Where is the mathematical proof that its identical to the non-compressed file after decompression? Like I said no one has provided that...
I literally gave you proof, and you didn't even recognise it as such. You don't have to take my word that it's an ljpeg92 encoding, I linked it on Rawtherapee's repo!
You literally cannot do that test you proposed because the sensor will always have random noise, thus two pictures (even if uncompressed) will literally never have the same raw acquisition.
Proof is there, again, not my problem or Sony's you don't understand it. Here it is again:
https://github.com/Beep6581/RawTherapee/blob/dev/rtengine/libraw/src/decoders/sonycc.cpp
Or if you want it straight from LibRaw (which is where RT poached it from):
https://github.com/LibRaw/LibRaw/blob/master/src/decoders/sonycc.cpp
If you want more proof, Darktable also supports it through their
rawspeed library: this one's a little bit easier to explain. See for their
ARW decoder, look at line 178 and follow from there: it calls the
DecodeLJpeg function which then, after scraping all the info necessary, passes it to
LJpegDecoder in line 381. There, in line 101 it calls
AbstractLJpegDecoder which is what actually decodes it.