SSLV1.1 builds & fairy tales

Which bit of the BIB guide do you want me to read again?

Just in case you didn't read my previous posts, they are quoted here
The output voltage is determined by the Vref string & the Vbe of the control transistor.
1 red LED @ ~1.9V & a 1k trimmer should be about right for a maximum of ~4V output.
I think you need to measure your voltages again and post the results.
You probably need two red LEDs & 1k for ~5V output (1.9+1.9+[0 to 2V]+0.6V = 4.4V to 6.4V).
From there you get the actual current passing and can use that to substitute for the 0.002 value that I guessed at for a 4.3mA Idss running @ 600mVds.
What is the actual diode Vdrop (Vf)?
I think you need to measure your voltages again and post the results.
 
Appendix 1
Examples for 3mA (in circuit) Q303 CCS current. R303=R103,203 also. Q303=Q103,203.
a. 2.5-5.5V Vout BJT output reg. 1 red 1.9V LED, 1K trimmer. Other parts jumper.
one red LED @~1.9V + one 1k trimmer set to 1k0 @ 3mA + Vbe @~0.6V comes to 5.5V for the output and setting the trimmer lower allows adjustment down to ~2.5Vdc.

You measured and posted a 2mA result for your Id. That changes the range of output voltage to ~2.5Vdc to ~4.5Vdc.

I have asked you to measure and post your results again.

Once you have done that we can maybe make some progress.
 
........... very important low ppm Vref resistance avoiding the trimmer to ensure no drift & no change of resistance due to the hot temperature of the regulator:).
have you compared the difference that a 5ppm vs a 50ppm resistor would make to the "change" in output voltage.
Have you compared these "resistor" tempcos to the semiconductor tempcos?

Balderdash !!
 
let's suppose the resistor sees a dynamic temperature change of 20C degrees due to varying signal.
The 5ppm resistor will have a dynamic change in resistance of 100ppm, the 50ppm resistor will have a dynamic change in resistance of 1000ppm or 0.1%

That change will result in possibly as much as 0.01% change in the output voltage if no other measures were in place to lower the impedance.

But compare the change in semiconductor parameters. They completely swamp these tiny resistor value changes.

If you now look at the ambient temperature changes in the PSU, you will find that the resistor change in resistance cannot be measured as a change in output voltage. It holds at it's new value. That new value might be 0.5% higher than when cold, or could be 0.005% higher than when cold. But you cannot measure that drift change because it is completely swamped by all the other changes in voltage. You cannot hear the drift change in resistor resistance for exactly the same reasons. 5ppm or 50ppm does not affect the sound at an amplifier fed with the regulator.
We hear AC we cannot hear DC.