I have a very low pitched tinnitus around 345 Hz (a little below F4 = 349 Hz), and by deliberately contracting some jaw/ear muscles (I believe stapedius and tensor tympani) the sound gets much more pronounced.

While it helps with starting on the right note when singing a song and deriving single pitches, it by no means makes me instantly know a note's pitch like someone with perfect pitch would experience. I still have to derive pitches manually, and while singing the sound of my voice is loud enough that I don't hear the tinnintus anymore and I often don't notice my singing going slightly out of tune.

I do have the ability to recognize relative pitches in relation to e. g. accompaniment playing in a given key, and this recognition is automatic in a way that the derive-from-tinnitus definitely isn't.

Also sometimes the tinnitus goes out of tune down to almost E4, this sucks.

It's not "cheating", but it's also not absolute pitch, by definition.

Absolute pitch (or perfect pitch) is the ability to identify a note without having any memory aid or reference tone to compare it to.

So if you have a constantly-present reference tone, due to tinnitus, and you figure everything out based on the interval from that tone, that's simple relative pitch and the ability to figure out intervals. Not perfect pitch.

Sure, that seems reasonable, although likely a different mechanism than the one I’m talking about, which seems to come from early life language acquisition. I think when people discuss absolute pitch, this is the type they have in mind, because using tinnitus is still using a reference tone. I believe there were early theories for absolute pitch around this idea (that those with absolute pitch used tinnitus to help them identify tones), but they have been made obsolete by more recent knowledge.

I have tinnitus as well, and while it is very mild, I am surprised at the idea it can be ‘stable’ enough to form a basis for absolute pitch. Most of the time I don’t experience it as a pitch layered on top of all other sounds. Even if I focus on it, it doesn’t feel like a sound that can be given a clear singular tone, if that makes sense. I do know experience of tinnitus varies, so perhaps there are forms that are more capable.

Wow I might have tinnitus, I read the yesterday night and was thinking I do often have ringing in my ears at night, it usually fades away during the day (or maybe get's filtered out by my brain). Tried mapping the tone I heard, at first I thought it was F#7 but after trying a pitch higher, F#8 it was obvious that it's the tone I'm hearing.