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Will this little neck support this tension?

That's less tension that a regular bass tuned BEAD (25" is approximately the same as 7th fret on a 34") so it should work just fine.
It will probably feel clumsy to play though.

It's actually much more tension. I have two 25 5/8" scale 5 strings tuned to BEADG using .130-.050 and I do not recommend tuning a .130 to E. I've tried EADGC with the .130 set and the tension is really up there. Personally I'd try a .115 set.

Here's one of mine.
Front-H.jpg


mech
 
Short answer: By my estimation 130s would be too much tension, I'd go with 105s or as others have mentioned 115s. Here's why.

Last year I worked out a few equations for strings thanks to D'addario. The one we need to answer your question is:
T = 0.001915 (Dfs)2​
T is the string tension in pounds.
D is the string diameter in inches.
f is the [Invalid or Expired Link Removed] you want to tune to.
s is the scale length of the instrument in inches.

In your case for your E string, s=25, f=41.2 (bass E), D=0.130
T = 34.3 lbs
A 115 E string, s=25, f=41.2, D=0.115
T = 26.9 lbs
If we do it for a 105 string, s=25, f=41.2, D=0.105
T = 22.4 lbs
A set of extra lights would be s=25, f=41.2, D=.095
T = 18.3 lbs
Generally 34" bass strings run around 40-50 lbs, 30" short scales 30-40 lbs, 25" 20-27 lbs for 4-strings, 6-string guitars are 15-23 lbs. 130s would probably stress the neck/rod, 95s would be a little floppy, 105s would be about right with 115s also in the right area. You'll want to do this calculation for all 4 strings, too. It is possible for one string in a set to produce significantly more or less tension than the others.

If you can find the factory string diameters and tuning you can calculate the ideal tensions. As long as you stick within a few pounds of those you'll be good. The factory numbers would definitely be better to use than my general numbers.

None of this considers the width of the nut slots, if the slot is cut for .100, a .130 won't sit properly.

This is based on my math and physics skills, D'addario's tables and equations, and my successful project to turn a SS VM Jaguar into a baritone.
As usual, I am not a professional, if you damage your instrument I am not responsible.
 
Fascinating thread. I found it because I'm building an instrument with a custom scale length and it's prompted me to do quite a bit of digging, and it's been a great learning process so far.

To Vic Kevlar: Your info here gave me a great jump start, and I've been calculating with various values for string diameter, scale length, pitch, etc. Is there a place where I can see a kind of sliding scale for recommended string tension at different scale lengths? I see you have general ranges for the common lengths, but I'm wondering if I shifted a scale length by an inch or so, how does that affect recommended tension?

John