I just bought the amp from a good builder and also got a constant noise that sounds like a ground loop pass around the 1 p.m. position, it's very very low but did increase in volume as I pass the 1 o'clock position (not very loud at all but still barely audibly present), where the top of the knob (around 50% position as you go up in volume is 12 o'clock position so noise came in at about 60% to 70% volume). I installed the C4S after testing everything and am very happy with the amp for my Micca RB42 (desktop setup) speakers in near field configuration sitting at about 1 to 1.5 meters. (When I have time I'll run a REW and put in a convolution filter to my Roon App). No hum from my speakers, it's dead quiet.
Then I did some testing and this is what I found. When I turned my audio interface (Antelope Audio Zen Q) volume all the way down I got that very very slight hum with volume all the way up. Now the weird part, I paused the music. After I paused the music, I waited approximately five seconds or so and the hum disappeared. My system is as follows.
Desktop PC running Roon with headroom management enabled (this lowers the volume by -3db), to Antelope Audio Zen Q through USB C, then 1/4 inch unbalanced monitor out to RCA, to my Senheisser HD6XX and also tested with my Dan Clark Aeon 2 Noire (hum a bit louder on the Dan Clarks, but again when I pause the music and wait five seconds, no hum). My audio interface has an output voltage of 4 volts, and I believe the Bottlehead clips at 4.6 volts, according to the Youtube from Korea (who I watched and decided to get this amp, I'm Korean btw.)
Additionally, I get hum from the following, the Astell and Kern SR35, but the hum is from a cable that I got off Amazon, which is a 3.5 to RCA. The hum is noticeable at the 50% volume level but changes volume based on how close I am to interferance sources so I know it's not the amp, but the cable. FYI, always get cables that have good shielding! I was having a heck of a time with my record player with hum, till I switched cables.
You say you get hum even with no inputs, which I don't get using those headphones above.
Now for kicks, I decided to use my Crinacle Red IEM's which impedance and sensitivity are not going to match with this amp. I get hum as well even with music paused (though the primary hum goes away), I hear a very noticeable hum, buzz and even me touching the amp is audible. However, you're NOT supposed to use most IEM's with this amp. What headphones are you using?