Could you in fact, use a wound 4th string and still have it be re-entrant, or high g?
no, it's impossible, simply because the high-G is a thin string at an higher pitch (one octave up). if you try to tune a big wound string one octave up, the string snaps.
string "science" is easy to understand: thinner the string, higher the pitch can be. bigger the string, lower the pitch.
when you start going down with the frequencies, however, there are many issues, like a sloppy string that don't vibrate much, or that alters the pitch at the attack of the note.
wound strings are there for this reason, exactly like on the guitar (same strings, actually). you have the first three strings (considering a classican nylon guitar) made of "plain" nylon; then they start going lower, so from the D to the Low E they are wound.
wound strings allow to use a thinner nylon core, reinforced with the metal winding; what happens is that the string is "firm" and not sloppy, and the sound is more focused.
on the ukulele we have the first string very thin, so it doesn't need any "help" to ring. the E string it's still small enough to ring without any help, and then comes the C string, which have to be bigger, due to the short scale of the ukulele (shorter the scale, lower the tension to reach the pitch); when you have a big nylon string, with low tension and a wide rage of vibration, it's easy to lose focus on the fundamental and alter the pitch while picking/strumming.
the fourth string is again very thin and high, but if you want to go one octave lower, you need an enormous mass. look at the difference between a C and an E string.
to make the Low G sound decent, the mass must be increased, but with just plain nylon it can be too sloppy. here it comes the metal
the winding reinforces the core so that the string is more focused and clear.
now, with the new technologies we have fluorocarbon strings and Aquila Reds: fluorocarbon is a dense material that can have higher tension with less mass (at the same pitch), so fluorcarbon strings are smaller than nylon and with an higher tension at the same pitch.
that means that a Low G can be plain, smaller and still sound good.
Aquila Red are a new concept, with copper mixed to nylon in different dose, so tha strings in a set have almost the same gauge, but they have a different density. the unwound Red LowG became stadard in many Aquila sets like the Super Nylgut or the Lava, being able to make the Low G sound nice without the winding.
