Just because a 1/4 of an inch (.7 %) of the vibrating length is unwound doesn't prove that the outer wrap has no effect , look at the d string of a guitar, it has a smaller or at most equal inner core compared to a plain G, which as you point out is all inner core, but if you tune it up to a G it likely won't make it before it snaps.
No effect on what? I have not even once discussed "tuned up to pitch". The inner core is still responsible for the tension, at least between 95 percent and 100. Please show me links to some site which provides other information.
I am still discussing tension only. Of course the pitch isn't reached if you keep the same tension of an unwound string, compared to a plain one. The reason it snaps is because of the following:
The hex core tugs into the wrap at certain nodes, and thus, provides a more prone to breaking point as the hex core "points" are used to stop the wrap from unraveling. Thus, it TUGS into the string and increases metal fatigue, and the strings elastic, plastic break point. Sure the mass increases, as well as stiffness, but please once again, don't ever mix those two things up with tension. Ever. On round core, THE TENSION is less, hence my notion of 95 percent, since the wrap doesn't brake or stop the inner core from being tensioned. Please, disregard anything to do with pitch and scale length. Still, TENSION ONLY comes ONLY from the inner core, just look at the ball end of the strings:
Why do you think the wraps doesn't ever go around the ball end? It's only and solely the inner core that makes that end point, and as such, are responsible for ALL tension. It's not responsible for pitch, or stiffness, or total mass
alone. I've never ever said that.
Thus, if the inner core is of a thicker gauge, regardless of the total strings gauge, the tension is higher, and requires higher tension to be brought up to the same pitch. A thinner inner core, regardless of that the total gauge of the string is the same, requires less tension to be brought up to pitch, and as such, I've never ever read on a strings package of how the inner core is made, apart from that it is hex core and/or round core. Round core strings do have slightly less tension that hex core, if all else is equal, hence my statement of the 95 percentage of the inner core responsible for all tension.
Now, manufacturers doesn't dabble with "equal tension" by providing some strings, say D and G string with round cores, and A and E string with hex core, to bring some more equal tension to them. The resulting timbre, and feel, stiffness, and mass, will be too unbalanced (as per OPs definition) between the pair of strings. There is a significant difference in timbre and balance between hex core and round core strings in tone and EQ, so it's best used either in a complete set. Now, the only way for manufacturers to do "equal tension" string is to alter the inner cores gauge, and of course, different alloy and material. But different alloy and material can be picked up different magnetically, so I don't think they're using one alloy on E and A strings, and another one at D and G strings. The output will be too different, and again, unbalanced as per the OPS definition.
If you now happen to be of the notion that "tension isn't what it is all about, there's pitch, stiffness and mass too" why does manufacturers produces "equal tension" strings then? They don't take into account all the other factors, but just lists "tension" as the main selling point incentive. Of course it all ties together, and plays an important factor on the final feel, output and timbre of any string. Still, tension is solely (at least 95 percent) for all the drag and string pull there is. There are even strings that has open core up at the tuner headstock end, and you can wind them several turns on the tuning posts. So verdict, still: Tension comes solely from the inner core. Leave all the rest for now, pitch, mass, stiffness, scale. That a hex core will STOP or brake the tension, is due to the sluggishness it imposes on the inner core. Call it speed bumps if you like. Whatever tension there is to be needed to bring up a string to a certain pitch at a certain scale, it still comes SOLELY from the inner core. Period.