Starts charging even at very low input voltages. Uses only 3 parts (or 4 parts if you count the cap/supercap) and can withstand any input voltage. Maximum input current should not exceed roughly 5 milliamps (10 milliamps is absolute maximum, as per datasheet: http://www.ti.com/lit/ds/symlink/tps3839.pdf).

I've tested the version 11 design, and it works.

Note#1: Version 11 of this circuit replaces an earlier design, which was centered around an LDO. For those who may have a PCB of that earlier design, I've kept its schematic as part of the design files, and I've retained its BOM list as an addendum to the current BOM.

Note#2: The photo of the Version 11 PCB happens to show an LED and a 100uF cap that are not a part of the official design per se, but I put them there to aid in testing. The 100uF substitutes for the supercap, and the LED blinks whenever there's a discharge event (since I also cut the trace between the voltage detector and the resistor because the LED now spans it). However, rest assured that everything will still work correctly with Version 11 as designed, without these additions/modifications.