All the sciatica symptoms in leg (various nerve pains), localised pain "in" buttock... but never really "back pain"?

So, just curious if other folks have / have had this kind of experience with their sciatica...

So, off the bat, I preface by saying, my symptoms are pretty consistent for weeks, I am visiting a physio & a general-practitioner doctor; I'm.. well, honestly, kinda half doing the exercises because there's so much work related stress that exercise commitment is pretty low, and the relief from the exercises is, well, fleeting. Anyway. I'm not using reddit as my only/main source of medical advice :)

So.. Based on all the movement twists and symptoms (leg raise test, seated leg extension; nerve pain increase when sitting, horrible pain increase when trying to bend and put on socks, tie shoes etc., bending forwards is painful, and at times even walking is compromised from the leg and buttock pain), it all seems to point to a disc issue. And the commonly cited "back extension" (i.e. pushup with pelvis on the floor) does seem to reduce the nerve pain... at least *while doing it*, though the relief does not stay for long...

But the weird thing is, I keep hearing about "centralization" and "back pain", but.. I don't really *feel* anything in my back or in the actual disc region. The first pain point is always "in" the buttock and "in" the hip. There may have been one or two times where I felt a random spiking ache around the disc region, but at this point, I don't trust if it wasn't imagined, compared to the far far more frequent/constant "in-buttock" stiffness/spasming and pain.

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So, my question to all of you who have had disc related sciatica and have gone through all the physio etc... how is the "centralization" supposed to feel? Is it supposed to literally move upwards during the exercise? Is it supposed to transition into a lower-back pain and relief the "inside buttock" pain?

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P.S. I would consider that maybe it's the piriformis rather than the disc, but basically all the "test movements" that should signal a disc based issue match up with what triggers an increase in the pain (except for the location of the pain, which - as said - never manifests exactly on top of the disc...)