.
Here, the same/similar for a really good MC cartridge :
https://www.gammaelectronics.xyz/audio_08-1986_technics.html
( At the bottom of each of these gammaelectronics adaptations, there are further links to objective measurements of phono equipment - do take time to explore what vinyl has been offering, by now over 40 years ago ... ! )
Scroll down to page 56:
https://www.worldradiohistory.com/Archive-All-Audio/Archive-Audio/80s/Audio-1986-08.pdf
There were better objective reviews than published by the US press from Europe; particularly those published by the Italian magazine
Suono and
Stereoplay
( this later having also its German version ).
All of these objective measurements have been made by
Instituto del'Alta Fedelta - IAF Roma . Contrary to most US reviews, which in the majority of cases do not measure phono cartridges beyond 20 kHz , Italian reviews from the period ALWAYS provide both picture of the square wave reproduction ( from CBS STR 112 test record )and frequency response to 50 kHz ( using either Bruel & Kjaer, JVC or Denon test records with sweep to 50 kHz ).
( At the moment, I can't find the Italian reviews in PDF - but, I can scan the original magazines from my library if the PDFs online are really gone )
However, latest stylus tip profiles made available AFTER any of the period objective phono cartridge reviews available online have extended the frequency response even higher up in range, directly proportional to the reduction of the scanning radius of the stylus.
The first generation of Namiki's Micro Line stylus had 3.5 micrometer scanning radius ( the best found in the period reviews ) , current has 2.5 micrometers; this gives a near perfect square wave reproduction, even at the innermost grooves of the 33 1/3 RPM record .
https://www.discogs.com/release/805...quare-Wave-Tracking-And-Intermodulation-Tests
Even at the innermost grooves, today's best cartridges make mockery out of anything RBCD can come up with regarding the extended frequency response.
Then, the final coup de grace to the RBCD can be delivered by having the truly state of the art vintage cartridges retipped with the latest Namiki Micro Line stylus; .
These can then exceed - with ease - 100 kHz .
Latest digital equipment has - finally (!) - caught up the level of quality to do justice to such extraordinary phono cartridges - requiring decent PCM of 384 kHz ( or higher ) sampling or DSD256 ( or higher ) to accurately capture the output of the medium that - according to some - can not reach 20 kHz ...