Ok, so the circuit can not put out 9V if you put in 9V because the LM317 drops the incoming voltage. Datasheet says about 3V, so it fits your measurements. According to the datasheet it can handle up to 40V input voltage and if everything is correct, R1 limits the maximum ouput voltage of the circuit to 9V, no matter if you put in 12, 18 or 40 volts.
To be able to dial in an output voltage of 9V to 4V, you need to have an input voltage of at least 12V. I guess that's why similar pedals like the JHS volture or the Potar Powerstarve that run on 9V input voltage have a switch incorporated in the design, so they are able to put out more than ~7V by simply switching them in bypass.
Question about power starve / voltage sag circuit
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Re: Question about power starve / voltage sag circuit
I added in/out jacks and test points to plug in my multimeter.