Well, first, I wouldn't call the voltage on the positive terminal of the Super Cap the "Reference Voltage". The voltage on the Non-Inverting input of U2:A is what I would call the "Ref Voltage", and I would call the Cap voltage, the "Sense Voltage".
tjones9163:
12v also feeds the input of the lm317 and puts out 5.3v regulated voltage on the output, according to the resistor feedback circuit.
More like 5.4V
1.25V/1K = 1.25mA
3.3k*1.25mA = 4.13V
4.13V + 1.25V = 5.38V
tjones9163:
R3 and R4 form a voltage divider that puts 4.86v on the non-inverting input of the amplifier when the reference voltage placed on the positive plate of the capacitor is fed into the inverting input.
The voltage on the Non-Inverting input will be 4.86V, regardless of what voltage is applied to the Inverting input -- as long as the voltages are within proper operating ranges.
tjones9163:
...allowing current o flow from the drain of the MOSFET and out of the collector to charge the capacitor.
Nope. Out of the Source of Q1. In other words, current [conventional current] will flow through Q1 from the Drain, to the Source, and out of the Source, into the Super Cap. Also, there is no "Collector" involved. Also, I wouldn't even do it this way. I would either use a P-Channel MOSFET, or an N-Channel, and place it between the Super Cap negative terminal, and ground [Drain to Super Cap neg, and Source to ground]. Especially since the worst-case Gate Threshold is 4V, and that doesn't allow much head room with the current circuit.
tjones9163:
...and at the same time turns on the PNP transistor Q2 lighting the Green LED...
Actually, Q2 should be an NPN transistor. Unless the idea is to use the BE junction as a Zener, but then, there would be no inversion, so the LED would light when Q1 is ON, not when it's OFF.
Other than that, pretty much correct.